Searching for dynamical black holes in various theories of gravity

TL;DR

This paper constructs models of dynamical black holes in Einstein and $f(R)$ gravity with scalar fields, analyzing their thermodynamics and addressing issues like ghost fields, providing new analytical solutions and thermodynamic insights.

Contribution

It introduces analytical models of time-varying black holes in Einstein and $f(R)$ gravity with scalar fields, and explores their thermodynamics and ghost field issues.

Findings

Time-dependent thermodynamical quantities are derived.

Ghost scalar fields are unavoidable in Einstein gravity but can be avoided in $f(R)$ gravity.

Analytical solutions for dynamical black holes are provided.

Abstract

We construct models of Einstein and $f(R)$ gravity with two scalar fields, which admit analytical solutions describing time-varying dynamical black holes. Their thermodynamics is investigated in the adiabatic approximation. In addition to the Misner-Sharp-Hernandez quasilocal mass, we provide time-dependent thermodynamical quantities, including the Hawking temperature, Helmholtz free energy, entropy, and thermodynamical energy. The latter does not always coincide with the Misner-Sharp-Hernandez mass at the horizon, although they coincide in the static limit. For Schwarzschild-type (i.e., $g_{tt}g_{rr}=-1$) black holes in Einstein gravity, one of the two scalars is always a ghost with negative kinetic energy. We show that this ghost can be avoided in $f(R)$ gravity.