Corrected first law of thermodynamics for dynamical regular black holes

TL;DR

This paper derives a corrected form of the first law of thermodynamics for dynamical regular black holes, accounting for the mass dependence of the energy-momentum tensor component, which affects the temperature and energy interpretation.

Contribution

It introduces a modified first law of thermodynamics for dynamical regular black holes, considering the mass dependence of the energy-momentum tensor component.

Findings

The temperature derived from the traditional first law differs from other methods.

The correction factor stems from the mass dependence of the energy-momentum tensor.

The black hole mass cannot be directly equated with internal energy in this context.

Abstract

In this work, we establish the corrected first law of thermodynamics for dynamical regular black holes on both the event horizon and apparent horizon. We find that the temperature of dynamical regular black holes derived from the traditional first law differs from that obtained through other approaches. This indicates that, similar to static cases, the first law of thermodynamics requires correction. We then derive the corrected first law of thermodynamics from the Einstein field equations. Our analysis reveals that the corrected factor originates from the fact that the $ T^v_v $ component of the energy-momentum tensor depends on the black hole mass. This dependence implies that the mass of a regular black hole can no longer be directly identified as the internal energy, leading to the corrections of the first law of thermodynamics.