Black holes in the scalartensor formulation of 4D EinsteinGaussBonnet gravity: Uniqueness of solutions, and a new candidate for dark matter
Abstract
In this work we study static black holes in the regularized 4D EinsteinGaussBonnet theory of gravity; a shiftsymmetric scalartensor theory that belongs to the Horndeski class. This theory features a simple black hole solution that can be written in closed form, and which we show is the unique static, spherically symmetric and asymptotically flat black hole vacuum solution of the theory. We further show that no asymptotically flat, timedependent, spherically symmetric perturbations to this geometry are allowed, which suggests that it may be the only spherically symmetric vacuum solution that this theory admits (a result analogous to Birkhoff's theorem). Finally, we consider the thermodynamic properties of these black holes, and find that their final state after evaporation is a remnant with a size determined by the coupling constant of the theory. We speculate that remnants of this kind from primordial black holes could act as dark matter, and we constrain the parameter space for their formation mass, as well as the coupling constant of the theory.
 Publication:

Physical Review D
 Pub Date:
 August 2021
 DOI:
 10.1103/PhysRevD.104.044029
 arXiv:
 arXiv:2107.00046
 Bibcode:
 2021PhRvD.104d4029F
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
 15 pages, 4 figures