Topics in General Relativity Theory: Gravitational - Measurements of Black-Hole Parameters; Gravitational Collapse of a Cylindrical Body; and Classical-Particle Evolution in the Presence of Closed, Timelike Curves
In this thesis I study three different topics in General Relativity. The first study investigates the accuracy with which the mass and angular momentum of a black hole can be determined by measurements of gravitational waves from the hole, using a gravitational-wave detector. The black hole is assumed to have been strongly perturbed and the detector measures the waves produced by its resulting vibration and ring-down. The uncertainties in the measured parameters arise from the noise present in the detector. It is found that the faster the hole rotates, the more accurate the measurements will be, with the uncertainty in the angular momentum decreasing rapidly with increasing rotation speed. The second study is an analysis of the gravitational collapse of an infinitely long, cylindrical dust shell, an idealization of more realistic, finite-length bodies. It is found that the collapse evolves into a naked singularity in finite time. Analytical expressions for the variables describing the collapse are found at late times, near the singularity. The collapse is also followed, with a numerical simulation, from the start until very close to the singularity. The singularity is found to be strong, in the sense that an observer riding on the shell will be infinitely stretched in one direction and infinitely compressed in another. The gravitational waves emitted from the collapse are also analyzed. The last study focuses on the consequences of the existence of closed timelike curves in a wormhole spacetime. One might expect that such curves might cause a system with apparently well-posed initial conditions to have no self -consistent evolution. We study the case of a classical particle with a hard-sphere potential, focusing attention on initial conditions for which the evolution, if followed naively, is self-inconsistent: the ball travels to the past through the wormhole colliding with its younger self, preventing itself from entering the wormhole. We find, surprisingly, that for all such "dangerous" initial conditions, there are an infinite number of self-consistent solutions. We also find that for many non-dangerous initial conditions, there also exist an infinity of possible evolutions.
- Pub Date:
- January 1993
- Physics: Astronomy and Astrophysics