Spherically symmetric static vacuum solutions in hybrid metricPalatini gravity
Abstract
We consider vacuum static spherically symmetric solutions in the hybrid metricPalatini gravity theory, which is a combination of the metric and Palatini f (R ) formalisms unifying local constraints at the Solar System level and the latetime cosmic acceleration. We adopt the scalartensor representation of the hybrid metricPalatini theory, in which the scalartensor definition of the potential can be represented as a Clairaut differential equation. Due to their mathematical complexity, it is difficult to find exact solutions of the vacuum field equations, and therefore we adopt a numerical approach in studying the behavior of the metric functions and of the scalar field. After reformulating the field equations in a dimensionless form, and by introducing a suitable independent radial coordinate, the field equations are solved numerically. We detect the formation of a black hole from the presence of the Killing horizon for the timelike Killing vector in the metric tensor components. Several models, corresponding to different functional forms of the scalar field potential, are considered. The thermodynamic properties of these black hole solutions (horizon temperature, specific heat, entropy, and evaporation time due to Hawking luminosity) are also investigated in detail.
 Publication:

Physical Review D
 Pub Date:
 March 2019
 DOI:
 10.1103/PhysRevD.99.064028
 arXiv:
 arXiv:1811.02742
 Bibcode:
 2019PhRvD..99f4028D
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena;
 High Energy Physics  Theory
 EPrint:
 22 pages, 11 figures, accepted for publication in PRD