Nonlinearly Charged Black Holes Research Articles

Thermodynamics of topological nonlinear charged Lifshitz black holes

In this paper, we construct a new class of analytic topological Lifshitz black holes with constant curvature horizon in the presence of a power-law Maxwell field in four or more dimensions. We find that in order to obtain these exact Lifshitz solutions, we need a dilaton and at least three electromagnetic fields. Interestingly enough, we find that the reality of the charge of the electromagnetic field which is needed for having solutions with a curved horizon rules out black holes with a hyperbolic horizon. Next, we study the thermodynamics of these nonlinear charged Lifshitz black holes with spherical and flat horizons by calculating all of the conserved and thermodynamic quantities of the solutions. Furthermore, we obtain a generalized Smarr formula and show that the first law of thermodynamics is satisfied. We also perform a stability analysis in both canonical and grand-canonical ensembles. We find that the solutions are thermally stable in proper ranges of the metric parameters. Finally, we comment on the dynamical stability of the obtained solutions under perturbations in four dimensions.

On the black hole mass decomposition in nonlinear electrodynamics

In the weak field limit of nonlinear Lagrangians for electrodynamics, i.e. theories in which the electric fields are much smaller than the scale (threshold) fields introduced by the nonlinearities, a generalization of the Christodoulou–Ruffini mass formula for charged black holes is presented. It proves that the black hole outer horizon never decreases. It is also demonstrated that reversible transformations are, indeed, fully equivalent to constant horizon solutions for nonlinear theories encompassing asymptotically flat black hole solutions. This result is used to decompose, in an analytical and alternative way, the total mass-energy of nonlinear charged black holes, circumventing the difficulties faced to obtain it via the standard differential approach. It is also proven that the known first law of black hole thermodynamics is the direct consequence of the mass decomposition for general black hole transformations. From all the above we finally show a most important corollary: for relevant astrophysical scenarios nonlinear electrodynamics decreases the extractable energy from a black hole with respect to the Einstein–Maxwell theory. Physical interpretations for these results are also discussed.

Extended phase space thermodynamics andP−Vcriticality of black holes with a nonlinear source

In this paper, we consider the solutions of Einstein gravity in the presence of a generalized Maxwell theory, namely power Maxwell invariant. First, we investigate the analogy of nonlinear charged black hole solutions with the Van der Waals liquid--gas system in the extended phase space where the cosmological constant appear as pressure. Then, we plot isotherm $P$--$V$ diagram and study the thermodynamics of AdS black hole in the (grand canonical) canonical ensemble in which (potential) charge is fixed at infinity. Interestingly, we find the phase transition occurs in the both of canonical and grand canonical ensembles in contrast to RN black hole in Maxwell theory which only admits canonical ensemble phase transition. Moreover, we calculate the critical exponents and find their values are the same as those in mean field theory. Besides, considerably, we find in the grand canonical ensembles universal ratio $\frac{P_{c}v_{c}}{T_{c}}$ is independent of spacetime dimensions.

NONLINEAR CHARGED BLACK HOLES IN AdS QUASI-TOPOLOGICAL GRAVITY

In this paper, we present the static charged solutions of quartic quasi-topological gravity in the presence of a nonlinear electromagnetic field. Two branches of these solutions present black holes with one or two horizons or a naked singularity depending on the charge and mass of the black hole. The entropy of the charged black holes of fourth-order quasi-topological gravity through the use of Wald formula is computed and the mass, temperature and the charge of these black holes are found as well. We show that black holes with spherical, flat and hyperbolical horizon in quasi-topological gravity are stable for any allowed quasi-topological parameters. We also investigate the stability of nonlinear charged black holes.

Thermodynamics of charged black holes with a nonlinear electrodynamics source

We study the thermodynamical properties of electrically charged black hole solutions of a nonlinear electrodynamics theory defined by a power p of the Maxwell invariant, which is coupled to Einstein gravity in four and higher spacetime dimensions. Depending on the range of the parameter p, these solutions present different asymptotic behaviors. We compute the Euclidean action with the appropriate boundary term in the grand canonical ensemble. The thermodynamical quantities are identified and in particular, the mass and the charge are shown to be finite for all classes of solutions. Interestingly, a generalized Smarr formula is derived and it is shown that this latter encodes perfectly the different asymptotic behaviors of the black hole solutions. The local stability is analyzed by computing the heat capacity and the electrical permittivity and we find that a set of small black holes are locally stable. In contrast to the standard Reissner-Nordstrom solution, there is a first-order phase transition between a class of these non-linear charged black holes and the Minkowski spacetime.

Non-linear charged black holes

Very strong electromagnetic fields are characterized by the appearance of non-linearities. In order to explore the consequences of such non-linearities we have solved exactly the combined gravitational non-linear electromagnetic field equations for a static and spherical symmetric spacetime, where the source of the curvature is a point electric charge. We have chosen a non-linear Lagrangian density in such a way that the Maxwell, the Born--Infeld, and the Heisenberg--Euler theories are included as particular cases. The general solution can represent a charged black hole with the same characteristics of the Reissner--Nordstrø m one (two horizons and timelike singularity), or it can have only one horizon and a spacelike singularity, as in the Schwarzschild solution.