Abstract
We construct a new class of asymptotically (a)dS black hole solutions of Einstein-Yang-Mills massive gravity in the presence of Born-Infeld nonlinear electrody namics. The obtained solutions possess a Coulomb electric charge, massive term and a non-abelian hair as well. We calculate the conserved and thermodynamic quantities, and investigate the validity of the first law of thermodynamics. Also, we investigate thermal stability conditions by using the sign of heat capacity through canonical ensemble. Next, we consider the cosmological constant as a thermodynamical pressure and study the van der Waals like phase transition of black holes in the extended phase space thermodynamics. Our results indicate the existence of a phase transition which is affected by the parameters of theory. Finally, we consider a massless scalar perturbation in the background of asymptotically adS solutions and calculate the quasinormal modes by employing the pseu dospectral method. The imaginary part of quasinormal frequencies is the time scale of a thermal state (in the conformal field theory) for the approach to thermal equilibrium.
Highlights
At the full nonlinear level due to the Hamiltonian constraint and generalize their ghost analysis to the most general case for arbitrary massive couplings ci’s
The dRGT massive gravity is almost a successful model in a sense that it does not lead to van DamVeltman-Zakharov discontinuity, it is free of Boulware-Deser ghost, and it can be used in higher dimensions with admissible validity
We show that how the free parameters affect the time scale that a thermal state in conformal field theory (CFT) needs to pass to meet the thermal equilibrium
Summary
We consider the following (3 + 1)-dimensional action of EYM-Massive gravity with BI NED for the model. It is easy to obtain three tensorial field equations which come from the variation of action (2.1) with respect to the metric tensor gμν, and the gauge potentials Aμ and A(μa) as. In order to obtain the spherically symmetric black hole solutions of EYM-Massive theory coupled to BI NED, we restrict attention to the following metric gμν = diag −f (r), f −1(r), r2, r2 sin θ ,. Considering the field equations (2.3) with the following radial gauge potential ansatz. The asymptotical behavior of the Kretschmann scalar for the large enough r confirms that the solutions are asymptotically (a)dS This singularity can be covered with an event horizon (for Λ < 0), and one can interpret the singularity as a black hole (figure 1). As a final point of this section, we should note that the metric function can possess more than two real positive roots which this behavior is due to giving mass to the gravitons (see [14, 16] for more details)
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