Higher Dimensional Black Hole Corrected Tunneling Radiation

high Dimensional Black Hole Corrected Tunneling RadiationCorrected tunneling ray of a higher dimensional erosive localisation and generalise due south lawS. S. Mortazavi*1, A. Farm some(prenominal)1, H. Noorizadeh2, V. Fayaz1, H. Hosseinkhani1AbstractStudy the quantum gravitational make on a higher dimensional horizon, the semi neoclassic s-wave tunneling beam of light of unappeasable gobs are calculated. It is shown that quantum gravitational upshots correct the semiclassical radiotherapy of the horizon length duration. Within this background, the generalized succor law of thermodynamics is utilize to the bleak hole haphazardness.1. IntroductionIt is interesting that that radiation of coloured holes send packing be viewed as simple tunneling phenomena. In this view, a particle-antiparticle pair may form close to a erosive hole event horizon. The ingoing mode is trapped inside the horizon while the outperform mode can tunnel through the event horizon. It is inte resting that this effect is a quantum mechanic eachy and the present of an event horizon is essential (Hawking, 1975). Recently, the semiclassical digest of this phenomenon carried out by Parikh and Wilczek (Parikh, Wilczek, 2000 Parikh, 2002 Parikh, 2004 Parikh, 2004). Parikh-Wilczek proposal of shocking hole tunneling radiation is base on the computation of incoming part of action for classically interdict 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 comparison mingled with Hawking original calculation and tunneling method acting, it is easy to see that the hawking method is a direct method but its complication to generalization to all other space times is failed while the Parikh-Wilczeck proposal, the tunneling approaches have been successfully appli ed to a wide range of both the black hole space time horizon and cosmological horizon. For example, 3- dimensional BTZ black holes (Agheben, Nadalini, Vanzo, Zerbini, 2005 Wu, Jiang, 2006), Vaidya space time(Ren, Zhang, Zhao, 2006), energising 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 line of reasoning 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, 2002 Medved, 2002 Sekiwa, 2008). The black hole tunneling method was studied in distinguishable space-times and different frames and the time contribution to the black hole radiation is authentic 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 parsimony matrix technique (Banerjee, Majhi, 2009). However the Parikh-Wilczek method is based on the classical outline, when it comes into the high-energy regime, for example a small black hole whose size of it can be compared with Planck collection plate, the effect of quantum graveness 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 tunnel ing mechanism it is interesting to bushel the analysis under a minimal length quantum 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 uncertainty precept. It is shown that the generalized second law of thermodynamics applie a specify on the tunneling radiation.2. The corrected Bekenstein-Hawking entropyA d-dimensional spherical symmetric black hole background is defined by (1)where . The uncertainty in the come out 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 mass. Temperature of black hole in a d-dimension space time may be obtained by place the radiated particle mass m to. The d-dimensional black hole temperature may b e obtained as, (4)where d3. Eqs. (4) shows the temperature of a d-dimensional 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 bla ck hole radiationAs shown by Parick and Wilczek (2000) the WKB approximation 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/ scope relation.Consider the above relation, eq.(13) can be written in the pastime general form, (16)The quantum gravity-corrected black hole entropy is given by eq.(12), so, (17)subbing (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 uni versal in the sense that it is supposed 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 limited self-gravity. Counterexamples can be easily found in systems undergoing gravitational collapse (Bousso, 1999). another(prenominal) 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 mien 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 blac k hole tunneling radiation is calculated by the Parikh-Wilczek tunneling 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. 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