Searching for dynamical black holes in various theories of gravity

Understand

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.