Classifying topology of consistent thermodynamics of the four-dimensional neutral Lorentzian NUT-charged spacetimes

In this paper, via employing the uniformly modified form of the generalized off-shell Helmholtz free energy, we investigate the topological numbers for the four-dimensional neutral Lorentzian Taub–NUT, Taub–NUT–AdS and Kerr–NUT spacetimes, and find that these solutions can also be classified into on...

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Published inThe European physical journal. C, Particles and fields Vol. 83; no. 5; pp. 365 - 10
Main Author Wu, Di
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2023
Springer
Springer Nature B.V
SpringerOpen
Subjects
Astronomy
Astrophysics and Cosmology
Black holes
Elementary Particles
Energy
Free energy
Hadrons
Heavy Ions
Measurement Science and Instrumentation
Nuclear Energy
Nuclear Physics
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Regular Article - Theoretical Physics
Spacetime
String Theory
Thermodynamics
Topology
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Abstract In this paper, via employing the uniformly modified form of the generalized off-shell Helmholtz free energy, we investigate the topological numbers for the four-dimensional neutral Lorentzian Taub–NUT, Taub–NUT–AdS and Kerr–NUT spacetimes, and find that these solutions can also be classified into one of three types of those well-known black hole solutions, which implies that these spacetimes should be viewed as generic black holes from the viewpoint of the thermodynamic topological approach.
AbstractList In this paper, via employing the uniformly modified form of the generalized off-shell Helmholtz free energy, we investigate the topological numbers for the four-dimensional neutral Lorentzian Taub–NUT, Taub–NUT–AdS and Kerr–NUT spacetimes, and find that these solutions can also be classified into one of three types of those well-known black hole solutions, which implies that these spacetimes should be viewed as generic black holes from the viewpoint of the thermodynamic topological approach.
Abstract In this paper, via employing the uniformly modified form of the generalized off-shell Helmholtz free energy, we investigate the topological numbers for the four-dimensional neutral Lorentzian Taub–NUT, Taub–NUT–AdS and Kerr–NUT spacetimes, and find that these solutions can also be classified into one of three types of those well-known black hole solutions, which implies that these spacetimes should be viewed as generic black holes from the viewpoint of the thermodynamic topological approach.
ArticleNumber 365
Audience Academic
Author Wu, Di
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  email: wdcwnu@163.com
  organization: School of Physics and Astronomy, China West Normal University
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Cites_doi 10.1016/j.physletb.2022.137591
10.1142/9789813237278_0001
10.1103/PhysRevD.103.126012
10.1103/PhysRevD.33.2092
10.1016/j.physletb.2019.134972
10.1140/epjc/s10052-021-09430-z
10.1007/JHEP10(2022)174
10.1063/1.1704018
10.1103/PhysRevD.60.104047
10.1007/JHEP01(2023)102
10.1088/1361-6382/ab3d4d
10.1103/PhysRevD.106.024022
10.1007/s002200100381
10.1016/j.physletb.2021.136568
10.1140/epjc/s10052-021-09643-2
10.1007/JHEP07(2012)033
10.1016/j.physletb.2022.137264
10.1016/j.physletb.2020.135270
10.1007/BF02451402
10.1007/JHEP07(2019)119
10.1103/PhysRevD.103.024052
10.1017/S0305004100049707
10.1103/PhysRevD.102.044007
10.1142/S0218271822500213
10.1140/epjc/s10052-019-6989-8
10.1103/PhysRevD.60.104001
10.1103/PhysRevLett.129.191101
10.1016/0550-3213(89)90175-2
10.1007/JHEP11(2021)031
10.1007/JHEP10(2022)044
10.1007/JHEP05(2020)084
10.1103/PhysRevD.100.104016
10.1088/0264-9381/31/23/235003
10.1103/PhysRevD.100.064055
10.1103/PhysRevD.105.124034
10.1103/PhysRevD.100.066007
10.1103/PhysRevD.60.104026
10.1103/PhysRevD.61.045004
10.1103/PhysRevD.101.024057
10.1103/PhysRevD.105.084030
10.1063/1.1704019
10.1016/j.physletb.2021.136213
10.1103/PhysRevD.102.124058
10.1007/BF03399503
10.1103/PhysRevD.106.064059
