Effective GUP-modified Raychaudhuri equation and black hole singularity: four models

A bstract The classical Raychaudhuri equation predicts the formation of conjugate points for a congruence of geodesics, in a finite proper time. This in conjunction with the Hawking-Penrose singularity theorems predicts the incompleteness of geodesics and thereby the singular nature of practically a...

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Published inThe journal of high energy physics Vol. 2021; no. 9; pp. 1 - 23
Main Authors Blanchette, Keagan, Das, Saurya, Rastgoo, Saeed
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 10.09.2021
Springer Nature B.V
SpringerOpen
Subjects
Algebra
Black Holes
Classical and Quantum Gravitation
Conjugate points
Cosmology
Dependent variables
Elementary Particles
Geodesy
Gravity
High energy physics
Models of Quantum Gravity
Physics
Physics and Astronomy
Polymers
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Singularities
Spacetime
Spacetime Singularities
String Theory
Uncertainty principles
Variables
Black Holes
Models of Quantum Gravity
Spacetime Singularities
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Summary:A bstract The classical Raychaudhuri equation predicts the formation of conjugate points for a congruence of geodesics, in a finite proper time. This in conjunction with the Hawking-Penrose singularity theorems predicts the incompleteness of geodesics and thereby the singular nature of practically all spacetimes. We compute the generic corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole, arising from modifications to the algebra inspired by the generalized uncertainty principle (GUP) theories. Then we study four specific models of GUP, compute their effective dynamics as well as their expansion and its rate of change using the Raychaudhuri equation. We show that the modification from GUP in two of these models, where such modifications are dependent of the configuration variables, lead to finite Kretchmann scalar, expansion and its rate, hence implying the resolution of the singularity. However, the other two models for which the modifications depend on the momenta still retain their singularities even in the effective regime.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP09(2021)062