Near-Horizon BMS Symmetry and Implications on Black Hole Entropy

Abstract

Thermodynamic significance of near-horizon symmetries remains an important open question in black hole physics, particularly in the context of black hole evaporation and information recovery. In this work, we investigate the role of horizon-adapted Bondi-van der Burg-Metzner-Sachs (BMS)-like supertranslations in the thermodynamic description of a dynamical Schwarzschild black hole. Working in a near-horizon Rindler coordinate system, we construct a class of diffeomorphisms that preserve the horizon structure and promote the associated supertranslation parameter to a Goldstone-like mode arising from the breaking of horizon symmetry. By expanding the Einstein-Hilbert action around the background geometry, we obtain the effective action for the Goldstone mode and identify the corresponding conserved horizon charge from the surface contribution of the action. The relevant horizon is defined at the future outer trapping horizon, while the surface gravity is computed using the Kodama-vector construction appropriate for dynamical spacetimes. We show that the horizon supertranslation mode contributes non-trivially to the surface gravity and modifies the thermodynamic description of the black hole beyond the stationary limit. Using the associated Noether charge, we derive the entropy of the horizon-BMS transformed geometry and find that the Bekenstein-Hawking area law is recovered at leading order, while subleading corrections depend explicitly on the supertranslation sector and the dynamical evolution of the black hole.