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Near-Horizon BMS Symmetry, Dimensional Reduction, and Black Hole Entropy

S. Carlip

TL;DR

The paper tackles the universality of black-hole entropy by positing that the essential degrees of freedom live in a near-horizon region endowed with a BMS${}_3$ symmetry. Through dimensional reduction to a two-dimensional dilaton gravity model, it shows that horizon diffeomorphisms supplemented by a shift symmetry generate a centrally extended BMS${}_3$ algebra with central charge $c_{LM}=1/(4G)$, enabling a Cardy-like state counting. The entropy is then shown to reproduce the Bekenstein-Hawking result $S = A/(4G\ħ)$ by summing over horizon generators, i.e., the full cross-sectional area, without resorting to stretched horizons or ad hoc angular dependencies. The work suggests a universal, symmetry-based foundation for black-hole entropy and points to connections with Hawking radiation and other quantum gravity frameworks.

Abstract

In an earlier short paper [Phys.\ Rev.\ Lett.\ 120 (2018) 101301, arXiv:1702.04439], I argued that the horizon-preserving diffeomorphisms of a generic black hole are enhanced to a larger BMS${}_3$ symmetry, which is powerful enough to determine the Bekenstein-Hawking entropy. Here I provide details and extensions of that argument, including a loosening of horizon boundary conditions and a more thorough treatment of dimensional reduction and meaning of a "near-horizon symmetry."

Near-Horizon BMS Symmetry, Dimensional Reduction, and Black Hole Entropy

TL;DR

The paper tackles the universality of black-hole entropy by positing that the essential degrees of freedom live in a near-horizon region endowed with a BMS symmetry. Through dimensional reduction to a two-dimensional dilaton gravity model, it shows that horizon diffeomorphisms supplemented by a shift symmetry generate a centrally extended BMS algebra with central charge , enabling a Cardy-like state counting. The entropy is then shown to reproduce the Bekenstein-Hawking result by summing over horizon generators, i.e., the full cross-sectional area, without resorting to stretched horizons or ad hoc angular dependencies. The work suggests a universal, symmetry-based foundation for black-hole entropy and points to connections with Hawking radiation and other quantum gravity frameworks.

Abstract

In an earlier short paper [Phys.\ Rev.\ Lett.\ 120 (2018) 101301, arXiv:1702.04439], I argued that the horizon-preserving diffeomorphisms of a generic black hole are enhanced to a larger BMS symmetry, which is powerful enough to determine the Bekenstein-Hawking entropy. Here I provide details and extensions of that argument, including a loosening of horizon boundary conditions and a more thorough treatment of dimensional reduction and meaning of a "near-horizon symmetry."

Paper Structure

This paper contains 13 sections, 85 equations, 1 figure.

Table of Contents

  1. Introduction
  2. BMS${}_3$ symmetry
  3. Reduction to two dimensions
  4. Dilaton gravity with null dyads
  5. Horizons
  6. Horizon symmetries
  7. Symplectic structure and generators
  8. Modes and zero-modes
  9. Entropy
  10. Conclusions and directions
  11. The covariant canonical formalism
  12. Gaussian null coordinates and dimensional reduction
  13. Some details of near-horizon symmetries

Figures (1)

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