The Final State of Black Strings and p-Branes, and the Gregory-Laflamme Instability

TL;DR

This paper investigates the end states of black strings and p-branes under Gregory-Laflamme instability, finding that entropy considerations support horizon fragmentation in some cases, while smooth phase transitions may lead to non-uniform black strings as final states.

Contribution

It provides a comparative analysis of different potential end states of black strings and p-branes, highlighting conditions under which horizon fragmentation or smooth phase transitions occur.

Findings

Entropy argument supports horizon fragmentation as the final state.

Second order phase transition suggests non-uniform black strings as end states.

Agreement with entropy estimates is within a few percent.

Abstract

It is shown that the usual entropy argument for the Gregory-Laflamme (GL) instability for $some$ appropriate black strings and $p$-branes gives surprising agreement up to a few percent. This may provide a strong support to the GL's horizon fragmentation, which would produce the array of higher-dimensional Schwarzschild-type's black holes finally. On the other hand, another estimator for the size of the black hole end-state relative to the compact dimension indicates a second order (i.e., smooth) phase transition for some $other$ appropriate compactifications and total dimension of spacetime wherein the entropy argument is not appropriate. In this case, Horowitz-Maeda-type's non-uniform black strings or $p$-branes can be the final state of the GL instability.