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Black Hole Entropy from BMS Symmetry at the Horizon

S. Carlip

TL;DR

This work argues that black hole entropy is dictated by horizon-local BMS3 (Galilean conformal) symmetries, not by asymptotic or stretched-horizon symmetries. By performing a dimensional reduction to 2D dilaton gravity and using the covariant phase space formalism, the author constructs horizon generators that realize a BMS3 algebra with a central term. A mode analysis yields a central charge $c_{LM}=1/(4G)$ and zero-modes whose Cardy-like counting reproduces the Bekenstein–Hawking entropy $S = \varphi_+/(4G)$. The results suggest a universal, symmetry-based origin of black hole entropy that does not rely on ad hoc boundary constructions and point toward broader applicability and generalizations.

Abstract

Near the horizon, the obvious symmetries of a black hole spacetime---the horizon-preserving diffeomorphisms---are enhanced to a larger symmetry group with a BMS${}_3$ algebra. Using dimensional reduction and covariant phase space techniques, I investigate this augmented symmetry, and show that it is strong enough to determine the black hole entropy.

Black Hole Entropy from BMS Symmetry at the Horizon

TL;DR

This work argues that black hole entropy is dictated by horizon-local BMS3 (Galilean conformal) symmetries, not by asymptotic or stretched-horizon symmetries. By performing a dimensional reduction to 2D dilaton gravity and using the covariant phase space formalism, the author constructs horizon generators that realize a BMS3 algebra with a central term. A mode analysis yields a central charge and zero-modes whose Cardy-like counting reproduces the Bekenstein–Hawking entropy . The results suggest a universal, symmetry-based origin of black hole entropy that does not rely on ad hoc boundary constructions and point toward broader applicability and generalizations.

Abstract

Near the horizon, the obvious symmetries of a black hole spacetime---the horizon-preserving diffeomorphisms---are enhanced to a larger symmetry group with a BMS algebra. Using dimensional reduction and covariant phase space techniques, I investigate this augmented symmetry, and show that it is strong enough to determine the black hole entropy.

Paper Structure

This paper contains 8 sections, 40 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Dilaton gravity with null dyads
  3. The covariant canonical formalism and symplectic structure
  4. Horizons and boundary conditions
  5. Symmetries and approximate symmetries
  6. Canonical generators and their algebra
  7. Modes, zero-modes, and entropy
  8. Conclusions

Figures (1)

  • Figure 1: Penrose diagram for the exterior of a black hole