Citation
Yurtsever, Ulvi (1989) Singularities and horizons in the collisions of gravitational waves. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:10242013145903390
Abstract
This thesis presents a study of the dynamical, nonlinear interaction of colliding gravitational waves, as described by classical general relativity. It is focused mainly on two fundamental questions: First, what is the general structure of the singularities and KillingCauchy horizons produced in the collisions of exactly planesymmetric gravitational waves? Second, under what conditions will the collisions of almostplane gravitational waves (waves with large but finite transverse sizes) produce singularities?
In the work on the collisions of exactlyplane waves, it is shown that Killing horizons in any planesymmetric spacetime are unstable against small planesymmetric perturbations. It is thus concluded that the KillingCauchy horizons produced by the collisions of some exactly plane gravitational waves are nongeneric, and that generic initial data for the colliding plane waves always produce "pure" spacetime singularities without such horizons. This conclusion is later proved rigorously (using the full nonlinear theory rather than perturbation theory), in connection with an analysis of the asymptotic singularity structure of a general colliding planewave spacetime. This analysis also proves that asymptotically the singularities created by colliding plane waves are of inhomogeneousKasner type; the asymptotic Kasner axes and exponents of these singularities in general depend on the spatial coordinate that runs tangentially to the singularity in the nonplanesymmetric direction.
In the work on collisions of almostplane gravitational waves, first some general properties of single almostplane gravitationalwave spacetimes are explored. It is shown that, by contrast with an exact plane wave, an almostplane gravitational wave cannot have a propagation direction that is Killing; i.e., it must diffract and disperse as it propagates. It is also shown that an almostplane wave cannot be precisely sandwiched between two null wavefronts; i.e., it must leave behind tails in the spacetime region through which it passes. Next, the occurrence of spacetime singularities in the collisions of almostplane waves is investigated. It is proved that if two colliding, almostplane gravitational waves are initially exactly planesymmetric across a central region of sufficiently large but finite transverse dimensions, then their collision produces a spacetime singularity with the same local structure as in the exactplanewave collision. Finally, it is shown that a singularity still forms when the central regions are only approximately planesymmetric initially. Stated more precisely, it is proved that if the colliding almostplane waves are initially sufficiently close to being exactly planesymmetric across a bounded central region of sufficiently large transverse dimensions, then their collision necessarily produces spacetime singularities. In this case, nothing is now known about the local and global structures of the singularities.
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:  Restricted to Caltech community only 
Research Advisor(s): 

Group:  TAPIR 
Thesis Committee: 

Defense Date:  29 September 1988 
Record Number:  CaltechTHESIS:10242013145903390 
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:10242013145903390 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  8009 
Collection:  CaltechTHESIS 
Deposited By:  John Wade 
Deposited On:  24 Oct 2013 23:02 
Last Modified:  18 Aug 2017 21:47 
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