## Citation

Redmount, Ian H.
(1984)
*Topics in Black-Hole Physics: Geometric Constraints on Noncollapsing, Gravitating Systems and Tidal Distortions of a Schwarzschild Black Hole.*
Dissertation (Ph.D.), California Institute of Technology.
http://resolver.caltech.edu/CaltechTHESIS:08232017-105535039

## Abstract

This dissertation consists of two studies on the general-relativistic theory of black holes. The first work concerns the fundamental issue of black-hole formation: in it I seek geometric constraints on gravitating matter systems, in the special case of axial symmetry, which determine whether or not those systems undergo gravitational collapse to form black holes. The second project deals with mechanical behavior of a black hole: specifically, I study the tidal deformation of a static black hole by the gravitational fields of external bodies.

In the first paper I approach the problem of geometric constraints determining gravitational collapse or non-collapse through the initial-value formalism of general relativity. I construct initial-value data representing noncollapsing, nonsingular, axisymmetric matter systems and examine the constraints imposed on this construction by the initial-value equation derived from the Einstein field equations. The construction consists of a nonsingular, momentarily static interior geometry with nonnegative mass-energy density, matched smoothly to a static, vacuum exterior geometry (described by a Weyl solution of the Einstein field equations) at a boundary surface. The initial-value equation is found to impose restrictions on the choice of the boundary surface for such a system. Two such constraints are obtained here, appropriate to spherical and toroidal interior-region topologies. These constraints are studied by applying them to simple examples of Weyl exterior geometries. The "hoop conjecture" for the general geometric-constraints problem states that a system must collapse to a black hole unless its circumference in some direction exceeds a lower bound of the order of the system's mass. The examples examined here show, however, that the constraints derived in this study are not generally correlated with any simple measure of system size, and thus that they do not embody the hoop conjecture.

The second paper examines the tidal distortion of a Schwarzschild black hole by bodies ("moons") suspended above the horizon on "ropes." A solution of the Einstein field equations is constructed describing this configuration, using the Weyl formalism for axisymmetric, static, vacuum geometries. The intrinsic geometry of the tidally deformed black-hole horizon is obtained from this solution; I construct embedding diagrams to represent the shape of the horizon and the tidal bulges raised on it for both weak and strong perturbations. The relations among the masses of the hole and moons, the binding energy of the system, and the rope density and tension are calculated from the solution and shown to be mutually consistent. Also, the Riemann curvature tensor representing the tidal fields near the horizon is calculated. This solution is found to agree with a previous calculation by Hartle of black-hole tides, in the limit of perturbing moons far from the horizon. In the opposite case of moons very near the horizon, this solution approaches the static limit of the distorted horizon in Rindler space calculated by Suen and Price. The results of this study thus support the use of the Rindler approximation to Schwarzschild spacetime in calculating static black-hole tides, and its extension to dynamical situations.

Item Type: | Thesis (Dissertation (Ph.D.)) | ||||||||||
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Subject Keywords: | Physics | ||||||||||

Degree Grantor: | California Institute of Technology | ||||||||||

Division: | Physics, Mathematics and Astronomy | ||||||||||

Major Option: | Physics | ||||||||||

Thesis Availability: | Restricted to Caltech community only | ||||||||||

Research Advisor(s): | - Thorne, Kip S.
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Group: | TAPIR | ||||||||||

Thesis Committee: | - Frautschi, Steven C. (chair)
- Price, Richard H.
- Phillips, Thomas G.
- Thorne, Kip S.
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Defense Date: | 23 September 1983 | ||||||||||

Funders: |
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Record Number: | CaltechTHESIS:08232017-105535039 | ||||||||||

Persistent URL: | http://resolver.caltech.edu/CaltechTHESIS:08232017-105535039 | ||||||||||

Related URLs: |
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Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||

ID Code: | 10385 | ||||||||||

Collection: | CaltechTHESIS | ||||||||||

Deposited By: | Benjamin Perez | ||||||||||

Deposited On: | 25 Aug 2017 15:35 | ||||||||||

Last Modified: | 09 Oct 2018 00:18 |

## Thesis Files

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