10.1088/0264-9381/26/19/195011
10.1140/epjp/i2015-15124-3
10.1007/JHEP03(2021)039
10.1017/S0305004100044807
10.1007/s002200050764
10.1103/PhysRevD.100.101501
10.1103/RevModPhys.70.427
10.1103/PhysRevLett.91.061301
10.1103/PhysRevD.89.084007
10.1140/epjc/s10052-019-6662-2
10.1103/PhysRevD.105.124013
10.1140/epjp/i2019-12937-x
10.1063/1.524839
10.1007/JHEP01(2014)127
10.1103/PhysRevD.107.064015
10.1063/1.1664958
10.1007/JHEP08(2021)152
10.1007/s11433-020-1659-0
10.1103/PhysRevD.103.104020
10.1142/S0217751X04019822
10.1140/epjc/s10052-020-08561-z
10.1103/PhysRevD.84.024037
10.1063/1.1666343
10.1103/PhysRevD.107.064023
10.1103/PhysRevD.105.104053
10.1016/S0550-3213(97)00777-3
10.1103/PhysRevD.107.024024
10.1103/PhysRevD.103.106011
10.1103/PhysRevD.102.064039
10.1103/PhysRevLett.115.031101
10.2307/1969567
10.1103/PhysRevD.101.124011
10.1007/BF01208266
10.1103/PhysRevD.101.064048
10.1016/j.nuclphysb.2003.09.039
10.1103/PhysRevD.107.084002
10.1103/PhysRevD.106.106015
10.1016/0550-3213(87)90404-4
10.1103/PhysRevD.103.044014
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References Chen, Jiang (CR9) 2019; 100
Yerra, Bhamidipati, Mukherji (CR55) 2022; 106
Kastor, Ray, Traschen (CR82) 2009; 26
Gnecchi, Hristov, Klemm, Toldo, Vaughan (CR72) 2014; 01
Wei, Liu, Mann (CR52) 2022; 129
Fu, Duan, Zhang (CR68) 2000; 61
Yang, Chen, Wan, Wei, Liu (CR30) 2020; 101
Cremonini, Jones, Liu, McPeak, Tang (CR31) 2021; 103
Hawking, Page (CR88) 1983; 87
Sakti, Suroso, Zen (CR27) 2019; 134
CR78
Mann (CR85) 1999; 60
CR76
Haro, Solodukhin, Skenderis (CR87) 2001; 217
Wei (CR69) 2020; 102
Misner (CR3) 1963; 4
Clarkson, Ghezelbash, Mann (CR49) 2004; 19
Kalamakis, Leigh, Petkou (CR37) 2021; 103
Wu, Wu (CR77) 2021; 11
Ramaswamy, Sen (CR41) 1981; 22
Siahaan (CR28) 2021; 820
Chamblin, Emparan, Johnson, Myers (CR84) 1999; 60
Balasubramanian, Kraus (CR86) 1999; 208
Clément, Gal’tsov (CR11) 2020; 802
Zhang, Jiang (CR29) 2021; 816
Hennigar, Kubizňák, Mann (CR4) 2019; 100
Feng, Yang, Tan, Yang, Liu (CR34) 2021; 64
Yerra, Bhamidipati (CR53) 2022; 105
Sackfield (CR46) 1971; 70
Kubizňàk, Mann (CR89) 2012; 07
Awad, Eissa (CR15) 2022; 105
Mukherjee, Chakraborty, Dadhich (CR35) 2019; 79
Wu (CR58) 2023; 107
Emparan, Johnson, Myers (CR83) 1999; 60
Ballon, Gray, Kubizňák (CR8) 2020; 05
Siahaan (CR26) 2020; 80
Jiang, Deng, Li (CR32) 2019; 100
Bombelli, Koul, Kunstatter, Lee, Sorkin (CR42) 1987; 289
Rodriguez, Rodriguez (CR24) 2022; 10
Johnson (CR50) 2014; 31
Miller (CR81) 1973; 14
Mukherjee, Chakraborty (CR36) 2020; 102
Li, Wang (CR64) 2022; 106
Ghezelbash, Siahaan (CR38) 2021; 81
Bordo, Gray, Hennigar, Kubizňák (CR7) 2019; 798
Clarkson, Ghezelbash, Mann (CR48) 2003; 674
Lynden-Bell, Nouri-Zonoz (CR44) 1998; 70
Wu, Wu (CR16) 2019; 100
CR19
Godazgar, Guisset (CR22) 2022; 106
Bordo, Gray, Hennigar, Kubizňák (CR5) 2019; 36
CR18
Clarkson, Ghezelbash, Mann (CR47) 2003; 91
Duan, Ge (CR65) 1979; 9
Nashed (CR23) 2015; 130
Ballon, Gray, Kubizňák (CR6) 2019; 07
Hennigar, Mann, Kubizňák (CR71) 2015; 115
Klemm (CR70) 2014; 89
York (CR62) 1986; 33
Newman, Tamburino, Unti (CR2) 1963; 4
Kinnersley (CR80) 1969; 10
Ciambelli, Corral, Figueroa, Giribet, Olea (CR20) 2021; 103
Duan, Li, Yang (CR67) 1998; 514
Taub (CR1) 1951; 53
Bai, Li, Tao (CR56) 2023; 107
Durka (CR12) 2022; 31
Liu, Lü, Ma (CR25) 2022; 10
Cvetič, Gibbons, Kubizňák, Pope (CR51) 2011; 84
Wu, Wu, Yu, Wu (CR75) 2020; 102
Abbasvandi, Tavakoli, Mann (CR13) 2021; 08
Wu, Wu (CR17) 2022; 105
Siahaan (CR39) 2021; 81
Deser, Soldate (CR43) 1989; 311
Awad, Eissa (CR14) 2020; 101
Long, Chen, Wang, Jing (CR33) 2019; 79
Liu, Wang (CR57) 2023; 107
Yang, Zhou, Wei, Liu (CR63) 2022; 105
Yerra, Bhamidipati (CR54) 2022; 835
CR66
Wu, Wu, Yu, Wu (CR74) 2020; 101
Dowker (CR40) 1974; 5
Bonnor (CR45) 1969; 66
Fang, Jiang, Zhang (CR59) 2023; 01
CR60
Mann, Zayas, Park (CR21) 2021; 03
Wu, Wu (CR73) 2021; 103
Carter (CR79) 1968; 10
Wu, Wu (CR61) 2023; 107
Frodden, Hidalgo (CR10) 2022; 832
L Bombelli (11561_CR42) 1987; 289
WB Feng (11561_CR34) 2021; 64
RB Mann (11561_CR85) 1999; 60
D Wu (11561_CR77) 2021; 11
D Wu (11561_CR75) 2020; 102
