Carroll black holes in (A)dS and their higher-derivative modifications

TL;DR

This paper introduces Carrollian black holes in (A)dS spacetimes and their higher-derivative modifications, analyzing particle motion and thermodynamics, revealing unique windings and divergent entropy behaviors.

Contribution

It defines and studies Carrollian black holes in (A)dS and quadratic gravity, analyzing particle dynamics and thermodynamics in these novel geometries.

Findings

Particles wind around extremal surfaces with finite or infinite windings depending on the spacetime.

Thermodynamics shows divergent entropy as temperature approaches zero in the Carroll limit.

The specific heat can be positive, negative, or zero, indicating diverse thermodynamic behaviors.

Abstract

We define the Carrollian black holes corresponding to the limit of Schwarzschild-(A)dS spacetime and its higher-derivative counterpart known as Schwarzschild-Bach-(A)dS spacetime, which is also a static spherically symmetric vacuum solution of quadratic gravity. By analyzing motion of massive particles in these geometries, we found that: In the case of Schwarzschild-(A)dS, a (nearly) tangential particle from infinity will wind around the extremal surface with a finite number of windings depending on the impact parameter and the cosmological constant. In Schwarzschild-Bach-(A)dS, a particle passing close enough to the extremal surface will have an infinite number of windings; hence, it will not escape to asymptotic infinity as in Schwarzschild-(A)dS. We also calculate the thermodynamical quantities for such black holes and argue that it is analogous to an incompressible thermodynamical system with divergent entropy when the temperature goes to zero (in the strict Carroll limit). We then define a divergent specific heat that can be positive, negative, or zero.