On the Gravitational Hysteresis in the Kinetic Theory

TL;DR

This paper explores how nonlinear general relativity can induce hysteresis effects in gravitational systems, demonstrated through kinetic theory in curved spacetime and specific solutions like black holes and cosmological models.

Contribution

It introduces the concept of gravitational hysteresis in kinetic theory, showing entropy rate hysteresis in various curved spacetimes, a novel insight into gravitational memory effects.

Findings

Entropy rate exhibits hysteresis in curved spacetimes.

Hysteresis observed in Schwarzschild black hole and cosmological solutions.

Effect also present in Minkowski spacetime with gravitational wave perturbation.

Abstract

General theory of relativity is non--linear in nature and therefore can result in hysteresis-like effects and cause systems to remember the footprint of the gravitational field. Here we have investigated this effect using the Kinetic theory in curved spacetime. It is shown that the entropy rate experiences this hysteresis behavior. The effect is then considered for some special spacetimes, including Schwarzschild black hole, Friedmann--Lema\^itre--Robertson--Walker cosmological solution, and the flat Minkowski spacetime perturbed by a gravitational wave pulse. It is shown that there is some hysteresis effect for the entropy rate.