Spherically symmetric static vacuum solutions in hybrid metric-Palatini gravity. (arXiv:1811.02742v1 [gr-qc])

<a href="http://arxiv.org/find/gr-qc/1/au:+Danila_B/0/1/0/all/0/1">Bogdan Danila</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Harko_T/0/1/0/all/0/1">Tiberiu Harko</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Lobo_F/0/1/0/all/0/1">Francisco S. N. Lobo</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Mak_M/0/1/0/all/0/1">Man Kwong Mak</a>

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 a singularity 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.

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 a singularity 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.

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