Eur. Phys. J. Plus (2022) 137: 827
https://doi.org/10.1140/epjp/s13360-022-03036-4

Regular Article

Remnants and thermal corrections in Horndeski black holes with non-minimal kinetic coupling

Department of Physics, National Institute of Technology, 190006, Srinagar, Kashmir, India

^a iyhkphy@gmail.com

Received: 29 September 2021
Accepted: 4 July 2022
Published online: 18 July 2022

Abstract

In this paper, we discuss the existence of remnants of the Horndeski black holes and analyze their stability. These black hole solutions belong to a class of Horndeski black holes which arises from the non-minimal kinetic coupling of a massless real scalar and the Einstein tensor. Our results show that the remnants exist in de-sitter space-time only. From the remnant size thus obtained, we estimate the bounds on values of parameters $\eta$ and $\alpha$. Exploring the statistical nature of black hole entropy, we then test the stability of remnants in the presence of thermal fluctuations. We observe that these statistical thermal fluctuations increase the entropy of the black hole at a certain value of horizon radius, which is exactly equal to the remnant radius. Finally using thermal fluctuations, we compute free energy potentials corrected by thermal fluctuations.