| Summary: | 博士 === 國立成功大學 === 物理學系 === 104 === In this work, exact solutions of General Relativity and its
generalization to theories without space-time four-covariance are investigated. The first class of solutions studied are Painleve-Gullstrand(PG) type solutions. These maintain Lorentzian signature (-,+,+,+) globally and possess no coordinate singularities at the horizon(s). For non-rotating black holes, generalized PG metrics with adjustable functions were established previously by Lin and Soo. The local Lorentz transformation between the PG solution and the corresponding metric in standard form is an infinite Lorentz boost at the horizon(s). Inserting suitable adjustable functions in the local Lorentz
transformation allow us to construct physical generalized PG
solutions which are completely free of coordinate singularities and remain real everywhere. The generalized PG solutions constructed include the complete Newman-Penrose family of charged rotating black holes in the presence of non-trivial cosmological constant. For
non-rotating black holes, our PG solutions possess constant
curvature slicings. We compare with well known solutions, some of which become complex when certain extreme ranges of the parameters are encountered. These problems are absent in our PG solutions which are also optimal in that only one extra function for each solution is introduced to cure the problem.
Intrinsic time geometrodynamics (ITG) was advocated in a series of work by Soo and co-authors. In the quantum context, the theory is described by a Schrodinger equation with a non-trivial physical Hamiltonian; and Einstein's GR is a special case of a wider class of theories described by (ITG). In this scheme without paradigm of space-time four-covariance, higher order spatial curvatures, including Ricci and Cotton-York terms are permitted, and are
introduced to improve the ultra-violet convergence. Constant
three-curvature solutions of Einstein's theory have the advantage of being also exact solutions of ITG. These include the Schwarzschild-de Sitter solution in PG form. Among other things, as well as the construction of new solutions, we explicitly demonstrate that the Schwarzschild-de Sitter PG form passes all the observational tests of GR, such as perihelion shift and the bending of light, whereas other known solutions of Horava gravity theories depart starkly from the predictions of Einstein's theory.
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