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osu1274838401.pdf (305.11 KB)
ETD Abstract Container
Abstract Header
Evolving Geometries in General Relativity
Author Info
Taliotis, Anastasios S.
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1274838401
Abstract Details
Year and Degree
2010, Master of Science, Ohio State University, Mathematics.
Abstract
The problem of collisions of shockwaves in gravity is well known and has been studied extensively in the literature. Recently, the interest in this area has been revived trough the anti-de-Sitter space/Conformal Field Theory correspondence (AdS/CFT) with the difference that in this case the background geometry is Anti de Sitter in five dimensions. In a recent project that we have completed in the context of AdS/CFT, we have gained insight in the problem of shockwaves and our goal in this work is to apply the technique we have developed in order to take some farther steps in the direction of shockwaves collisions in ordinary gravity. In the current project, each of the shockwaves correspond to a point-like Stress-Energy tensor that moves with the speed of light while the collision is asymmetric and involves an impact parameter (b). Our method is to expand the metric (
g
μν
) in the background of flat space-time in the presence of the two shockwaves and compute corrections that satisfy causal boundary conditions taking into account back-to-back reactions of the Stress-Energy tensor of the two point-like particles. Therefore, using Einstein’s equations we predict the future of space-time using the fact that we know the past geometry. The expansion we construct is valid for large transverse (to the initial direction of motion of the initial point-like particles) distances (
r
) and large proper times (
τ
) compared to the energy carried by the shockwaves. Our solution respects causality as expected but this casual dependence takes place in an intuitive way. In particular,
g
μν
at any given point
r⃗
on the transverse plane at fixed
τ
evolves according from whether the propagation from the center of each of the shockwaves or from both shockwaves has enough proper time (
τ
) to reach the point under consideration or not. Simultaneously around the center of each shockwave, the future metric develops a
δ
-function profile with radius
τ
; therefore this profile expands outwards from the centers (of the shockwaves) with the speed of light.
Committee
Ulrich Gerlach, Prof. (Advisor)
Andrzej Derdzinski, Prof. (Committee Member)
Pages
59 p.
Subject Headings
Mathematics
Keywords
Evolving Metric
;
Evolving Stress-Energy Tensor and Back-to-Back Reactions
;
Geodesics
;
Shockwaves Collisions
;
Boosted Black Hole
;
Impact Parameter
;
Causality
;
Gravitational Radiation
Recommended Citations
Refworks
EndNote
RIS
Mendeley
Citations
Taliotis, A. S. (2010).
Evolving Geometries in General Relativity
[Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1274838401
APA Style (7th edition)
Taliotis, Anastasios.
Evolving Geometries in General Relativity.
2010. Ohio State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1274838401.
MLA Style (8th edition)
Taliotis, Anastasios. "Evolving Geometries in General Relativity." Master's thesis, Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1274838401
Chicago Manual of Style (17th edition)
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Document number:
osu1274838401
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Copyright Info
© 2010, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.