Solutions and Thermodynamics of Noncommutative Liouville Black Hole

Abstract

Motivated by string theory results, we study Liouville black hole solutions and their thermodynamics on noncommutative space. In particular, we present explicit solutions of black hole equations of motion, then we find their classical properties such as the ADMmass, the horizon geometry and the scalar Ricci curvature. Thermodynamic properties of such noncommutative black hole solutions including the Hawking temperature and entropy function are also discussed for three different regions of the moduli space of the theory.

Critical behaviors of 3D black holes with a scalar hair

“…To get the state equation P = P(T, r + ), we plug equation (9) in (7). Indeed, the direct calculation produces the pressure function as follows…”

“…Thermodynamic behaviors of black holes in various dimensions have received a particular interest through recent important works [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The equation of state for certain black holes has been established using an analysis that involves some characteristics similar to the Van der Waals P-V diagram [1,3,16,19,20].…”

On thermodynamics of 2D black holes in brane inflationary potentials

“…The black hole thermodynamics in two dimensional dilatonic models have been also studied by several investigation groups [16,17,18,19]. It has been shown, in many places, that the black hole thermodynamics can open gates to understand the quantum features of gravity theory.…”