Phase and stability of black strings in Einstein-Gauss-Bonnet theory at large D

TL;DR

This paper analyzes the phase structure and stability of black strings in Einstein-Gauss-Bonnet theory at large dimensions, revealing how the Gauss-Bonnet coupling affects instability wavelengths and stability transitions.

Contribution

It extends the large D effective theory to Einstein-Gauss-Bonnet gravity, deriving thermodynamics and stability criteria including NLO corrections.

Findings

Entropy obeys the second law with NLO corrections.

Large Gauss-Bonnet coupling lengthens the instability wavelength.

Critical dimension for stability increases with Gauss-Bonnet coupling.

Abstract

The phase and stability of black strings in the Einstein-Gauss-Bonnet (EGB) theory are investigated by using the large D effective theory approach. The spacetime metric and thermodynamics are derived up to the next-to-leading order (NLO) in the 1/D expansion. We find that the entropy current defined by the Iyer-Wald formula follows the second law. As in the Einstein theory, the entropy difference from the total mass produces an entropy functional for the effective theory. Including the NLO correction, we find that for the large Gauss-Bonnet coupling constant $\alpha_{\rm GB}$, the Gregory-Laflamme instability of uniform black strings needs longer wavelength. Moreover, we show that the critical dimension, beyond which non-uiform black strings becomes more stable than uniform ones, increases as $\alpha_{\rm GB}$ becomes large, and approaches to a finite value for $\alpha_{\rm GB}\to \infty$.