Hawking Radiation of the Charged Particles via Tunneling from the (n+2)-Dimensional Topological Reissner-Nordström-de Sitter Black Hole
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- Yan, H. Int J Theor Phys (2012) 51: 2392. doi:10.1007/s10773-012-1118-6
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Extending Parikh-Wilczek’s semi-classical tunneling method, we discuss the Hawking radiation of the charged massive particles via tunneling from the cosmological horizon of (n+2)-dimensional Topological Reissner-Nordström-de Sitter black hole.The result shows that, when energy conservation and electric charge conservation are taken into account, the derived spectrum deviates from the pure thermal one, but satisfies the unitary theory, which provides a probability for the solution of the information loss paradox.
KeywordsQuantum tunnelingEnergy conservationElectric charge conservationHawking radiation
In 1974, Stephen Hawking discovered the black hole radiate thermally [1, 2]. Hawking predicted that with the process of the thermal radiation, the black hole could lose energy, shrink, and finally evaporate completely, and owing to the pure thermality of the radiation, the information carried by the matter that initially formed the black hole would be lost after the black hole had disappeared. This implied, however, a pure quantum state would evolve into a mixed one, and violate the unitarity of evolution in Quantum Mechanics. Thereby, the famous paradox of information loss was produced. A great deal of work has been done in an attempt to overcome this paradox, but without any way to solve it. Also, it was claimed that this problem could be settled in favor of conservation of information by ADS/CFT which is a conjectured duality between string theory in anti-de Sitter space and a conformal field theory on the boundary of anti-de Sitter space at infinity . But it still was not clear how information could get out of a black hole.
Hawking radiation can be attributed to the spontaneous creation of a pair of virtual particles at a point just inside of the black hole horizon. One of the particles with positive energy tunnels out to the opposite site of the horizon and materializes a real particle, while another one with negative energy remains behind the horizon and is absorbed by the black hole. Basing on the above tunneling picture, a new method utilized dynamic geometry to depict particle tunneling radiation was developed by Kraus and Wilczek and elaborated upon by Parikh and Wilczek [4–7]. In their methodology, two key points are necessary. First, energy conservation, which was often neglected in other former treatments of Hawking radiation, was taken into account. When this effect is included, Parikh regarded the potential barrier is created by the effect of the outgoing particle itself, and thereby the problem of no pre-existing barrier was overcome. Second, to remove the coordinate singularity at the black hole horizon, they introduced the Painlevé coordinate transformation. Finally, it is found that the derived spectrum deviates from the pure thermal one, but satisfies the unitary theory, which provides a probability for the solution of the information loss paradox. Later on, some attempts towards this direction have been broadly discussed in [8–27].
In this letter, we extend Parikh-Wilczek’s work to discuss the Hawking radiation of the charged and massive particle via tunneling from (n+2)-dimensional Topological Reissner- Nordström-de Sitter (TRNdS) black hole. Our result shows the derived spectrum deviates from the pure thermal one when the conservation of energy and charge are taken into account, but satisfies the unitary theory.
In the next section, we introduce the Painlevé coordinate to eliminate the coordinate singularity. Also, the geodesics of the charged massive particles is obtained. In Sect. 3, the Hawking radiation of the charged massive particles via tunneling from the cosmological horizon is discussed. In Sect. 4, some discussion and conclusion are included.