Higher Dimensional Black Hole Corrected Tunneling Radiation

Higher Dimensional Black Hole Corrected Tunneling RadiationCorrected tunneling radiation therapy of a higher(prenominal) dimensional dingy holler and reason out assist lawS. S. Mortazavi*1, A. Farmany1, H. Noorizadeh2, V. Fayaz1, H. Hosseinkhani1AbstractStudy the quantum gravitational effects on a higher dimensional horizon, the semi authorized s-wave tunneling radiation of black localizations are calculated. It is shown that quantum gravitational effects correct the semiclassical radiation of the horizon space quantify. Within this ground, the generalized second law of thermodynamics is use to the black mountain siemens.1. IntroductionIt is interesting that that radiation of black smothers can be viewed as simple tunneling phenomena. In this view, a particle-antiparticle pair may melodic phrase close to a black hole event horizon. The ingoing mode is trapped inside the horizon while the outgoing mode can tunnel finished the event horizon. It is interesting that this ef fect is a quantum mechanic eachy and the present of an event horizon is essential (Hawking, 1975). Recently, the semiclassical analysis of this phenomenon carried out by Parikh and Wilczek (Parikh, Wilczek, 2000 Parikh, 2002 Parikh, 2004 Parikh, 2004). Parikh-Wilczek proposal of black hole tunneling radiation is base on the computation of incoming part of action for classically forbidden of s-wave emission across the horizon (Parikh, Wilczek, 2000 Parikh, 2002 Parikh, 2004 Parikh, 2004 Kraus, Wilczek, 1994 Kraus, Wilczek, 1995 Kraus, Wilczek, 1995 Kraus, Keski-Vakkuri, 1997 Berezin, Boyarsky, Neronov, 1999 Volovik, 19991999 Calogeracos, Volovik,1999). As a relation between Hawking original calculation and tunneling method, it is easy to see that the hawking method is a direct method but its complication to generalization to all other space magazines is failed while the Parikh-Wilczeck proposal, the tunneling approaches have been successfully applied to a wide range of both the bla ck hole space time horizon and cosmogenic horizon. For example, 3- dimensional BTZ black holes (Agheben, Nadalini, Vanzo, Zerbini, 2005 Wu, Jiang, 2006), Vaidya space time(Ren, Zhang, Zhao, 2006), dynamical black holes(Di Criscienzo, Nadalini, Vanzo, Zerbini, Zoccatelli, 2007), black rings(Zhao, 2006), Kerr and Kerr-Newman black holes(Jiang, Wu, Cai, 2006 Zhang, Zhao, 2006 Hu, Zhang, Zhao, 2006 Kerner, Mann, 2006), Taub-NUT space time(Kerner, Mann, 2006), Gdel space time (Kerner, Mann, 2007), dynamical horizons(Di Criscienzo, Nadalini, Vanzo, Zerbini, Zoccatelli, 2007), cosmological horizons(Parikh, 2002 Medved,2002 Sekiwa, 2008), Rindler space time (Medved, 2002), de Sitter space time. Of course in all of these approaches the Unruh temperature is recovered successfully (Unruh, 1976 Akhmedova, Pilling, Gill, Singleton, 2008 Banerjee, Kulkarni, 2008 Banerjee, Majhi, 2008).This model is applied to not only the black hole event horizon, but also to the cosmological horizon (Parikh, 20 02 Medved, 2002 Sekiwa, 2008). The black hole tunneling method was studied in different space-times and different frames and the time contribution to the black hole radiation is developed in (Chowdhury, 2008 Akhmedov, Akhmedova, Pilling, Singleton, 2007 Zhang, Cai, Zhan, 2009 Banerjee, Majhi, 2009 Akhmedov, et al, 2006 Akhmedov, Pilling, Singleton, 2008). In continue, the spectrum form of the tunneling mechanism is analyzed using the density matrix technique (Banerjee, Majhi, 2009). However the Parikh-Wilczek method is based on the classical analysis, when it comes into the high-energy regime, for example a small black hole whose size can be compared with Planck scale, the effect of quantum gravity should not be forbidden. In this case, the conventional semiclassical approaches are not proper and the complete quantum gravity analysis is required. To study the quantum gravitational effects on the tunneling mechanism it is interesting to cite the analysis under a minimal length quant um gravity scale ( Adler, Chen, Santiago, 2001 Han, Li, Ling, 2008 Farmany, et al, 2008 Shu, Shen, 2008 Wang, Gui, Ma, 2008 Setare, 2004 Kim, Park, 2007 Nouicer, 2007 Zhao, Zhang, 2006 Xiang, 2006 Dehghani, Farmany, 2009). In this paper, the black hole tunneling radiation is studied based on the generalized suspicion principle. It