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Geometrical resolution of spacetime singularities

Frederik De Roo (UGent)
(2010)
Author
Promoter
Ben Craps and Greet Maenhout
Organization
Abstract
General relativity predicts the existence of gravitational singularities at the classical level: our universe started with the big bang, and massive stars can collapse into black holes. A theory that describes quantum gravitational effects should elucidate our understanding of these singularities. The existence of these singularities also raises the question whether propagation of quantum fields through a singularity is possible (and how it should be formulated). String theory can already deal with some timelike singularities but not yet with spacelike singularities like the big bang. Near singularities, strings often interact strongly. A formulation of string theory that allows to take strong interactions between strings into account is given by matrix theory. Matrix theory models that describe singularities often have a dual translation in terms of a quantum field theory that is defined on a singular background spacetime. In this dissertation we investigate these issues. We use a geometric regularization prescription to define the evolution of a free scalar field and of a free string through a singularity in an unambiguous manner. Remarkably, this geometric regularization seems to reveal there is a certain feature of discreteness related to the evolution across the singularity. We also consider an important class of time-dependent backgrounds that can be investigated in string theory. This class is called gravitational plane waves. These plane waves can be used to investigate the strong curvature effects related to a singularity. Our study shows that it is necessary to take into account that the strings can interact strongly near the singularity. In order to obtain a better understanding of matrix theory on a plane wave background we investigate solutions that describes D-branes in plane wave backgrounds. D-branes are objects that appear in string theory besides strings, and that are important for the formulation of matrix theory.

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Citation

Please use this url to cite or link to this publication:

Chicago
De Roo, Frederik. 2010. “Geometrical Resolution of Spacetime Singularities”. Brussels ; Ghent, Belgium: Vrije Universiteit Brussel. Faculty of Science and Bio-engineering Sciences ; Ghent University. Faculty of Engineering.
APA
De Roo, F. (2010). Geometrical resolution of spacetime singularities. Vrije Universiteit Brussel. Faculty of Science and Bio-engineering Sciences ; Ghent University. Faculty of Engineering, Brussels ; Ghent, Belgium.
Vancouver
1.
De Roo F. Geometrical resolution of spacetime singularities. [Brussels ; Ghent, Belgium]: Vrije Universiteit Brussel. Faculty of Science and Bio-engineering Sciences ; Ghent University. Faculty of Engineering; 2010.
MLA
De Roo, Frederik. “Geometrical Resolution of Spacetime Singularities.” 2010 : n. pag. Print.
@phdthesis{1029255,
  abstract     = {General relativity predicts the existence of gravitational singularities at the classical level: our universe started with the big bang, and massive stars can collapse into black holes. A theory that describes quantum gravitational effects should elucidate our understanding of these singularities. The existence of these singularities also raises the question whether propagation of quantum fields through a singularity is possible (and how it should be formulated). String theory can already deal with some timelike singularities but not yet with spacelike singularities like the big bang. Near singularities, strings often interact strongly. A formulation of string theory that allows to take strong interactions between strings into account is given by matrix theory. Matrix theory models that describe singularities often have a dual translation in terms of a quantum field theory that is defined on a singular background spacetime.
In this dissertation we investigate these issues. We use a geometric regularization prescription to define the evolution of a free scalar field and of a free string through a singularity in an unambiguous manner. Remarkably, this geometric regularization seems to reveal there is a certain feature of discreteness related to the evolution across the singularity. We also consider an important class of time-dependent backgrounds that can be investigated in string theory. This class is called gravitational plane waves. These plane waves can be used to investigate the strong curvature effects related to a singularity. Our study shows that it is necessary to take into account that the strings can interact strongly near the singularity. In order to obtain a better understanding of matrix theory on a plane wave background we investigate solutions that describes D-branes in plane wave backgrounds. D-branes are objects that appear in string theory besides strings, and that are important for the formulation of matrix theory.},
  author       = {De Roo, Frederik},
  isbn         = {9789085783664},
  language     = {eng},
  pages        = {XX, 270},
  publisher    = {Vrije Universiteit Brussel. Faculty of Science and Bio-engineering Sciences ; Ghent University. Faculty of Engineering},
  school       = {Ghent University},
  title        = {Geometrical resolution of spacetime singularities},
  year         = {2010},
}