Temperature and thermodynamic structure of Einstein's equations for a cosmological black hole

Understand

It is expected that the cosmological black holes are the closest realistic solutions of gravitational theories and they evolve with time.

• Moreover, the natural way of defining thermodynamic entities for the stationary ones is not applicable in the case of a time dependent spacetime.
• Here we confine our discussion within the Sultana-Dyer metric which is a cosmological black hole solution of Einstein's gravity.
• In literature, there exists two expressions of horizon temperature -- one is time dependent and the other does not depend on time.