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T-Witts from the horizon

H. Adami, D. Grumiller, S. Sadeghian, M. M. Sheikh-Jabbari, C. Zwikel

TL;DR

This work develops a near-horizon framework for generic Kerr black holes using co-rotating Kruskal–Israel-like coordinates. It identifies a rich symmetry structure on null hypersurfaces, introducing the T-Witt algebra as a two-tower extension of supertranslations that coexists with superrotations; crucially, the associated surface charges are generically non-integrable, with a Barnich–Troessaert modified bracket yielding a central-extension-free algebra and a generalized charge conservation law that relates charge evolution to horizon flux. The analysis distinguishes between integrable (conserved) and non-integrable (flux) contributions, and shows that appropriate gauge fixing aligns the on-shell phase space with the symmetry generators, recovering familiar near-horizon algebras as special cases. The results provide a structured path toward soft hair and semi-classical Kerr microstate studies, while also clarifying the role of horizon flux in the dynamics of boundary charges and entropy.

Abstract

Expanding around null hypersurfaces, such as generic Kerr black hole horizons, using co-rotating Kruskal-Israel-like coordinates we study the associated surface charges, their symmetries and the corresponding phase space within Einstein gravity. Our surface charges are not integrable in general. Their integrable part generates an algebra including superrotations and a BMS_3-type algebra that we dub "T-Witt algebra". The non-integrable part accounts for the flux passing through the null hypersurface. We put our results in the context of earlier constructions of near horizon symmetries, soft hair and of the program to semi-classically identify Kerr black hole microstates.

T-Witts from the horizon

TL;DR

This work develops a near-horizon framework for generic Kerr black holes using co-rotating Kruskal–Israel-like coordinates. It identifies a rich symmetry structure on null hypersurfaces, introducing the T-Witt algebra as a two-tower extension of supertranslations that coexists with superrotations; crucially, the associated surface charges are generically non-integrable, with a Barnich–Troessaert modified bracket yielding a central-extension-free algebra and a generalized charge conservation law that relates charge evolution to horizon flux. The analysis distinguishes between integrable (conserved) and non-integrable (flux) contributions, and shows that appropriate gauge fixing aligns the on-shell phase space with the symmetry generators, recovering familiar near-horizon algebras as special cases. The results provide a structured path toward soft hair and semi-classical Kerr microstate studies, while also clarifying the role of horizon flux in the dynamics of boundary charges and entropy.

Abstract

Expanding around null hypersurfaces, such as generic Kerr black hole horizons, using co-rotating Kruskal-Israel-like coordinates we study the associated surface charges, their symmetries and the corresponding phase space within Einstein gravity. Our surface charges are not integrable in general. Their integrable part generates an algebra including superrotations and a BMS_3-type algebra that we dub "T-Witt algebra". The non-integrable part accounts for the flux passing through the null hypersurface. We put our results in the context of earlier constructions of near horizon symmetries, soft hair and of the program to semi-classically identify Kerr black hole microstates.

Paper Structure

This paper contains 34 sections, 106 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Kerr geometry and metric near its bifurcate horizon
  3. Near horizon coordinates
  4. Bifurcation 2-sphere
  5. Near horizon symmetries at the bifurcation surface
  6. Fall-off conditions
  7. Near bifurcation Killing vectors
  8. Near bifurcation Killing vector algebra
  9. Conserved charges and their algebra
  10. T-Witt symmetries on null hypersurfaces
  11. Near null hypersurface expansion and on-shell conditions
  12. Near null hypersurface Killing vectors and field variations
  13. T-Witt and null hypersurface symmetry algebras
  14. Charges, fluxes and generalized charge conservation
  15. Charge variations and non-integrability of the charge
  16. ...and 19 more sections

Figures (1)

  • Figure 1: Selected infinite subalgebras of T-Witt algebra. The null hypersurface symmetry algebra consists of superrotations and the T-Witt. Some physically motivated restrictions, such as vanishing expansion, leave intact the superrotations but reduce T-Witt to one of its subalgebras discussed in appendix \ref{['Appen:B']}. Particularly the assumption of Gaussian null coordinates reduces T-Witt to S-Witt. Assuming additionally constant surface gravity and/or stationarity yields further reductions, recovering near horizon symmetries also found in previous literature.