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

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 αGB, 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 αGB becomes large, and approaches to a finite value for αGB→ ∞.

Metric fluctuations in higher-dimensional black holes

“…It has been applied to investigate a wide range of topics, including the spectra of quasi-normal modes and the stability of static black holes [37,38], rotating black holes [39][40][41][42], (A)dS black holes [43][44][45], and black string and brane solutions [46][47][48][49]. Furthermore, the large D limit has also been employed to explore the dynamics of solutions in the Einstein-Gauss-Bonnet theory [50][51][52][53].…”

“…As a result, the dynamics of the black hole horizon can be reduced to a simple and effective theory. Recent research utilizing this 'large D effective theory' has examined various black hole models [44][45][46], and investigated the phases and instabilities of black strings/branes [47][48][49][50]. The large D limit offers a rich landscape for analysis, furnishing new perspectives [51][52][53][54][55][56][57][58][59].…”