Abbott-Deser-Tekin like conserved quantities in Lanczos-Lovelock gravity: beyond Killing diffeomorphisms

TL;DR

This paper extends the concept of conserved quantities in Lanczos-Lovelock gravity to non-Killing horizons, providing a generalized ADT-like current applicable beyond traditional Killing vectors, with implications for gravitational thermodynamics.

Contribution

It introduces a generalized ADT-like conserved current for Lanczos-Lovelock gravity applicable to non-Killing horizons, connecting it with Noether potentials and broadening thermodynamic analysis.

Findings

Conserved current formulated for non-Killing horizons.

Connection established between ADT-like current and Noether potential.

Results reduce to known ADT case for Killing vectors.

Abstract

We obtain the conserved Abbott-Deser-Tekin (ADT)-{\it like} current for the Lanczos-Lovelock gravity for a diffeomorphism vector, which defines the horizon of a spacetime and, importantly, is not necessarily a Killing vector. As the original ADT current is defined only for the presence of a background Killing vector, one cannot use it extensively for the thermodynamic description of the wide classes of non-Killing horizons which appear in gravity. On the other hand, this general approach can be utilized for those horizons. Here, the conserved current can be written as the derivative of the two-rank anti-symmetric potential, the connection of which is apparent with the conserved Noether potential from our analysis. If one assumes the diffeomorphism vector as the Killing one, the results match to the ADT case, whereas non-trivial result comes for the conformal Killing vectors and other horizon defining diffeomorphism vectors.