The structure of general relativity with a numerical illustration : the collision of two black holes

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dc.contributor.advisorDeWitt, Bryce S. (Bryce Seligman), 1923-2004
dc.creatorSmarr, Larry L.
dc.date.accessioned2019-02-11T21:04:11Z
dc.date.available2019-02-11T21:04:11Z
dc.date.issued1975
dc.description.abstractThe splitting of spacetime into space and time is analyzed by abstract methods, coordinate methods, and numerical computer methods. General relativity is assumed to be the correct theory of gravity and the Einstein field equations are studied in their canonical form. A comparison is made of the initial value and evolution equations for gravity in different formalisms (ADM, geometry of spacelike hypersurfaces, timelike congruences). These equations are then illustrated by a number of cosmological and black hole space-times. A study of coordinate conditions is undertaken. The axisymmetric (non-stationary and non-spherical) Einstein equations are discussed, and it is shown how to set up a numerical computer program to integrate these equations starting with a given initial data set. Various applications of this computer approach are discussed: collapse of rotating non-spherical stars, "runaway" collapse, and headon collisions of black holes. All of these situations would involve generation of gravitational radiation from the formation of black holes. The particular case of two nonrotating black holes colliding headon is chosen as a test case for the computer. The initial value problem is reviewed and then a computer program is written to generate the spacetime. This generation involves solving four coupled quasilinear hyperbolic (evolution) equations and one linear elliptic equation (maximal slicing) on each spacelike sheet. The numerical difficulties are discussed and graphical methods are used to present the result of the computations.en_US
dc.description.departmentPhysicsen_US
dc.format.mediumelectronicen_US
dc.identifier.urihttps://hdl.handle.net/2152/72872
dc.identifier.urihttp://dx.doi.org/10.26153/tsw/27
dc.language.isoengen_US
dc.relation.ispartofUT Electronic Theses and Dissertationsen_US
dc.rightsCopyright © is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en_US
dc.rights.restrictionOpenen_US
dc.subject.lcshGeneral relativity (Physics)
dc.subject.lcshGravitational collapse
dc.subject.lcshSpace and time
dc.titleThe structure of general relativity with a numerical illustration : the collision of two black holesen_US
dc.typeThesisen_US
dc.type.genreThesisen_US
thesis.degree.departmentPhysicsen_US
thesis.degree.disciplinePhysicsen_US
thesis.degree.grantorUniversity of Texas at Austinen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US

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