Mass formulae and staticity condition for dark matter charged black holes

• Published in: The European physical journal. C, Particles and fields Vol. 80; no. 9; pp. 1 - 12
• Main Author: Rogatko, Marek
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2020; Springer; Springer Nature B.V; SpringerOpen
• Subjects: Angular momentum; Astronomy; Astrophysics and Cosmology; Bifurcations; Black holes; Dark matter; Dark matter (Astronomy); Elementary Particles; Hadrons; Heavy Ions; Inspection; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; String Theory; Topology
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-020-08432-7

The Arnowitt–Deser–Misner formalism is used to derive variations of mass, angular momentum and canonical energy for Einstein–Maxwell dark matter gravity in which the auxiliary gauge field coupled via kinetic mixing term to the ordinary Maxwell one, which mimics properties of hidden sector . Inspection of the initial data for the manifold with an interior boundary, having topology of S 2 , enables us to find the generalised first law of black hole thermodynamics in the aforementioned theory. It has been revealed that the stationary black hole solution being subject to the condition of encompassing a bifurcate Killing horizon with a bifurcation sphere, which is non-rotating, must be static and has vanishing magnetic Maxwell and dark matter sector fields, on static slices of the spacetime under consideration.