A Gnecchi (11561_CR72) 2014; 01
11561_CR78
R Clarkson (11561_CR47) 2003; 91
11561_CR76
CW Misner (11561_CR3) 1963; 4
G Clément (11561_CR11) 2020; 802
JG Miller (11561_CR81) 1973; 14
NH Rodriguez (11561_CR24) 2022; 10
PK Yerra (11561_CR55) 2022; 106
D Wu (11561_CR73) 2021; 103
R Li (11561_CR64) 2022; 106
CX Fang (11561_CR59) 2023; 01
R Clarkson (11561_CR48) 2003; 674
M Zhang (11561_CR29) 2021; 816
S Ramaswamy (11561_CR41) 1981; 22
S Deser (11561_CR43) 1989; 311
B Carter (11561_CR79) 1968; 10
ET Newman (11561_CR2) 1963; 4
M Ghezelbash (11561_CR38) 2021; 81
MFAR Sakti (11561_CR27) 2019; 134
AB Bordo (11561_CR7) 2019; 798
D Kubizňàk (11561_CR89) 2012; 07
D Kastor (11561_CR82) 2009; 26
H-S Liu (11561_CR25) 2022; 10
PK Yerra (11561_CR53) 2022; 105
E Frodden (11561_CR10) 2022; 832
S-J Yang (11561_CR30) 2020; 101
D Klemm (11561_CR70) 2014; 89
JS Dowker (11561_CR40) 1974; 5
M Cvetič (11561_CR51) 2011; 84
R Durka (11561_CR12) 2022; 31
S Haro (11561_CR87) 2001; 217
AB Ballon (11561_CR6) 2019; 07
AH Taub (11561_CR1) 1951; 53
F Long (11561_CR33) 2019; 79
HM Siahaan (11561_CR28) 2021; 820
N Abbasvandi (11561_CR13) 2021; 08
A Sackfield (11561_CR46) 1971; 70
SW Hawking (11561_CR88) 1983; 87
HM Siahaan (11561_CR26) 2020; 80
AM Awad (11561_CR14) 2020; 101
D Wu (11561_CR17) 2022; 105
GGL Nashed (11561_CR23) 2015; 130
R Emparan (11561_CR83) 1999; 60
G Kalamakis (11561_CR37) 2021; 103
D Lynden-Bell (11561_CR44) 1998; 70
Y-S Duan (11561_CR67) 1998; 514
AB Ballon (11561_CR8) 2020; 05
S-J Yang (11561_CR63) 2022; 105
R Clarkson (11561_CR49) 2004; 19
RA Hennigar (11561_CR4) 2019; 100
D Wu (11561_CR58) 2023; 107
D Wu (11561_CR74) 2020; 101
RA Hennigar (11561_CR71) 2015; 115
M Godazgar (11561_CR22) 2022; 106
V Balasubramanian (11561_CR86) 1999; 208
S Cremonini (11561_CR31) 2021; 103
L Ciambelli (11561_CR20) 2021; 103
AB Bordo (11561_CR5) 2019; 36
ZH Chen (11561_CR9) 2019; 100
L-B Fu (11561_CR68) 2000; 61
S Mukherjee (11561_CR35) 2019; 79
PK Yerra (11561_CR54) 2022; 835
J Jiang (11561_CR32) 2019; 100
CH Liu (11561_CR57) 2023; 107
CV Johnson (11561_CR50) 2014; 31
Y-S Duan (11561_CR65) 1979; 9
11561_CR19
D Wu (11561_CR61) 2023; 107
A Chamblin (11561_CR84) 1999; 60
S Mukherjee (11561_CR36) 2020; 102
W Kinnersley (11561_CR80) 1969; 10
11561_CR18
N-C Bai (11561_CR56) 2023; 107
RB Mann (11561_CR21) 2021; 03
11561_CR66
S-W Wei (11561_CR52) 2022; 129
S-Q Wu (11561_CR16) 2019; 100
WB Bonnor (11561_CR45) 1969; 66
11561_CR60
HM Siahaan (11561_CR39) 2021; 81
AM Awad (11561_CR15) 2022; 105
JW York (11561_CR62) 1986; 33
S-W Wei (11561_CR69) 2020; 102
References_xml – volume: 835
  year: 2022
  ident: CR54
  article-title: Topology of Born–Infeld AdS black holes in 4D novel Einstein–Gauss–Bonnet gravity
  publication-title: Phys. Lett. B
  doi: 10.1016/j.physletb.2022.137591
– volume: 9
  start-page: 1072
  year: 1979
  ident: CR65
  article-title: (2) gauge theory and electrodynamics of moving magnetic monopoles
  publication-title: Sci. Sin.
  doi: 10.1142/9789813237278_0001
– volume: 103
  year: 2021
  ident: CR37
  article-title: Aspects of holography of Taub–NUT–AdS spacetimes
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.103.126012
– volume: 33
  start-page: 2092
  year: 1986
  ident: CR62
  article-title: Black-hole thermodynamics and the Euclidean Einstein action
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.33.2092
– volume: 798
  year: 2019
  ident: CR7
  article-title: The first law for rotating NUTs
  publication-title: Phys. Lett. B
  doi: 10.1016/j.physletb.2019.134972
– volume: 81
  start-page: 621
  year: 2021
  ident: CR38
  article-title: Magnetized Kerr–Newman–Taub–NUT spacetimes
  publication-title: Eur. Phys. J. C
  doi: 10.1140/epjc/s10052-021-09430-z
– volume: 10
  start-page: 174
  year: 2022
  ident: CR25
  article-title: Thermodynamics of Taub–NUT and Plebanski solutions
  publication-title: JHEP
  doi: 10.1007/JHEP10(2022)174
– volume: 4
  start-page: 915
  year: 1963
  ident: CR2
  article-title: Empty-space generalization of the Schwarzschild metric
  publication-title: J. Math. Phys. (N.Y.)
