Cloud of strings in third order Lovelock gravity
Abstract
Lovelock theory is a natural extension of the Einstein theory of general relativity to higher dimensions in which the first and second orders correspond, respectively, to general relativity and Einstein--Gauss--Bonnet gravity. We present exact black hole solutions of $D\ensuremath{\ge}4$-dimensional spacetime for first-, second-, and third-order Lovelock gravities in a string cloud background. Further, we compute the mass, temperature, and entropy of black hole solutions for the higher-dimensional general relativity and Einstein--Gauss--Bonnet theories and also perform thermodynamic stability of black holes. It turns out that the presence of the Gauss--Bonnet term and/or background string cloud completely changes the black hole thermodynamics. Interestingly, the entropy of a black hole is unaffected due to a background string cloud. We rediscover several known spherically symmetric black hole solutions in the appropriate limits.