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Spherically symmetric static vacuum solutions in hybrid metric-Palatini gravity

B. Dănilă, T. Harko, F. S. N. Lobo, M. K. Mak

We consider vacuum static spherically symmetric solutions in the hybrid metric-Palatini gravity theory, which is a combination of the metric and Palatini f(R) formalisms unifying local constraints at the Solar System level and the late-time cosmic acceleration. We adopt the scalar-tensor representation of the hybrid metric-Palatini theory, in which the scalar-tensor 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.

General Relativity and Quantum Cosmology; Astrophysics - High Energy Astrophysical Phenomena; High Energy Physics - Theory

Physical Review D
Volume 99, Issue 6
2019 March

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Faculdade de Ciências da Universidade de Lisboa Universidade do Porto Faculdade de Ciências e Tecnologia da Universidade de Coimbra
Fundação para a Ciência e a Tecnologia COMPETE 2020 PORTUGAL 2020 União Europeia