Geometrothermodynamics of Myers-Perry Black Holes

Abstract

We consider the thermodynamics and Geometrothermodynamics of the Myers-Perry black holes in five dimensions for three different cases, depending on the values of the angular momenta. We follow Davies approach to study the thermodynamics of black holes and find a nontrivial thermodynamic structure in all cases, which is fully reproduced by the analysis performed with the techniques of Geometrothermodynamics. Moreover, we observe that in the cases when only one angular momentum is present or the two angular momenta are fixed to be equal, i.e. when the thermodynamic system is two dimensional, there is a complete agreement between the divergences of the generalized susceptibilities and the singularities of the equilibrium manifold, whereas when the two angular momenta are fully independent, that is, when the thermodynamic system is three dimensional, additional singularities in the curvature appear. However, we prove that such singularities are due to the changing from a stable phase to an unstable one.

New perspective for black hole thermodynamics in Gauss–Bonnet–Born–Infeld massive gravity

“…Now, by using the total mass of black holes (20) with entropy (19) and electric charge (17), one can construct the phase space and calculate its Ricci scalar. Due to economical reasons, we will not present the Ricci scalar obtained but rather present its results in the following diagrams (Figs.…”

“…There are several methods regarding thermodynamical geometry which are; Weinhold [7,8], Ruppeiner [9,10], Quevedo [11,12] and HPEM [13][14][15]. The geometrical thermodynamics has been employed in the context of different types of black holes [16][17][18][19][20][21][22]. In addition, this method was also used to study the phase transition of superconductors [23].…”

Hessian matrix, specific heats, Nambu brackets, and thermodynamic geometry

“…Recently, the Myers-Perry black hole [26] has been of the particular interest due to its rich thermodynamics [27][28][29][30][31][32][33]. This black hole is a direct generalization of the Kerr black hole in higher dimensions with rotation in more than one plane.…”

“…Although the thermodynamics of the Myers-Perry black hole with two rotating planes, equal spins, and a particular number of nonzero equal spins have been extensively explored [27,[32][33][34].The Hawking temperature for a Myers-Perry black hole with more than two and unequal spins have been obtianed in [34]. However, specific heats and phase transitions have not yet been reported for more than two and unequal spins.…”

Charged BTZ black holes in the context of massive gravity’s rainbow

“…Several investigations regarding thermodynamics of the black holes through these methods were done in Refs. [89][90][91][92][93][94][95][96].…”