Quantum Aspects of Spacetime and Semi-Classical Tunnelings of Black Holes

• Main Authors: Yao-Chieh Hu, 胡耀傑
• Other Authors: Pisin Chen
• Format: Others
• Language: en_US
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/8e6945

碩士 === 國立臺灣大學 === 天文物理研究所 === 105 === The first part of my thesis is about a spinorial quantization of spacetime. Motivated by both concepts of R.J. Adler’s recent work on utilizing Clifford algebra as the linear line element ds = γμ dXμ, and the fermionization of the cylindrical world-sheet Polyakov action, we introduce a new type of spacetime quantization that is fully covariant. The theory is based on the reinterpretation of Adler’s linear line element as ds = γμ λγμ , where λ is the characteristic length of the theory. We name this new operator as "spacetime interval operator", and argue that it can be regarded as a natural extension to the one-forms in the U(su(2)) non-commutative geometry. By treating Fourier momentum as the particle momentum, the generalized uncertainty principle of the U(su(2)) non-commutative geometry, as an approximation to the generalized uncertainty principle of our theory, is derived, and is shown to have a lowest order correction term of the order p2 similar to that of Snyder’s. The holography nature of the theory is demonstrated, and the predicted fuzziness of the geodesic is shown to be much smaller than conceivable astrophysical bounds. The second part of my thesis is about semiclassical solution in black hole physics. For O(4)-symmetric instantons, there are two complementary interpretations for their analytic continuations. One is the nothing-to-something interpretation, where the initial and the final hypersurfaces are disconnected by Euclidean manifolds. The other is the something-to-something interpretation, introduced by Brown and Weinberg, where the initial and the final hypersurfaces are connected by the Euclidean manifold. These interpretations have their own pros and cons and hence these are complementary. In this paper, we consider analytic continuations of thin-shell instantons that have less symmetry, i.e., the spherical symmetry. When we consider the Farhi-Guth-Guven/Fischler-Morgan-Polchinski tunneling, the something- to-something interpretation has been used in the usual literature. On the other hand, we can apply the nothing-to-something interpretation with some limited conditions. We argue that even for both interpretations, we can give the consistent decay rate. As we apply and interpret following the nothing-to-something interpretation, a stationary black hole can emit an expanding shell that results a spacetime without a singularity nor an event horizon. The third part of my these is about asymptotic electromagnetic field behaviors on null infinities, which is based on my studies at Stockholm University and NORDITA in Sweden.