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Register a new userPhase transitions in four-dimensional AdS black holes with a nonlinear electrodynamics source
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In this work we consider black hole solutions to Einstein theory coupled to a nonlinear power-law electromagnetic field with a fixed exponent value. We study the extended phase space thermodynamics in canonical and grand canonical ensembles where the varying cosmological constant plays the role of an effective thermodynamic pressure. We examine thermodynamical phase transitions in such black hols and find that both first and second order phase transitions can occur in the canonical ensemble, while for the grand canonical ensemble the Hawking-Page and second order phase transitions are allowed.
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We present a new family of asymptotically AdS four-dimensional black hole solutions with scalar hair of a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential. For a certain profile of the scalar field we solve the Einstein equations and we determine the scalar potential. Thermodynamically we show that there is a critical temperature below which there is a phase transition of a black hole with hyperbolic horizon to the new hairy black hole configuration.
Using Maxwells equal area law, we discuss the phase transition of higher dimensional charged topological dilaton AdS black holes with a nonlinear source. The coexisting region of the two phases is found and we depict the coexistence region in $P-v$ diagrams. The two-phase equilibrium curves in $P-T$ diagrams are plotted, and we take the first order approximation of volume $v$ in the calculation. To better compare with a general thermodynamic system, the Clapeyron equation is derived for higher dimensional charged topological black hole with a nonlinear source. The latent heat of isothermal phase transition is investigated. We also study the effect of the parameters of the black hole on the region of two-phases coexistence. The results show that the black hole may go through a small-large phase transition similar to those of usual non-gravity thermodynamic systems.
We study the propagation of scalar fields in the background of $2+1$-dimensional Coulomb like AdS black holes, and we show that such propagation is stable under Dirichlet boundary conditions. Then, we solve the Klein-Gordon equation by using the pseudospectral Chevyshev method, and we find the quasinormal frequencies. Mainly, we find that the quasinormal frequencies are purely imaginary for a null angular number and they are complex and purely imaginary for a non null value of the angular number, which depend on the black hole charge, angular number and overtone number. On the other hand, the effect of the inclusion of a Coulomb like field from non lineal electrodynamics to General Relativity for a vanishing angular number is the emergence of two branches of quasinormal frequencies in contrast with the static BTZ black hole.
An exact hairy asymptotically locally AdS black hole solution with a flat horizon in the Einstein-nonlinear sigma model system in (3+1) dimensions is constructed. The ansatz for the nonlinear $SU(2)$ field is regular everywhere and depends explicitly on Killing coordinates, but in such a way that its energy-momentum tensor is compatible with a metric with Killing fields. The solution is characterized by a discrete parameter which has neither topological nor Noether charge associated with it and therefore represents a hair. A $U(1)$ gauge field interacting with Einstein gravity can also be included. The thermodynamics is analyzed. Interestingly, the hairy black hole is always thermodynamically favored with respect to the corresponding black hole with vanishing Pionic field.
Motivated by black hole solutions with matter fields outside their horizon, we study the effect of these matter fields in the motion of massless and massive particles. We consider as background a four-dimensional asymptotically AdS black hole with scalar hair. The geodesics are studied numerically and we discuss about the differences in the motion of particles between the four-dimensional asymptotically AdS black holes with scalar hair and their no-hair limit, that is, Schwarzschild AdS black holes. Mainly, we found that there are bounded orbits like planetary orbits in this background. However, the periods associated to circular orbits are modified by the presence of the scalar hair. Besides, we found that some classical tests such as perihelion precession, deflection of light and gravitational time delay have the standard value of general relativity plus a correction term coming from the cosmological constant and the scalar hair. Finally, we found a specific value of the parameter associated to the scalar hair, in order to explain the discrepancy between the theory and the observations, for the perihelion precession of Mercury and light deflection.
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