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Nonspherical perturbations of relativistic gravitational collapse


Price, Richard H. (1971) Nonspherical perturbations of relativistic gravitational collapse. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1EGC-Y160.


It is known that there can be no gravitational, electromagnetic, or scalar field perturbations (except angular momentum) of a Schwarzschild black hole. A gravitationally collapsing star with nonspherical perturbations must therefore radiate away its perturbations or halt its collapse. The results of computations in comoving coordinates are presented to show that the scalar field in a collapsing star neither disappears nor halts the collapse, as the star passes inside its gravitational radius. On the star's surface, near the event horizon, the scalar field varies as a_1 + a_2 exp (-t/2M) due to time dilation. The dynamics of the field outside the star can be analyzed with a simple wave equation containing a spacetime-curvature induced potential. This potential is impenetrable to zero-frequency waves and thus a_1, the final value of the field on the stellar surface, is not manifested in the exterior; the field vanishes. The monopole perturbation falls off as t^(-2); higher ℓ-poles fall off as ℓn t/t^(2ℓ+3). The analysis of scalar-field perturbations works as well for electromagnetic and gravitational perturbations and also for zero-restmass perturbation fields of arbitrary integer spin. All these perturbation fields obey wave equations with curvature potentials that differ little from one field to another. For all fields, radiatable multipoles (ℓ ≥ spin of the field) fall off as ℓnt/t^(2ℓ+3).

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Physics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Thorne, Kip S.
Group:TAPIR, Astronomy Department
Thesis Committee:
  • Unknown, Unknown
Defense Date:15 April 1971
Funding AgencyGrant Number
Record Number:CaltechTHESIS:01192010-090920179
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5526
Deposited By: Tony Diaz
Deposited On:19 Jan 2010 17:27
Last Modified:10 Mar 2020 23:39

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