  doi: 10.1063/1.1704018
– volume: 60
  year: 1999
  ident: CR85
  article-title: Misner string entropy
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.60.104047
– volume: 01
  start-page: 102
  year: 2023
  ident: CR59
  article-title: Revisiting thermodynamic topologies of black holes
  publication-title: JHEP
  doi: 10.1007/JHEP01(2023)102
– volume: 36
  year: 2019
  ident: CR5
  article-title: Misner gravitational charges and variable string strengths
  publication-title: Class. Quantum Gravity
  doi: 10.1088/1361-6382/ab3d4d
– volume: 106
  year: 2022
  ident: CR22
  article-title: Dual charges for AdS spacetimes and the first law of black hole mechanics
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.106.024022
– volume: 217
  start-page: 595
  year: 2001
  ident: CR87
  article-title: Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence
  publication-title: Commun. Math. Phys.
  doi: 10.1007/s002200100381
– volume: 820
  year: 2021
  ident: CR28
  article-title: Magnetized Kerr–Taub–NUT spacetime and Kerr/CFT correspondence
  publication-title: Phys. Lett. B
  doi: 10.1016/j.physletb.2021.136568
– volume: 81
  start-page: 838
  year: 2021
  ident: CR39
  article-title: Magnetized Reissner–Nordström–Taub–NUT spacetime and microscopic entropy
  publication-title: Eur. Phys. J. C
  doi: 10.1140/epjc/s10052-021-09643-2
– volume: 07
  start-page: 033
  year: 2012
  ident: CR89
  article-title: P–V criticality of charged AdS black holes
  publication-title: JHEP
  doi: 10.1007/JHEP07(2012)033
– volume: 832
  year: 2022
  ident: CR10
  article-title: The first law for the Kerr-NUT spacetime
  publication-title: Phys. Lett. B
  doi: 10.1016/j.physletb.2022.137264
– volume: 802
  year: 2020
  ident: CR11
  article-title: On the Smarr formulas for electrovac spacetimes with line singularities
  publication-title: Phys. Lett. B
  doi: 10.1016/j.physletb.2020.135270
– volume: 5
  start-page: 603
  year: 1974
  ident: CR40
  article-title: The nut solution as a gravitational dyon
  publication-title: Gen. Relativ. Gravit.
  doi: 10.1007/BF02451402
– volume: 07
  start-page: 119
  year: 2019
  ident: CR6
  article-title: Thermodynamics and phase transitions of NUTty dyons
  publication-title: JHEP
  doi: 10.1007/JHEP07(2019)119
– volume: 103
  year: 2021
  ident: CR20
  article-title: Topological terms and the Misner string entropy
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.103.024052
– volume: 70
  start-page: 89
  year: 1971
  ident: CR46
  article-title: Physical interpretation of NUT metric
  publication-title: Proc. Camb. Philos. Soc.
  doi: 10.1017/S0305004100049707
– volume: 102
  year: 2020
  ident: CR75
  article-title: Are ultraspinning Kerr–Sen–AdS black holes always superentropic?
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.102.044007
– ident: CR19
– volume: 31
  start-page: 2250021
  year: 2022
  ident: CR12
  article-title: The first law of black hole thermodynamics for Taub–NUT spacetime
  publication-title: Int. J. Mod. Phys. D
  doi: 10.1142/S0218271822500213
– volume: 79
  start-page: 466
  year: 2019
  ident: CR33
  article-title: Electromagnetic emissions from near-horizon region of an extreme Kerr–Taub–NUT black hole
  publication-title: Eur. Phys. J. C
  doi: 10.1140/epjc/s10052-019-6989-8
– volume: 60
  year: 1999
  ident: CR83
  article-title: Surface terms as counterterms in the AdS/CFT correspondence
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.60.104001
– volume: 129
  year: 2022
  ident: CR52
  article-title: Black hole solutions as topological thermodynamic defects
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.129.191101
– volume: 311
  start-page: 739
  year: 1989
  ident: CR43
  article-title: Gravitational energy in spaces with compactified dimensions
  publication-title: Nucl. Phys. B
  doi: 10.1016/0550-3213(89)90175-2
– volume: 11
  start-page: 031
  year: 2021
  ident: CR77
  article-title: Ultra-spinning Chow’s black holes in six-dimensional gauged supergravity and their thermodynamical properties
  publication-title: JHEP
  doi: 10.1007/JHEP11(2021)031
– volume: 10
  start-page: 044
  year: 2022
  ident: CR24
  article-title: First law for Kerr Taub–NUT AdS black holes
  publication-title: JHEP
  doi: 10.1007/JHEP10(2022)044
– volume: 05
  start-page: 084
  year: 2020
  ident: CR8
  article-title: Thermodynamics of rotating NUTty dyons
  publication-title: JHEP
  doi: 10.1007/JHEP05(2020)084
– volume: 100
  year: 2019
  ident: CR9
  article-title: General Smarr relation and first law of a NUT dyonic black hole
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.100.104016
– volume: 31
  year: 2014
  ident: CR50
  article-title: Thermodynamic Volumes for AdS–Taub–NUT and AdS–Taub–Bolt
  publication-title: Class. Quantum Gravity
  doi: 10.1088/0264-9381/31/23/235003
– volume: 100
  year: 2019
  ident: CR4
  article-title: Thermodynamics of Lorentzian Taub–NUT spacetimes
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.100.064055
– volume: 105
  year: 2022
  ident: CR15
  article-title: Lorentzian Tuab–NUT spacetimes: Misner string charges and the first law
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.105.124034
– volume: 100
  year: 2019
  ident: CR32
  article-title: Holographic complexity of charged Taub–NUT–AdS black holes
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.100.066007
– ident: CR60
– volume: 60
  year: 1999
  ident: CR84
  article-title: Holography, thermodynamics and fluctuations of charged AdS black holes
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.60.104026
– volume: 61
  year: 2000
  ident: CR68
  article-title: Evolution of the Chern–Simons vortices
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.61.045004
– ident: CR78
– volume: 101
  year: 2020
  ident: CR74
  article-title: Notes on the thermodynamics of superentropic AdS black holes
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.101.024057
– volume: 105
  year: 2022
  ident: CR63
  article-title: Dynamics and kinetics of phase transition for Kerr AdS black hole on free energy landscape
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.105.084030
– volume: 4
  start-page: 924
  year: 1963
  ident: CR3
  article-title: The flatter regions of Newman, Unti, and Tamburino’s generalized Schwarzschild space
  publication-title: J. Math. Phys. (N.Y.)
