Statistics – Computation
Scientific paper
Jan 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phdt........61k&link_type=abstract
Thesis (PH.D.)--MASSACHUSETTS INSTITUTE OF TECHNOLOGY, 1995.Source: Dissertation Abstracts International, Volume: 56-06, Secti
Statistics
Computation
Hawking Radiation, Quantum Field Theory, Black Hole
Scientific paper
This thesis focuses in understanding various concepts and aspects related to the black hole information puzzle and in developing new way's to test the validity of the assumptions that are behind Hawking's original proposal. We start in chapter 2 with a brief discussion of particle production and entropy generation in scalar quantum field theory in expanding spacetimes with many-particle initial states. In chapter 3, we study the Hawking radiation for the geometry of an evaporating 1 + 1 dimensional black hole. We compute Bogoliubov coefficients and the stress tensor. We calculate the entropy of entanglement produced in the evaporation process, both for a 1 + 1 dimensional and 3 + 1 dimensional black hole. We present a straightforward computation through the density matrix of Hawking radiation. On the other hand, we use a recent result of Srednicki to estimate the entropy. It is found that the one space dimensional result of Srednicki is the pertinent one to use, in both the 1 + 1 and the 3 + 1 dimensional cases. In chapters 4 and 5, we investigate the validity of the semiclassical approximation in the black hole evaporation. First, we consider the definition of matter states on spacelike hypersurfaces. We take into account the quantum fluctuations in the black hole background spacetime and study their effect on the time evolution of matter states. We show that on any hypersurface that captures both infalling matter near the horizon and Hawking radiation, quantum fluctuations in the background become important. This suggests that we cannot describe the matter state by a semiclassical evolution up to this stage. We estimate that the correlations between the matter and gravity are so strong that a fluctuation of order exp( -/M/M_{rm Planck}) in the mass of the black hole produces a macroscopic change in the matter state. In chapter 5 we discuss how the existence of classical turning points can affect the validity of the semiclassical approximation. We show how turning points can appear in the evolution of a two dimensional black hole. We argue that turning points can create more complicated phase correlations than what can be seen in the leading order semiclassical approximation without back reaction. We demonstrate this in the context of simple quantum mechanical models. However, we show that the effect is not present in a simple minisuperspace model of quantum matter in a closed universe. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617 -253-5668; Fax 617-253-1690.).
No associations
LandOfFree
Topics in Semiclassical and Quantum Gravity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Topics in Semiclassical and Quantum Gravity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Topics in Semiclassical and Quantum Gravity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-837839