Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, and Woods Hole Oceanographic Institution, 1990. / Vita. / Includes bibliographical references. Includes bibliographical references. / by Mark A. McCaffrey. / Ph.D.

The production of axisymmetric initial data for distorted black holes at a moment of time symmetry is considered within the (3+1) context of general relativity. The initial data is made to contain a distorted marginally trapped surface ensuring that, modulo cosmic censorship, the spacetime will contain a black hole. The resulting equations on the complicated domain are solved using the piecewise linear finite element method which adapts to the curved surface of the marginally trapped surface. The initial data is then analyzed to calculate the mass of the space time as well as an upper bound on the fraction of the total energy available for radiation. The families of initial data considered contain no more than few percent of the total energy available for radiation even in cases of extreme distortion. It is shown that the mass of certain initial data slices depend to first order on the area of the marginally trapped surface and the gaussian curvature of prominent features.

Methods are described that implement a branch-and-price decomposition approach to solve the maximum weight independent set (MWIS) problem. The approach is first described by Warrier et. al, and herein our contributions to this research are presented. The decomposition calls for the exact solution of the MWIS problem on induced subgraphs of the original graph. The focus of our contribution is the use of chordal graphs as the induced subgraphs in this solution framework. Three combinatorial branch-and-bound solvers for the MWIS problem are described. All use weighted clique covers to generate upper bounds, and all branch according to the method of Balas and Yu. One extends and speeds up the method of Babel. A second one modifies a method of Balas and Xue to produce clique covers that share structural similarities with those produced by Babel. Each of these improves on its predecessor. A third solver is a hybrid of the other two. It yields the best known results on some graphs. The related matter of deciding the imperfection or perfection of a graph is also addressed. With the advent of the Strong Perfect Graph Theorem, this problem is reduced to the detection of odd holes and anti-holes or the proof of their absence. Techniques are provided that, for a given graph, find subgraphs in polynomial time that contain odd holes whenever they are present in the given graph. These techniques and some basic structural results on such subgraphs narrow the search for odd holes. Results are reported for the performance of the three new solvers for the MWIS problem that demonstrate that the third, hybrid solver outperforms its clique-cover-based ancestors and, in some cases, the best current open-source solver. The techniques for narrowing the search for odd holes are shown to provide a polynomial-time reduction in the size of the input required to decide the perfection or imperfection of a graph.

In this dissertation, we systematically construct non-extremal charged rotating anti-de Sitter black hole solutions in four, five and seven dimensions. In four dimensions, we first obtain the rotating Kerr-Taub-NUT metric with four independent charges, as solutions of N = 2 supergravity coupled to three abelian vector multiplets by the solution generating technique. Then we generalise the four-dimensional rotating solutions to the solutions of gauged N = 4 supergravity with charges set pairwise equal. In five dimensions, the most general charged rotating black hole solution has three charge and two rotation parameters. We obtain several special cases of the general solution. To be specific, we obtain the first example of a non-extremal rotating black hole solution with two independent rotation parameters, which has two charge parameters set equal and the third vanishing. In another example, we obtain the nonextremal charged rotating black hole solution with three charge parameters set equal and non-equal rotation parameters. We are also able to construct the single-charge solution with two independent rotation parameters. In seven dimensions, we obtain the solution for non-extremal charged rotating black holes in gauged supergravity, in the case where the three rotation parameters are set equal. There are two independent charges, corresponding to gauge fields in the U(1) × U(1) abelian subgroup of the SO(5) gauge group.

This report looks closer on the physics of black holes and their related phenomena. Particularly, this report studies a certain black hole called Gargantua that is portrayed in the movie Interstellar. By using this as a source of inspiration we look at Gargantua’s effect on time, planetary orbits and tidalforces. The following report showed that the physics studied here corresponded fully to the physics represented in Interstellar, making the movie very credible from a physics point of view. I show that the black hole portrayed in Interstellar needed to spin at a rate of 1.33*10^-14 percent less than its maximum possible to achieve a timedilation of 61320 at the distance where stable planetary orbits are found. At a spin this high, planets can have stable orbits as close as half the Schwarzschild radius which means they are located just outside the event horizon of a maximally rotating black hole. The enormous timedilation at planets orbiting near the event horizon is a result of the planets close proximity to the black hole, its orbital velocity and frame dragging. Frame dragging describes the effects on spacetime on account of the rotation of the black hole. Looking at the tidal forces on objects surrounding the black hole it was found that an increasing mass would actually decrease the tidal forces on objects outside the event horizon. For a sufficiently large mass on the black hole, a planet could avoid being ripped apart but this restricted its size to a radial extension of about 5500 km which corresponds to 0.86 earth radiuses.

The production of axisymmetric initial data for distorted black holes at a moment of time symmetry is considered within the (3+1) context of general relativity. The initial data is made to contain a distorted marginally trapped surface ensuring that, modulo cosmic censorship, the spacetime will contain a black hole. The resulting equations on the complicated domain are solved using the piecewise linear finite element method which adapts to the curved surface of the marginally trapped surface. The initial data is then analyzed to calculate the mass of the space time as well as an upper bound on the fraction of the total energy available for radiation. The families of initial data considered contain no more than few percent of the total energy available for radiation even in cases of extreme distortion. It is shown that the mass of certain initial data slices depend to first order on the area of the marginally trapped surface and the gaussian curvature of prominent features.

The production of axisymmetric initial data for distorted black holes at a moment of time symmetry is considered within the (3+1) context of general relativity. The initial data is made to contain a distorted marginally trapped surface ensuring that, modulo cosmic censorship, the spacetime will contain a black hole. The resulting equations on the complicated domain are solved using the piecewise linear finite element method which adapts to the curved surface of the marginally trapped surface. The initial data is then analyzed to calculate the mass of the space time as well as an upper bound on the fraction of the total energy available for radiation. The families of initial data considered contain no more than few percent of the total energy available for radiation even in cases of extreme distortion. It is shown that the mass of certain initial data slices depend to first order on the area of the marginally trapped surface and the gaussian curvature of prominent features. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 1991. / Includes bibliographical references (p. 177-183). / by Alison Marguerite Macdonald. / M.S.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 1990. / Includes bibliographical references. / Ph.D.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 1992. / Includes bibliographical references (p. 49-52). / by Marjorie Anne MacWhorter Friedrichs. / M.S.