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Register a new userGeodesic Structure of the Schwarzschild Black Hole in Rainbow Gravity
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In this paper we study the geodesic structure of the Schwarzschild black hole in rainbow gravity analyzing the behavior of null and time-like geodesic. We find that the structure of the geodesics essentially does not change when the semi-classical effects are included. However, we can distinguish different scenarios if we take into account the effects of rainbow gravity. Depending on the type of rainbow functions under consideration, inertial and external observers see very different situations in radial and non radial motion of a test particles.
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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, 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.
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The analysis of gravitino fields in curved spacetimes is usually carried out using the Newman-Penrose formalism. In this paper we consider a more direct approach with eigenspinor-vectors on spheres, to separate out the angular parts of the fields in a Schwarzschild background. The radial equations of the corresponding gauge invariant variable obtained are shown to be the same as in the Newman-Penrose formalism. These equations are then applied to the evaluation of the quasinormal mode frequencies, as well as the absorption probabilities of the gravitino field scattering in this background.
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