Clouds of strings in 4D Einstein–Gauss–Bonnet black holes

Abstract

Abstract Recently there has been significant interest in regularizing, a D → 4 limit, of EGB gravity, and the resulting regularized 4 D EGB gravities have nontrivial gravitational dynamics — namely the 4 D EGB gravity. We present an exact charged black hole solution to the 4 D EGB gravity surrounded by clouds of string (CS) and also analyse their thermodynamic properties. Owing to the corrected black hole due to the background CS, the thermodynamic quantities have also been corrected except for the entropy, which remains unaffected by a CS background. However, as a result of the 4 D EGB theory, the Bekenstein–Hawking area law turns out to be corrected by a logarithmic area term. The heat capacity C + diverges at a critical radius r = r C , where incidentally the temperature has a maximum, and C + > 0 for r + r C allowing the smaller black hole to become locally stable. Interestingly, due to the surrounding cloud of strings, we have phase transition from globally thermodynamically small stable black holes with negative free energy ( F + 0 ) to large unstable black holes. Our solution can also be identified as a 4 D monopole-charged EGB black hole. Our results demonstrate that the Hawking’s evaporation leads to a thermodynamically stable remnant with vanishing temperature. We regain results of spherically symmetric black hole solutions of general relativity and that of 4 D EGB, respectively, in the limits α → 0 and a = 0 .