  doi: 10.1063/1.1704019
– volume: 816
  year: 2021
  ident: CR29
  article-title: NUT charges and black hole shadows
  publication-title: Phys. Lett. B
  doi: 10.1016/j.physletb.2021.136213
– volume: 102
  year: 2020
  ident: CR36
  article-title: Multipole moments of compact objects with NUT charge: theoretical and observational implications
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.102.124058
– volume: 10
  start-page: 280
  year: 1968
  ident: CR79
  article-title: Hamilton–Jacobi and Schrodinger separable solutions of Einstein’s equations
  publication-title: Commun. Math. Phys.
  doi: 10.1007/BF03399503
– volume: 106
  year: 2022
  ident: CR55
  article-title: Topology of critical points and Hawking–Page transition
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.106.064059
– volume: 26
  year: 2009
  ident: CR82
  article-title: Enthalpy and the mechanics of AdS black holes
  publication-title: Class. Quantum Gravity
  doi: 10.1088/0264-9381/26/19/195011
– ident: CR18
– volume: 130
  start-page: 124
  year: 2015
  ident: CR23
  article-title: Kerr–NUT black hole thermodynamics in f(T) gravity theories
  publication-title: Eur. Phys. J. Plus
  doi: 10.1140/epjp/i2015-15124-3
– ident: CR66
– volume: 03
  start-page: 039
  year: 2021
  ident: CR21
  article-title: Complement to thermodynamics of dyonic Taub–NUT–AdS spacetime
  publication-title: JHEP
  doi: 10.1007/JHEP03(2021)039
– volume: 66
  start-page: 145
  year: 1969
  ident: CR45
  article-title: A new interpretation of the NUT metric in general relativity
  publication-title: Proc. Camb. Philos. Soc.
  doi: 10.1017/S0305004100044807
– volume: 208
  start-page: 413
  year: 1999
  ident: CR86
  article-title: A stress tensor for anti-de Sitter gravity
  publication-title: Commun. Math. Phys.
  doi: 10.1007/s002200050764
– volume: 100
  start-page: 101501(R)
  year: 2019
  ident: CR16
  article-title: Thermodynamical hairs of the four-dimensional Taub–Newman–Unti–Tamburino spacetimes
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.100.101501
– volume: 70
  start-page: 427
  year: 1998
  ident: CR44
  article-title: Classical monopoles: Newton, NUT space, gravomagnetic lensing and atomic spectra
  publication-title: Rev. Mod. Phys.
  doi: 10.1103/RevModPhys.70.427
– volume: 91
  year: 2003
  ident: CR47
  article-title: Mass, action and entropy of Taub-Bolt–de Sitter spacetimes
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.91.061301
– volume: 89
  year: 2014
  ident: CR70
  article-title: Four-dimensional black holes with unusual horizons
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.89.084007
– volume: 79
  start-page: 161
  year: 2019
  ident: CR35
  article-title: On some novel features of the Kerr–Newman–NUT spacetime
  publication-title: Eur. Phys. J. C
  doi: 10.1140/epjc/s10052-019-6662-2
– volume: 105
  year: 2022
  ident: CR17
  article-title: Consistent mass formulas for the four-dimensional dyonic NUT-charged spacetimes
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.105.124013
– volume: 134
  start-page: 580
  year: 2019
  ident: CR27
  article-title: Kerr/CFT correspondence on Kerr–Newman–NUT–Quintessence black hole
  publication-title: Eur. Phys. J. Plus
  doi: 10.1140/epjp/i2019-12937-x
– volume: 22
  start-page: 2612
  year: 1981
  ident: CR41
  article-title: Dual-mass in general relativity
  publication-title: J. Math. Phys. (N.Y.)
  doi: 10.1063/1.524839
– volume: 01
  start-page: 127
  year: 2014
  ident: CR72
  article-title: Rotating black holes in 4d gauged supergravity
  publication-title: JHEP
  doi: 10.1007/JHEP01(2014)127
– volume: 107
  year: 2023
  ident: CR56
  article-title: Topology of black hole thermodynamics in Lovelock gravity
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.107.064015
– volume: 10
  start-page: 1195
  year: 1969
  ident: CR80
  article-title: Type D vacuum metrics
  publication-title: J. Math. Phys. (N.Y.)
