Interacting Black Holes

TL;DR

This paper analyzes the geometry and thermodynamics of collinear Schwarzschild black holes, including charged and string-theoretic cases, revealing how their mutual attraction deforms horizons and affects entropy and free energy.

Contribution

It provides a detailed analysis of interacting black holes' geometry and thermodynamics, extending to charged and string theory contexts with exact entropy calculations.

Findings

Horizon deformation due to mutual attraction

Agreement with Newtonian gravity at large distances

Exact entropy matching in string theory models

Abstract

We revisit the geometry representing l collinear Schwarzschild black holes. It is seen that the black holes' horizons are deformed by their mutual gravitational attraction. The geometry has a string like conical singularity that connects the holes but has nevertheless a well defined action. Using standard gravitational thermodynamics techniques we determine the Free energy for two black holes at fixed temperature and distance, their entropy and mutual force. When the black holes are far apart the results agree with Newtonian gravity expectations. This analyses is generalized to the case of charged black holes. Then we consider black holes embedded in String/M-theory as bound states of branes. Using the effective string description of these bound states and for large separation we reproduce exactly the semi-classical result for the entropy, including the correction associated with the interaction between the holes.