Quantum Tunnelling And Anomaly, And Hawking Radiation From Black Holes

Hawking radiation of black hole is an important discovery in Theoretical Physics,which is an output of the combination among General Relativity,Quantum Mechanics and Thermodynamic. After studying over 30 years,people no longer doubt its theoretical rightness,but its experimental test has not been presented till now.Fortunately,if the energy level of quantum gravity is Tev, the Large Hadron Collider in CERN will produce a mini black hole per second.This mini black hole evaporates almost at the same time when it appears,and its existence can only be observed by Hawking radiation from the final black hole explosion.This opinion provides a new possibility to detect Hawking radiation of black hole,thus it has been once again becoming the hot research topic in theoretical physics.Since Stephen Hawking discovered black hole is not completely black and can evaporate different particles from its horizon in 1974,many physicists have developed different methods to discuss Hawking radiation of black hole.But most of them supposed the spacetime background is fixed,and did not consider the reaction of Hawking radiation.In this approximation,the emission spectrum is purely thermal,which results in the loss of the information and the breakdown of the unitary theory.To correctly describe quantum effect of black hole,we must take the spacetime background as a dynamic variable.Taking into account the emitted particles' self-interaction, Frank Wilczek,who is awarded the 2004 Nobel Prize in Physics,and Per Kraus first treated Hawking radiation as a semi-classical quantum tunneling effect,and produced a modified radiation spectrum.Then,Based on this opinion,Frank Wilczek and Maulik K.Parikh developed Kraus-Wilczek quantum tunneling method,and presented a semi-classical but definite calculation to recover the information conservation and the unitary theory.Hereafter,applying the quantum anomaly technique in Quantum Field Theory,Frank Wilczek and Sean P.Robinson once again studied Hawking radiation of black hole through investigating the quantum anomaly in chiral theory.The main task of this dissertation is to develop and improve quantum tunneling and anomaly method to make each of their own become a more complete theoretical system.This dissertation sums up author's doctoral research in four areas.The first one is to reinvestigate Kraus-Wilczek quantum tunneling method,and derive the correct Hawking radiation spectrum.The second one is to develop and improve Parikh-Wilczek quantum tunneling approach.The third one is to develop complex path integral method to study fermion tunneling effect.The last one is to develop the Iso-Umetsu-Wilczek quantum anomaly model.This dissertation is divided into seven chapters,and its specific details can be listed as followsThe chapterⅠbriefly introduces Hawking radiation mechanism of quantum tunneling and anomaly method,and its historical development.The chapterⅡgives a general frame about the theoretical knowledge of quantum tunneling and anomaly method,specifically including Kraus-Wilczek quantum tunneling method,Parikh-Wilczek quantum tunneling method and complex path integral method(that is the theoretical basis of fermion tunneling mode) as well as quantum anomaly method.The chapterⅢto the chapterⅥsummarize the author's work during the three-year studies for PhD:·Considering the emitted particle's self-gravitational interaction,the original work of F. Wilczek and P.Kraus[32]first carried on a modification for Hawking radiation spectrum of black hole.Taking an arbitrarily spherically symmetric black hole as an example,the chapterⅢchecks Kraus-Wilczek quantum tunneling mode,and points out that the literature [32]only presents an approximate amendment to Hawking radiation spectrum.When considering the emitted particle's self-interaction,the true emission spectrum is not only deviated from the purely thermal one,but also related to the change of Bekensten-Hawking entropy before and after the particle emission,and satisfies the unitary theory.ChapterⅣaims to develop and improve Parikh-Wilczek quantum tunneling method:·E.C.Vagenas applied Parikh-Wilczek quantum tunneling method to study Hawking radiation of the(2+1)-dimensional rotating BTZ black hole,and pointed out the self-interaction would modify Bekenstein-Hawking entropy[48].Considering the emitted particle's self-interaction, Sec.4.1 reexamines the quantum tunneling effect of the(2+1)-dimensional rotating BTZ black hole.The result shows that the self-interaction will not modify Bekenstein-Hawking entropy,and the error in the literature[48]is due to omit the angular momentum conservation when applying the semi-classical quantum tunneling method to discuss Hawking radiation of the(2+1)-dimensional rotating BTZ black hole.·Parikh-Wilczek quantum tunneling mode introduced the coordinate transformation proposed first by P.Painlev(?) in 1921 to eliminate the coordinate singularity of the black hole horizon,and provided a superior tunneling environment for the emitted particle.Later, Zhang and Zhao developed the Painlev(?) coordinate transformation to the case of general stationary black holes.In Sec.4.2,we introduce a new Painlev(?)