  doi: 10.1063/1.1664958
– volume: 08
  start-page: 152
  year: 2021
  ident: CR13
  article-title: Thermodynamics of dyonic NUT charged black holes with entropy as Noether charge
  publication-title: JHEP
  doi: 10.1007/JHEP08(2021)152
– volume: 64
  year: 2021
  ident: CR34
  article-title: Overcharging a Reissner–Nordström Taub–NUT regular black hole
  publication-title: Sci. China: Phys. Mech. Astron.
  doi: 10.1007/s11433-020-1659-0
– volume: 103
  year: 2021
  ident: CR73
  article-title: Null hypersurface caustics for high-dimensional superentropic black holes
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.103.104020
– volume: 19
  start-page: 3987
  year: 2004
  ident: CR49
  article-title: A review of the N-bound and the maximal mass conjectures using NUT-charged dS spacetimes
  publication-title: Int. J. Mod. Phys. A
  doi: 10.1142/S0217751X04019822
– volume: 80
  start-page: 1000
  year: 2020
  ident: CR26
  article-title: Kerr–Sen–Taub–NUT spacetime and circular geodesics
  publication-title: Eur. Phys. J. C
  doi: 10.1140/epjc/s10052-020-08561-z
– volume: 84
  year: 2011
  ident: CR51
  article-title: Black hole enthalpy and an entropy inequality for the thermodynamic volume
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.84.024037
– volume: 14
  start-page: 486
  year: 1973
  ident: CR81
  article-title: Global analysis of the Kerr–Taub–NUT metric
  publication-title: J. Math. Phys. (N.Y.)
  doi: 10.1063/1.1666343
– volume: 107
  year: 2023
  ident: CR57
  article-title: The topological natures of the Gauss–Bonnet black hole in AdS space
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.107.064023
– volume: 105
  year: 2022
  ident: CR53
  article-title: Topology of black hole thermodynamics in Gauss–Bonnet gravity
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.105.104053
– volume: 514
  start-page: 705
  year: 1998
  ident: CR67
  article-title: The bifurcation theory of the Gauss–Bonnet–Chern topological current and Morse function
  publication-title: Nucl. Phys. B
  doi: 10.1016/S0550-3213(97)00777-3
– volume: 107
  year: 2023
  ident: CR58
  article-title: Topological classes of rotating black holes
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.107.024024
– volume: 103
  year: 2021
  ident: CR31
  article-title: NUT charge weak gravity conjecture from dimensional reduction
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.103.106011
– volume: 102
  year: 2020
  ident: CR69
  article-title: Topological charge and black hole photon spheres
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.102.064039
– volume: 115
  year: 2015
  ident: CR71
  article-title: Entropy inequality violations from ultraspinning black holes
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.115.031101
– ident: CR76
– volume: 53
  start-page: 472
  year: 1951
  ident: CR1
  article-title: Empty space-times admitting a three parameter group of motions
  publication-title: Ann. Math.
  doi: 10.2307/1969567
– volume: 101
  year: 2020
  ident: CR14
  article-title: Topological dyonic Taub-Bolt/NUT-AdS solutions: Thermodynamics and first law
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.101.124011
– volume: 87
  start-page: 577
  year: 1983
  ident: CR88
  article-title: Thermodynamics of black holes in anti-de Sitter space
  publication-title: Commun. Math. Phys.
  doi: 10.1007/BF01208266
– volume: 101
  year: 2020
  ident: CR30
  article-title: Weak cosmic censorship conjecture for a Kerr–Taub–NUT black hole with a test scalar field and particle
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.101.064048
– volume: 674
  start-page: 329
  year: 2003
  ident: CR48
  article-title: Entropic N bound and maximal mass conjectures violation in four-dimensional Taub-Bolt(NUT)-dS space-times
  publication-title: Nucl. Phys. B
  doi: 10.1016/j.nuclphysb.2003.09.039
– volume: 107
  year: 2023
  ident: CR61
  article-title: Topological classes of thermodynamics of rotating AdS black holes
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.107.084002
– volume: 106
  year: 2022
  ident: CR64
  article-title: Generalized free energy landscape of a black hole phase transition
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.106.106015
– volume: 289
  start-page: 735
  year: 1987
  ident: CR42
  article-title: On energy in 5-dimensional gravity and the mass of the Kaluza–Klein monopole
  publication-title: Nucl. Phys. B
  doi: 10.1016/0550-3213(87)90404-4
– volume: 100
  year: 2019
  ident: 11561_CR4
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.100.064055
– ident: 11561_CR60
– volume: 816
  year: 2021
  ident: 11561_CR29
  publication-title: Phys. Lett. B
  doi: 10.1016/j.physletb.2021.136213
– volume: 103
  year: 2021
  ident: 11561_CR20
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.103.024052
– volume: 802
  year: 2020
  ident: 11561_CR11
  publication-title: Phys. Lett. B
  doi: 10.1016/j.physletb.2020.135270
– volume: 100
  start-page: 101501(R)
  year: 2019
  ident: 11561_CR16
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.100.101501
– volume: 91
  year: 2003
  ident: 11561_CR47
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.91.061301
– volume: 103
  year: 2021
  ident: 11561_CR37
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.103.126012
– volume: 70
  start-page: 427
  year: 1998
  ident: 11561_CR44
  publication-title: Rev. Mod. Phys.
