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Register a new userRegular Black Holes in Rainbow Gravity
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In this work, we consider that in energy scales greater than the Planck energy, the geometry, fundamental physical constants, as charge, mass, speed of light and Newtonian constant of gravitation, and matter fields will depend on the scale. This type of theory is known as Rainbow Gravity. We coupled the nonlinear electrodynamics to the Rainbow Gravity, defining a new mass function $M(r,epsilon)$, such that we may formulate new classes of spherically symmetric regular black hole solutions, where the curvature invariants are well-behaved in all spacetime. The main differences between the General Relativity and our results in the the Rainbow gravity are: a) The intensity of the electric field is inversely proportional to the energy scale. The higher the energy scale, the lower the electric field intensity; b) the region where the strong energy condition (SEC) is violated decrease as the energy scale increase. The higher the energy scale, closer to the radial coordinate origin SEC is violated.
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In this paper, we investigate thermodynamical structure of dyonic black holes in the presence of gravitys rainbow. We confirm that for super magnetized and highly pressurized scenarios, the number of black holes phases is reduced to a single phase. In addition, due to specific coupling of rainbow functions, it is possible to track the effects of temporal and spatial parts of our setup on thermodynamical quantities/behaviors including equilibrium point, existence of multiple phases, possible phase transitions and conditions for having a uniform stable structure.
In this work, we study the possibility of generalizing solutions of regular black holes with an electric charge, constructed in general relativity, for the $f(G)$ theory, where $G$ is the Gauss-Bonnet invariant. This type of solution arises due to the coupling between gravitational theory and nonlinear electrodynamics. We construct the formalism in terms of a mass function and it results in different gravitational and electromagnetic theories for which mass function. The electric field of these solutions are always regular and the strong energy condition is violated in some region inside the event horizon. For some solutions, we get an analytical form for the $f(G)$ function. Imposing the limit of some constant going to zero in the $f(G)$ function we recovered the linear case, making the general relativity a particular case.
In this paper, the thermodynamic property of charged AdS black holes is studied in rainbow gravity. By the Heisenberg Uncertainty Principle and the modified dispersion relation, we obtain deformed temperature. Moreover, in rainbow gravity we calculate the heat capacity in a fixed charge and discuss the thermal stability. We also obtain a similar behaviour with the liquid-gas system in extending phase space (including (P) and (r)) and study its critical behavior with the pressure given by the cosmological constant and with a fixed black hole charge (Q). Furthermore, we study the Gibbs function and find its characteristic swallow tail behavior, which indicates the phase transition. We also find there is a special value about the mass of test particle which would lead the black hole to zero temperature and a diverging heat capacity with a fixed charge.
Using the covariant phase space formalism, we compute the conserved charges for a solution, describing an accelerating and electrically charged Reissner-Nordstrom black hole. The metric is regular provided that the acceleration is driven by an external electric field, in spite of the usual string of the standard C-metric. The Smarr formula and the first law of black hole thermodynamics are fulfilled. The resulting mass has the same form of the Christodoulou-Ruffini mass formula. On the basis of these results, we can extrapolate the mass and thermodynamics of the rotating C-metric, which describes a Kerr-Newman-(A)dS black hole accelerated by a pulling string.
A common argument suggests that non-singular geometries may not describe black holes observed in nature since they are unstable due to a mass-inflation effect. We analyze the dynamics associated with spherically symmetric, regular black holes taking the full backreaction between the infalling matter and geometry into account. We identify the crucial features taming the growth of the mass function and a diminished curvature singularity at the Cauchy horizon and demonstrate that the regular black hole solutions proposed by Hayward and obtained from Asymptotic Safety satisfy these properties.
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