Corrected first law of thermodynamics for dynamical regular black holes

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.