Thermodynamic instability of topological black holes with nonlinear source

In this paper, we obtain higher dimensional topological black hole solutions of Einstein-$\Lambda$ gravity in the presence of a class of nonlinear electrodynamics. First, we calculate the conserved and thermodynamic quantities of ($n+1$)-dimensional asymptotically flat solutions and show that they satisfy the first law of thermodynamics. Also, we investigate the stability of these solutions in the (grand) canonical ensemble. Second, we endow a global rotation to the static Ricci-flat solutions and calculate the conserved quantities of solutions by using the counterterm method. We obtain a Smarr-type formula for the mass as a function of the entropy, the angular momenta and the electric charge, and show that these quantities satisfy the first law of thermodynamics. Then, we perform a stability analysis of the rotating solutions both in the canonical and the grand canonical ensembles.Comment: 17 pages with 14 figures, accepted in EPJ

Magnetic Strings in Einstein-Born-Infeld-Dilaton Gravity

A class of spinning magnetic string in 4-dimensional Einstein-dilaton gravity with Liouville type potential which produces a longitudinal nonlinear electromagnetic field is presented. These solutions have no curvature singularity and no horizon, but have a conic geometry. In these spacetimes, when the rotation parameter does not vanish, there exists an electric field, and therefore the spinning string has a net electric charge which is proportional to the rotation parameter. Although the asymptotic behavior of these solutions are neither flat nor (A)dS, we calculate the conserved quantities of these solutions by using the counterterm method. We also generalize these four-dimensional solutions to the case of $(n+1)$-dimensional rotating solutions with $k\leq[n/2]$ rotation parameters, and calculate the conserved quantities and electric charge of them.Comment: 15 pages, references added, to appear in Phys. Lett.

Thermodynamic instability of nonlinearly charged black holes in gravity's rainbow

Motivated by the violation of Lorentz invariancy in quantum gravity, we study black hole solutions in gravity's rainbow in context of Einstein gravity coupled with various models of nonlinear electrodynamics. We regard an energy dependent spacetime and obtain related metric functions and electric fields. We show that there is an essential singularity at the origin which is covered with an event horizon. We also compute the conserved and thermodynamical quantities and examine the validity of the first law of thermodynamics in the presence of rainbow functions. Finally, we investigate thermal stability conditions for these black hole solutions in context of canonical ensemble. We show that thermodynamical structure of the solutions depends on the choices of nonlinearity parameters, charge and energy functions.Comment: 13 pages, 5 figure

A new approach toward geometrical concept of black hole thermodynamics

Motivated by the energy representation of Riemannian metric, in this paper we study different approaches toward the geometrical concept of black hole thermodynamics. We investigate thermodynamical Ricci scalar of Weinhold, Ruppeiner and Quevedo metrics and show that their number and location of divergences do not coincide with phase transition points arisen from heat capacity. Next, we introduce a new metric to solve these problems. We show that the denominator of the Ricci scalar of the new metric contains terms which coincide with different types of phase transitions. We elaborate the effectiveness of the new metric and shortcomings of the previous metrics with some examples. Furthermore, we find a characteristic behavior of the new thermodynamical Ricci scalar which enables one to distinguish two types of phase transitions. In addition, we generalize the new metric for the cases of more than two extensive parameters and show that in these cases the divergencies of thermodynamical Ricci scalar coincide with phase transition points of the heat capacity.Comment: 13 pages with 7 figures, accepted in EPJ

Three dimensional nonlinear magnetic AdS solutions through topological defects

Inspired by large applications of topological defects in describing different phenomena in physics, and considering the importance of three dimensional solutions in AdS/CFT correspondence, in this paper we obtain magnetic anti-de Sitter solutions of nonlinear electromagnetic fields. We take into account three classes of nonlinear electrodynamic models; first two classes are the well-known BornInfeld like models including logarithmic and exponential forms and third class is known as the power Maxwell invariant nonlinear electrodynamics. We investigate the effects of these nonlinear sources on three dimensional magnetic solutions. We show that these asymptotical AdS solutions do not have any curvature singularity and horizon. We also generalize the static metric to the case of rotating solutions and find that the value of the electric charge depends on the rotation parameter. Finally, we consider the quadratic Maxwell invariant as a correction of Maxwell theory and in other words, we investigate the effects of nonlinearity as a correction. We study the behavior of the deficit angle in presence of these theories of nonlinearity and compare them with each other. We also show that some cases with negative deficit angle exists which are representing objects with different geometrical structure. We also show that in case of the static only magnetic field exists whereas by boosting the metric to rotating one, electric field appear too.Comment: 22 pages with 24 figures. Accepted for publication in Eur. Phys. J.