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 ≥ 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.

Quintessence background for 5D Einstein–Gauss–Bonnet black holes

“…which is exactly same as the Einstein-Gauss-Bonnet case [23,28]. We again recall that, for C > 0 (C < 0), the black hole is thermodynamically stable (unstable).…”

“…(3) surrounded by the quintessence matter and investigate its properties. We assume that the metric has the form [18,19,28] …”

“…To discuss the thermodynamics of the metric (5) with the function (13), we start with the Hawking temperature. The Hawking temperature associated with the black hole is defined by T = κ/2π , where κ is the surface gravity defined by [23,28],…”

“…(18) modifies the Gauss-Bonnet black hole temperature [23,28], and taking the limit q → 0, we recover the Gauss-Bonnet black hole temperature as…”

“…The spherically symmetric static black hole solution for the Einstein-Gauss-Bonnet theory was first obtained by Boulware and Deser [3][4][5], and later several authors explored exact black hole solutions and their thermodynamical properties [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The generalization of the Boulware-Desser solution has been obtained with a source as a cloud of strings, in Einstein-Gauss-Bonnet gravity [24,25], and also in Lovelock gravity [26][27][28].…”