  doi: 10.1103/RevModPhys.70.427
– volume: 31
  year: 2014
  ident: 11561_CR50
  publication-title: Class. Quantum Gravity
  doi: 10.1088/0264-9381/31/23/235003
– volume: 798
  year: 2019
  ident: 11561_CR7
  publication-title: Phys. Lett. B
  doi: 10.1016/j.physletb.2019.134972
– volume: 79
  start-page: 466
  year: 2019
  ident: 11561_CR33
  publication-title: Eur. Phys. J. C
  doi: 10.1140/epjc/s10052-019-6989-8
– volume: 107
  year: 2023
  ident: 11561_CR58
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.107.024024
– volume: 81
  start-page: 621
  year: 2021
  ident: 11561_CR38
  publication-title: Eur. Phys. J. C
  doi: 10.1140/epjc/s10052-021-09430-z
– volume: 87
  start-page: 577
  year: 1983
  ident: 11561_CR88
  publication-title: Commun. Math. Phys.
  doi: 10.1007/BF01208266
– volume: 105
  year: 2022
  ident: 11561_CR15
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.105.124034
– volume: 80
  start-page: 1000
  year: 2020
  ident: 11561_CR26
  publication-title: Eur. Phys. J. C
  doi: 10.1140/epjc/s10052-020-08561-z
– volume: 217
  start-page: 595
  year: 2001
  ident: 11561_CR87
  publication-title: Commun. Math. Phys.
  doi: 10.1007/s002200100381
– volume: 84
  year: 2011
  ident: 11561_CR51
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.84.024037
– volume: 60
  year: 1999
  ident: 11561_CR85
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.60.104047
– volume: 60
  year: 1999
  ident: 11561_CR84
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.60.104026
– volume: 674
  start-page: 329
  year: 2003
  ident: 11561_CR48
  publication-title: Nucl. Phys. B
  doi: 10.1016/j.nuclphysb.2003.09.039
– ident: 11561_CR76
  doi: 10.1103/PhysRevD.103.044014
– volume: 81
  start-page: 838
  year: 2021
  ident: 11561_CR39
  publication-title: Eur. Phys. J. C
  doi: 10.1140/epjc/s10052-021-09643-2
– volume: 4
  start-page: 924
  year: 1963
  ident: 11561_CR3
  publication-title: J. Math. Phys. (N.Y.)
  doi: 10.1063/1.1704019
– volume: 835
  year: 2022
  ident: 11561_CR54
  publication-title: Phys. Lett. B
  doi: 10.1016/j.physletb.2022.137591
– volume: 100
  year: 2019
  ident: 11561_CR9
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.100.104016
– volume: 22
  start-page: 2612
  year: 1981
  ident: 11561_CR41
  publication-title: J. Math. Phys. (N.Y.)
  doi: 10.1063/1.524839
– volume: 106
  year: 2022
  ident: 11561_CR55
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.106.064059
– volume: 33
  start-page: 2092
  year: 1986
  ident: 11561_CR62
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.33.2092
– volume: 64
  year: 2021
  ident: 11561_CR34
  publication-title: Sci. China: Phys. Mech. Astron.
  doi: 10.1007/s11433-020-1659-0
– volume: 11
  start-page: 031
  year: 2021
  ident: 11561_CR77
  publication-title: JHEP
  doi: 10.1007/JHEP11(2021)031
– volume: 07
  start-page: 119
  year: 2019
  ident: 11561_CR6
  publication-title: JHEP
  doi: 10.1007/JHEP07(2019)119
– volume: 36
  year: 2019
  ident: 11561_CR5
  publication-title: Class. Quantum Gravity
  doi: 10.1088/1361-6382/ab3d4d
– volume: 10
  start-page: 1195
  year: 1969
  ident: 11561_CR80
  publication-title: J. Math. Phys. (N.Y.)
  doi: 10.1063/1.1664958
– volume: 107
  year: 2023
  ident: 11561_CR61
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.107.084002
– volume: 10
  start-page: 280
  year: 1968
  ident: 11561_CR79
  publication-title: Commun. Math. Phys.
  doi: 10.1007/BF03399503
– volume: 102
  year: 2020
  ident: 11561_CR69
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.102.064039
– volume: 89
  year: 2014
  ident: 11561_CR70
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.89.084007
– ident: 11561_CR18
– volume: 103
  year: 2021
  ident: 11561_CR31
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.103.106011
– volume: 4
  start-page: 915
  year: 1963
  ident: 11561_CR2
  publication-title: J. Math. Phys. (N.Y.)
  doi: 10.1063/1.1704018
– volume: 03
  start-page: 039
  year: 2021
  ident: 11561_CR21
  publication-title: JHEP
  doi: 10.1007/JHEP03(2021)039
– volume: 79
  start-page: 161
  year: 2019
  ident: 11561_CR35
  publication-title: Eur. Phys. J. C
  doi: 10.1140/epjc/s10052-019-6662-2
– volume: 101
  year: 2020
  ident: 11561_CR74
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.101.024057
– volume: 102
  year: 2020
  ident: 11561_CR75
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.102.044007
– volume: 115
  year: 2015
  ident: 11561_CR71
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.115.031101
– volume: 66
  start-page: 145
  year: 1969
  ident: 11561_CR45
  publication-title: Proc. Camb. Philos. Soc.
  doi: 10.1017/S0305004100044807
– volume: 129
  year: 2022
  ident: 11561_CR52
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.129.191101
– volume: 10
  start-page: 044
  year: 2022
  ident: 11561_CR24
  publication-title: JHEP
  doi: 10.1007/JHEP10(2022)044
– volume: 208
  start-page: 413
  year: 1999
  ident: 11561_CR86
  publication-title: Commun. Math. Phys.
