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

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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