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Register a new userThermodynamical Analysis of a Black Hole with a Global Monopole Within a Class of a f(R) Gravity
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Cristine Nunes Ferreira crisnfer
Publication date
2015
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English
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We analyze the thermodynamics of a black hole in a region that contains a global monopole in the framework of a particular class of a f(R) gravity. Specifically, we study the case in which df(R)/dR = F(R) is a power law function of the radial coordinate of the monopole spacetime, i.e., F(r) = 1 + psi_n r^n, where psi_n is the fine-tuned parameter corresponding to the f(R) gravity. We obtain explicit expressions for the local thermodynamic quantities of the black hole as a function of the event horizon, the parameter describing the monopole and the measurable corrections due to the f(R) theory modifications of the General Relativity. We also discussed the implications of the particular case of n=2, where the parameter psi_2 can be related to a positive cosmological constant, that in monopole presence is characterized by a non-trivial topology observed as a deficit solid angle.
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The fragmentation of black hole containing $f(R)$ global monopole under GUP is studied. We focus on that the black hole breaks into two parts. We derive the entropies of the initial black hole and the broken parts while the generalization of Heisenbergs uncertainty principle is introduced. We find that the $f(R)$ global monopole black hole keeps stable instead of breaking because the entropy difference is negative without the generalization. The fragmentation of the black hole will happen if the black hole entropies are limited by the GUP and the considerable deviation from the general relativity leads the case that the mass of one fragmented black hole is extremely small and the other one is extremely large.
The Parikh-Kraus-Wilczeck tunneling radiation of black hole involving a $f(R)$ global monopole is considered based on the generalized uncertainty principle. The influences from global monopole, $f(R)$ gravity and the corrections to the uncertainty appear in the expression of black hole entropy difference. It is found that the global monopole and the revision of general relativity both hinder the black hole from emitting the photons. The two parts as corrections to the uncertainty make the entropy difference of this kind of black hole larger or smaller respectively.
We consider the evolution of black hole involving an $f(R)$ global monopole based on the Extended Uncertainty Principle (EUP). The black hole evolutions refer to the instability due to the Parikh-Kraus-Wilczeck tunneling radiation or fragmentation. It is found that the EUP corrections make the entropy difference larger to encourage the black hole to radiate more greatly. We also show that the appearance of the EUP effects result in the black holes division. The influence from global monopole and the revision of general relativity can also adjust the black hole evolution simultaneously, but can not change the final result that the black hole will not be stable because of the EUPs effects.
Hawking flux from the Schwarzschild black hole with a global monopole is obtained by using Robinson and Wilczeks method. Adopting a dimension reduction technique, the effective quantum field in the (3+1)--dimensional global monopole background can be described by an infinite collection of the (1+1)--dimensional massless fields if neglecting the ingoing modes near the horizon, where the gravitational anomaly can be cancelled by the (1+1)--dimensional black body radiation at the Hawking temperature.
We extend the work by S. Iso, H. Umetsu and F. Wilczek [Phys. Rev. Lett. 96 (2006) 151302] to derive the Hawking flux via gauge and gravitational anomalies of a most general two-dimensional non-extremal black hole space-time with the determinant of its diagonal metric differing from the unity ($sqrt{-g} eq 1$) and use it to investigate Hawking radiation from the Reissner-Nordstrom black hole with a global monopole by requiring the cancellation of anomalies at the horizon. It is shown that the compensating energy momentum and gauge fluxes required to cancel gravitational and gauge anomalies at the horizon are precisely equivalent to the $(1+1)$-dimensional thermal fluxes associated with Hawking radiation emanating from the horizon at the Hawking temperature. These fluxes are universally determined by the value of anomalies at the horizon.
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