  doi: 10.1007/s002200050764
– volume: 08
  start-page: 152
  year: 2021
  ident: 11561_CR13
  publication-title: JHEP
  doi: 10.1007/JHEP08(2021)152
– volume: 105
  year: 2022
  ident: 11561_CR53
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.105.104053
– ident: 11561_CR66
– volume: 31
  start-page: 2250021
  year: 2022
  ident: 11561_CR12
  publication-title: Int. J. Mod. Phys. D
  doi: 10.1142/S0218271822500213
– volume: 5
  start-page: 603
  year: 1974
  ident: 11561_CR40
  publication-title: Gen. Relativ. Gravit.
  doi: 10.1007/BF02451402
– volume: 107
  year: 2023
  ident: 11561_CR57
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.107.064023
– volume: 101
  year: 2020
  ident: 11561_CR14
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.101.124011
– volume: 134
  start-page: 580
  year: 2019
  ident: 11561_CR27
  publication-title: Eur. Phys. J. Plus
  doi: 10.1140/epjp/i2019-12937-x
– volume: 102
  year: 2020
  ident: 11561_CR36
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.102.124058
– volume: 311
  start-page: 739
  year: 1989
  ident: 11561_CR43
  publication-title: Nucl. Phys. B
  doi: 10.1016/0550-3213(89)90175-2
– volume: 101
  year: 2020
  ident: 11561_CR30
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.101.064048
– volume: 14
  start-page: 486
  year: 1973
  ident: 11561_CR81
  publication-title: J. Math. Phys. (N.Y.)
  doi: 10.1063/1.1666343
– volume: 60
  year: 1999
  ident: 11561_CR83
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.60.104001
– volume: 70
  start-page: 89
  year: 1971
  ident: 11561_CR46
  publication-title: Proc. Camb. Philos. Soc.
  doi: 10.1017/S0305004100049707
– volume: 107
  year: 2023
  ident: 11561_CR56
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.107.064015
– volume: 01
  start-page: 102
  year: 2023
  ident: 11561_CR59
  publication-title: JHEP
  doi: 10.1007/JHEP01(2023)102
– ident: 11561_CR19
– volume: 01
  start-page: 127
  year: 2014
  ident: 11561_CR72
  publication-title: JHEP
  doi: 10.1007/JHEP01(2014)127
– volume: 10
  start-page: 174
  year: 2022
  ident: 11561_CR25
  publication-title: JHEP
  doi: 10.1007/JHEP10(2022)174
– ident: 11561_CR78
– volume: 103
  year: 2021
  ident: 11561_CR73
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.103.104020
– volume: 289
  start-page: 735
  year: 1987
  ident: 11561_CR42
  publication-title: Nucl. Phys. B
  doi: 10.1016/0550-3213(87)90404-4
– volume: 106
  year: 2022
  ident: 11561_CR64
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.106.106015
– volume: 832
  year: 2022
  ident: 11561_CR10
  publication-title: Phys. Lett. B
  doi: 10.1016/j.physletb.2022.137264
– volume: 61
  year: 2000
  ident: 11561_CR68
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.61.045004
– volume: 514
  start-page: 705
  year: 1998
  ident: 11561_CR67
  publication-title: Nucl. Phys. B
  doi: 10.1016/S0550-3213(97)00777-3
– volume: 53
  start-page: 472
  year: 1951
  ident: 11561_CR1
  publication-title: Ann. Math.
  doi: 10.2307/1969567
– volume: 05
  start-page: 084
  year: 2020
  ident: 11561_CR8
  publication-title: JHEP
  doi: 10.1007/JHEP05(2020)084
– volume: 130
  start-page: 124
  year: 2015
  ident: 11561_CR23
  publication-title: Eur. Phys. J. Plus
  doi: 10.1140/epjp/i2015-15124-3
– volume: 820
  year: 2021
  ident: 11561_CR28
  publication-title: Phys. Lett. B
  doi: 10.1016/j.physletb.2021.136568
– volume: 100
  year: 2019
  ident: 11561_CR32
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.100.066007
– volume: 106
  year: 2022
  ident: 11561_CR22
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.106.024022
– volume: 105
  year: 2022
  ident: 11561_CR17
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.105.124013
– volume: 19
  start-page: 3987
  year: 2004
  ident: 11561_CR49
  publication-title: Int. J. Mod. Phys. A
  doi: 10.1142/S0217751X04019822
– volume: 105
  year: 2022
  ident: 11561_CR63
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.105.084030
– volume: 9
  start-page: 1072
  year: 1979
  ident: 11561_CR65
  publication-title: Sci. Sin.
  doi: 10.1142/9789813237278_0001
– volume: 26
  year: 2009
  ident: 11561_CR82
  publication-title: Class. Quantum Gravity
  doi: 10.1088/0264-9381/26/19/195011
– volume: 07
  start-page: 033
  year: 2012
  ident: 11561_CR89
  publication-title: JHEP
  doi: 10.1007/JHEP07(2012)033
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Snippet In this paper, via employing the uniformly modified form of the generalized off-shell Helmholtz free energy, we investigate the topological numbers for the...
Abstract In this paper, via employing the uniformly modified form of the generalized off-shell Helmholtz free energy, we investigate the topological numbers...
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SubjectTerms Astronomy
Astrophysics and Cosmology
Black holes
Elementary Particles
Energy
Free energy
Hadrons
Heavy Ions
Measurement Science and Instrumentation
Nuclear Energy
Nuclear Physics
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Regular Article - Theoretical Physics
Spacetime
String Theory
Thermodynamics
Topology
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Title Classifying topology of consistent thermodynamics of the four-dimensional neutral Lorentzian NUT-charged spacetimes
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