Potential Reconstruction, Gravitational Collapse, and Time Evolution of Thermodynamic Quantities
Halstead, Evan Mark
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This thesis consists of three parts. In Part I, we consider the appearance of a second vacuum—using higher dimensional non-renormalizable operators—in the Standard Model Higgs Potential which may modify the physics of electroweak symmetry breaking without affecting electroweak precision tests. For a certain range of parameters, the usual second order electroweak phase transition is followed by a first order phase transition. This subsequent phase transition may even drive the late time accelerated expansion of the universe, though the usual fine tuning of the value of the vacuum energy density is required. The advantage is that such a potential contains kink-like solutions which in turn can play a crucial role in reconstructing the global shape of the potential in colliders, as is explicitly demonstrated. In Parts II and III, we investigate the influence of topology and the existence of a cosmological constant on the time-dependent behavior of gravitational collapse. Specifically, the metrics that we will focus on are Schwarzschild, de Sitter Schwarzschild, and (3+1) BTZ (representing a cylinder). In Part II, we look at the equation of motion of the gravitational collapse, both from an asymptotic observer's point of view and from an infalling observer's point of view. Then, in Part III we analyze the time evolution of the temperature and entropy of a gravitationally collapsing domain wall, as seen by an asymptotic observer. We do this by coupling a scalar field to the background of the domain wall, then evaluating the occupation number of the scalar field as a function of frequency. The resulting distribution is very close to a Planck distribution, so we can determine the temperature and therefore the entropy. Since the collapsing domain wall is what forms a black hole, we can compare the results to those of the standard Hawking temperature and entropy. We find that the temperature and entropy do in fact approach constants that are very close to the expected results. We find that while the equations of motion are qualitatively the same for all three metrics, there are differences in how the temperature and entropy evolve in each case.