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Evolving Geometries in General Relativity

2010, Master of Science, Ohio State University, Mathematics.
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 (gμν) 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, gμν 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.
Ulrich Gerlach, Prof. (Advisor)
Andrzej Derdzinski, Prof. (Committee Member)
59 p.

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Taliotis, Anastasios. "Evolving Geometries in General Relativity." Electronic Thesis or Dissertation. Ohio State University, 2010. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Taliotis, Anastasios "Evolving Geometries in General Relativity." Electronic Thesis or Dissertation. Ohio State University, 2010.


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