is shown that the generalized second law of thermodynamics applie a bound on the tunneling radiation.2. The corrected Bekenstein-Hawking selective informationA d-dimensional spherical symmetric black hole background is defined by (1)where . The uncertainty in the position of a particle, during the emission, (2)where applying the uncertainty principle, we obtain the energy of radiated particle, (3)Where and Mpl is Planck mount. Temperature of black hole in a d-dimension space time may be obtained by setting the radiated particle mass m to. The d-dimensional black hole temperature may be obtained as, (4)where d3. Eqs. (4) shows the temperature of a d-dim ensional black hole with . The Bekenstein-Hawking entropy is usually derived from the Hawking temperature. The entropy S may be found from the well known thermodynamics relation, (5)From (3-5) we obtain, (6)Quantum gravitational effects of horizon may affect on the thermodynamics of black hole and modifies its usual thermodynamical behavior. Study of black hole thermodynamics in the quantum gravity theory was made using a generalized uncertainty principle (Adler, 1999 Hossenfelder et al, 2004 Maggiore, 1994 Kempf, Managano, 1997 Farmany, Abbasi, Naghipour, 2007) (7)Where lpl is the Planck length. Setting 2rh as , we obtain, (8)Solving for minimum and expanding around lpl2=0, eq. (8) reads, (9)Comparing (9) with (7) we obtain, (10)inserting (4) into (10), the d-dimensional black hole temperature me be obtained, (11)The corrected entropy S may be obtained from the thermodynamics relation (5), (12)3. The corrected black hole radiationAs shown by Parick and Wilczek (2000) the WKB approx imation relate the tunneling probability to the imaginary part of the action (13)Where I is the classical action of trajectory. The difference between all approaches of tunneling method is in how the action is calculated. As shown by Arzano et al (Arzano, Medved, Vagenas, 2005), (14)in terms of black hole mass M and energy E, which is correspond to (15)provided the Bekenstein-Hawking entropy/area relation.Consider the above relation, eq.(13) can be written in the following general form, (16)The quantum gravity-corrected black hole entropy is given by eq.(12), so, (17)Substituting (17) into (16) we obtain, (18)which shows the corrected tunneling probability and.4. Generalized second law of thermodynamics and modified black hole tunneling radiationBekenstein (1981) has conjectured that the entropy S and energy E of any thermodynamic system must obey, (19)where R is defined as the circumferential radius. This bound is universal in the sense that it is divinatory to hold in any matter system. The Bekenstein bound has been confirmed in wide classes of systems. However, as pointed by Bekenstein, the bound is valid for systems with finite size and express mail self-gravity. Counterexamples can be easily found in systems undergoing gravitational collapse (Bousso, 1999). Another entropy bound is related to the holographic principle, which says that the entropy in a spherical volume satisfies (20)where A is the area of the system. It was shown that this bound is violated for sufficiently large volumes (Fischler and Susskind, 1998). As shown by eqs.(19-20), there is a bound on the entropy of the black hole when it related to the black hole area. While the black hole entropy bound applied to eq. (7), we obtain, (21)So, in the presence of entropy bound, eq. (16) may be, (22)Combining eq.(22) and (18) we obtain the corrected tunneling probability of black hole radiation. (23)ConclusionThe semiclassical black hole tunneling radiation is calculated by the Parikh-Wilczek tun neling proposal of black hole radiation based on the generalized uncertainty principle. It is shown that the Bekenstein-Hawking entropy of black holes receives a correction that affects on the radiation tunneling probability. In continue applying the generalized second law of thermodynamics to the modified black hole tunneling radiation is obtained.ReferencesAgheben, M., M. Nadalini, L. Vanzo, S. Zerbini, JHEP 0505 (2005) 014,Akhmedova, V., T. Pilling, A. de Gill, D. Singleton, arXiv0808.3413hep-thAkhmedov, E. T., V. Akhmedova, T. Pilling, D. Singleton, Int. J. Mod.Phys. A 221705- 1715, 2007Akhmedov, E. T., V. Akhmedova, D. Singleton, Phys. Lett. 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