The Correction for Entropy and Quantum Ergospheres of Black Holes
|Keywords||Hawking radiation Tunneling Framework WKB Approximation Quantum Ergosphere Entropy Correction|
In2000, by holding that the Hawking radiation can be described by the vacuumfluctuation in the vicinity of the inner surface of the horizon equivalently, Parikh andWilczek proposed a tunneling framework to solve the serious problem of the informationlost in the theory of Hawking radiation. That is, when a pair of virtual particles isproduced, the negative one will move inward and merge with the black hole, while thepositive one will form a real particle after the quantum tunneling and flee to infinity, whichis just called the Hawking radiation. As dictated by the theory, if the self-gravitation or theback reaction on the geometry of the black hole is contained, the total energy conservationof the system will be enforced, where the potential barrier is set by the tunneling processof the particles. Because the background space time during the tunneling is consideredas the dynamic one when using the WKB approximation, their research arrives at theconclusions that the Hawking radiation is deviated from that of the black body, whilewhich still accords with an underlying unitary theory. Although the Parikh–Wilczektunneling framework is a semi-classical theory, it is very simple and useful, which hassolved some problems in the Hawking radiation. At present, it has been applied toresearch the following work:1) By treating the massive particles as the S wave, the theory is applied to study thetunneling process of the uncharged, charged, charged and magnetized particles. Byconstructing a new line element of the space time in Painleve′–Kerr–Newman coordi-nates system, the corrected entropy of the Kerr–Newman black hole to the first orderwas calculated using the tunneling framework in2005. The conclusions of the worksabove show that the Hawking radiation does not violate an underlying unitary theoryof the quantum mechanics. In2008, in terms of the tunneling framework and the WKBapproximation, the corrected entropy to the second order and the corresponding emis-sion spectrum of the spherically symmetrical black holes were successfully calculated.The study displays that the corrected entropy contains three components: Bekenstein–Hawking entropy, an inverse area term and a logarithmic term, which is very similar tothat obtained from the loop quantum gravity, and the information during the radiationis still conserved.2) According to the correspondence in General Relativity and the tunneling framework,the process of particles’ tunneling across the event horizon of a stationary black holecould be adopted to described the evolution of its dynamic counterparts. It is obviousthat the tunneling process happens simultaneously with the contraction of the horizon, more precisely, the contraction speed equals that of particles’ tunneling, then theshrinkage speed and the location of the local horizon of the dynamic black hole can beworked out. In2010, based on the thinking, the tunneling framework was adopted tostudy the location of the ergospheres of the Vaidya and Vaidya–Bonner black hole, andanalyze the origin of the Hawking radiation. The research shows that the ergosphere isequivalent to the potential barrier set by particles’ tunneling, and Hawking radiationcomes from the vacuum fluctuation near the apparent horizon.In view of this, the dissertation will discuss the extended application of the frameworkon two points: entropy correction of spherically symmetrical de Sitter black holes, thequantum ergospheres and the origin of the dynamic black holes’ Hawking radiation.Thedissertation involves four chapters, whose details can be expanded as follows:ⅰ) The1st chapter shows the research history of the theory on black holes firstly, andgoes into the details about the important theory of black holes physics and difcultiesin it, i.e., Hawking radiation and information loss. According to the progress ofthe relevant work recently, the work in the thesis and its significance are brieflyintroduced;ⅱ) The2nd chapter is intended to extend the framework to calculate the corrected en-tropy of the spherically symmetrical de Sitter black holes, i.e., the entropy correctionof the event horizons and the cosmological horizons. And the results will be comparedwith the general corrected form for the entropy of general black holes;ⅲ) The3rd chapter is to further study the local horizons and the quantum ergosphereof the dynamic black holes using the framework, and to discuss where the Hawkingradiation comes from. The scheme is applied to study the dynamic spherically sym-metrical black holes at first, and is modified in order to study the dynamic rotatingblack holes;ⅳ) The4th chapter ends up with the summary and outlook, and puts forward some newideas for the future work.