# Carrollian Physics at the Black Hole Horizon

## TL;DR

This paper demonstrates that black hole horizons can be described as Carrollian geometries emerging from an ultra-relativistic limit, revealing new conservation laws and symmetries related to horizon dynamics and charges.

## Contribution

It introduces a Carrollian geometric framework for black hole horizons and connects horizon laws to ultra-relativistic limits, extending the understanding of horizon symmetries and conserved charges.

## Key findings

- Horizon dynamics follow Carrollian conservation laws.
- Carrollian Killing vectors include BMS-like symmetries.
- New generalized angular momentum for non-stationary black holes.

## Abstract

We show that the geometry of a black hole horizon can be described as a Carrollian geometry emerging from an ultra-relativistic limit where the near-horizon radial coordinate plays the role of a virtual velocity of light tending to zero. We prove that the laws governing the dynamics of a black hole horizon, the null Raychaudhuri and Damour equations, are Carrollian conservation laws obtained by taking the ultra-relativistic limit of the conservation of an energy-momentum tensor; we also discuss their physical interpretation. We show that the vector fields preserving the Carrollian geometry of the horizon, dubbed Carrollian Killing vectors, include BMS-like supertranslations and superrotations and that they have non-trivial associated conserved charges on the horizon. In particular, we build a generalization of the angular momentum to the case of non-stationary black holes. Finally, we discuss the relation of these conserved quantities to the infinite tower of charges of the covariant phase space formalism.