-like coordinate transformation to eliminate the coordinate singularity of the black hole horizon,and apply Parikh- Wilczek quantum tunneling method to study Hawking radiation from the stationary Kerr and Kerr-Newman black holes when considering the energy conservation,the angular momentum conservation and the charge conservation.·The basic idea of Parikh-Wilczek quantum tunneling model is to consider the energy conservation during the particle tunneling from the black hole horizon.It demands to learn the spacetime ADM energy and the quantum tunneling behavior at the horizon first.In Sec.4.3,when considering the emitted particle's self-interaction,we apply Parikh-Wilczek quantum tunneling method to study Hawking radiation from the event and cosmological horizon of Reissner-Nordstr(o|¨)m-de Sitter black hole with a global monopole.The black hole in de Sitter space with topological defect has special characters:its total ADM energy and charge is no longer taken the same form as the mass and charge of black hole,and differed by a constant factor(1-8πη~2).At the same time,the different points of the future light-cone at the event and cosmological horizon will result in the different quantum tunneling behavior.·Finally,to further verify the universality of Parikh-Wilczek quantum tunneling method, considering the emitted particle's self-interaction we successfully apply quantum tunneling approach to study Hawking radiation from the higher dimensional black hole.ChapterⅤis intended to promote and develop fermion quantum tunneling method:·Fermion tunneling mode proposed by R.Kerner and R.B.Mann is based on complex path integral method,whose key technique is to choose an appropriateγmatrix to describe the particle's motion in the spacetime.To extend fermion tunneling method,we choose an appropriateγmatrix for a class of stationary axisymmetric black holes in the dragging coordinate system,and study charged fermions quantum tunneling effect,specifically including charged fermions tunneling from the stationary Kaluza-Klein black hole and the event and cosmological horizon of Kerr-Newman-de Sitter black hole.·Then,choosing an appropriateγmatrix for the five-dimensional black ring,Sec.5.2 applies fermions tunneling model to study fermions tunneling from the horizons of the charged and uncharged black rings.·Finally,to further verify the reliability of the five-dimensional tunneling mode,an an example, Sec.5.3 studies fermions tunneling effect of the non-extremal DI-D5 black hole.ChapterⅥis to further develop and improve quantum anomaly method: ·Basing on Robinson-Wilczek quantum anomaly method,S.Iso,H.Umetsu and F.Wilczek studied Hawking radiation from the charged black hole by considering gauge and gravitational anomaly at the horizon.In Sec.6.1,we develop Iso-Umetsu-Wilczek quantum anomaly model to study Hawking radiation from the rotating Kerr and Kerr-Newman black holes in Anti-de Sitter space.This spacetime have an axial symmetry,and its two-dimensional effective theory after a dimensional reduction technique takes a U(1)gauge symmetry,whose gauge charge is angular quantum number.This character is similar to that of two-dimensional effective theory for the spherically symmetric charged black hole, then we can apply quantum anomaly method proposed by S.Iso,H.Umetsu and F.Wilczek to correctly reproduce Hawking radiation of the rotating black hole.·When omitting the classically irrelevant ingoing modes at the horizon,the two-dimensional effective theory for the rotating black hole has U(1)gauge and gravitational anomalies. In the dragging coordinate system,however,the rotation freedom for the rotating black hole is eliminated due to the nonexistence of the frame dragging effect for the matter field.Then the reduced two-dimensional effective theory does not take gauge symmetry for the original rotation symmetry,so the effective chiral theory has no gauge anomaly. Considering gravitational anomaly at the horizon,Sec.6.2 studies Hawking radiation from the(2+1)-dimensional rotating BTZ black hole in the dragging coordinate system.·The dilatonic black holes obtained from the low-energy effective field theory have qualitatively different properties from those in the ordinary Einstein gravity.To verify the universality of quantum anomaly method,taking a class of Dilaton black hole(specifically including the spherically symmetric dilatonic black hole with arbitrary coupling constant, and the rotating Kaluza-Klein black hole as well as the rotating Kerr-Sen black hole)as an example,Sec.6.3 applies quantum anomaly method to study their quantum emission effect.·The effective quantum field theory in the original reference proposed by S.Iso,H.Umetsu and F.Wilczek is formulated outside the black hole horizon.Gauge and gravitational anomalies arise from the fact that the classically irrelevant ingoing mode has been integrated out.For de Sitter black hole,although the black hole horizon and the cosmological horizon share many similar properties,their radiation behavior behaves differently,so the effective field theory should formulate between the EH and the CH.gauge and gravitational anomalies arise from integrating out the classically irrelevant ingoing modes at the EH and the classically irrelevant outgoing modes at the CH.Sec.6.4 develops quantum anomaly method to successfully study Hawking radiation from the CH of the higher dimensional Schwarzschild-de Sitter black hole and the higher dimensional Kerr-de Sitter black hole.ChapterⅡends up with summary and outlook,and puts forward some ideas of our future work.