Carrollian physics at the black hole horizon

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 nonstationary black holes. Finally, we discuss the relation of these conserved quantities to the infinite tower of charges of the covariant phase space formalism.

Torsion and anomalies in the warped limit of Lifschitz theories

“…However in that case one expects anomalies to be only present in odd dimensionality, due to the interpretation of Galileian theories as coming from null reductions. In the Carrollian case this is not a problem, since they can be seen as the theories which arise on null embeddings in Bargmann spacetime [14,27] and anomalies can be realized via the inflow mechanism. Furthermore, torsional anomalies in the Galileian case are not to be expected based on the dimensionality of the translations generators (minus one and minus two respectively).…”

Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity

“…On the other hand, the ultra-relativistic expansion of general relativity has been explored in[68], while the Carrollian limit at the level of the Einstein-Hilbert action has been studied in[49]. It is also important to mention the realisation of the Carroll symmetry in the near horizon limit of black holes[69].…”

Near horizon dynamics of three dimensional black holes

“…Inspection of the explicit results above shows compatibility with (75), which is a simple, yet non-trivial, cross-check on the correctness of the equations displayed in this appendix. Starting with the general form of the Hamiltonian density (136), analytically continuing in N ≤ 1, assuming N = ε → 0 + , inserting J = Φ and dropping total derivative terms yields the limiting Hamiltonian density…”