Blaise TCHAPNDA - Academia.edu (original) (raw)
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Papers by Blaise TCHAPNDA
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2002
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An idea which has been around in general relativity for more than forty years is that in the appr... more An idea which has been around in general relativity for more than forty years is that in the approach to a big bang singularity solutions of the Einstein equations can be approximated by the Kasner map, which describes a succession of Kasner epochs. This is already a highly non-trivial statement in the spatially homogeneous case. There the Einstein equations reduce to ordinary differential equations and it becomes a statement that the solutions of the Einstein equations can be approximated by heteroclinic chains of the corresponding dynamical system. For a long time progress on proving a statement of this kind rigorously was very slow but recently there has been new progress in this area, particularly in the case of the vacuum Einstein equations. In this paper we generalize some of these results to the Einstein-Maxwell equations. It turns out that this requires new techniques since certain eigenvalues are in a less favourable configuration in the case with a magnetic field. The diff...
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Classical and Quantum Gravity, 2004
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Classical and Quantum Gravity, 2003
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Mathematical Proceedings of the Cambridge Philosophical Society, 2005
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Annales Henri Poincaré, 2007
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Advances in Theoretical and Mathematical Physics, 2011
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We revisit and generalize, to the Einstein-Yang-Mills-Higgs system, previous results of D. Christ... more We revisit and generalize, to the Einstein-Yang-Mills-Higgs system, previous results of D. Christodoulou and D. Chae concerning global solutions for the Einstein-scalar field and the Einstein-Maxwell-Higgs equations. The novelty of the present work is twofold. For one thing the assumption on the self-interaction potential is improved. For another thing explanation is furnished why the solutions obtained here and those proved by Chae for the Einstein-Maxwell-Higgs decay more slowly than those established by Christodoulou in the case of self-gravitating scalar fields. Actually this latter phenomenon stems from the non-vanishing local charge in Einstein-Maxwell-Higgs and Einstein-Yang-Mills-Higgs models.
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Structure of solutions near the initial singularity
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The Einstein-Vlasov system describes a self-gravitating, collision-less gas within the framework ... more The Einstein-Vlasov system describes a self-gravitating, collision-less gas within the framework of general relativity. We investigate the initial value problem in a cosmological setting with surface symmetry and a non-zero cosmological constant and prove local existence and continuation criteria in both time directions. The continuation criterion says that as long as the maximum velocity remains bounded and the lapse function remains bounded then the solution can be continued. This applies to either time direction.
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We prove a local in time existence theorem for the Cauchy problem for the Yang-Mills system in te... more We prove a local in time existence theorem for the Cauchy problem for the Yang-Mills system in temporal gauge, with current generated both by a distribution function that satisfies the Vlasov equation, and an unknown Yang-Mills charge density, subject to a conservation equation. We prove a global in time existence theorem in the case of massless particles.
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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012
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Journal of Hyperbolic Differential Equations, Sep 1, 2008
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Proceedings of the Royal Society of London a Mathematical Physical and Engineering Sciences, Aug 8, 2002
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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2002
Bookmarks Related papers MentionsView impact
An idea which has been around in general relativity for more than forty years is that in the appr... more An idea which has been around in general relativity for more than forty years is that in the approach to a big bang singularity solutions of the Einstein equations can be approximated by the Kasner map, which describes a succession of Kasner epochs. This is already a highly non-trivial statement in the spatially homogeneous case. There the Einstein equations reduce to ordinary differential equations and it becomes a statement that the solutions of the Einstein equations can be approximated by heteroclinic chains of the corresponding dynamical system. For a long time progress on proving a statement of this kind rigorously was very slow but recently there has been new progress in this area, particularly in the case of the vacuum Einstein equations. In this paper we generalize some of these results to the Einstein-Maxwell equations. It turns out that this requires new techniques since certain eigenvalues are in a less favourable configuration in the case with a magnetic field. The diff...
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Classical and Quantum Gravity, 2004
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Classical and Quantum Gravity, 2003
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Mathematical Proceedings of the Cambridge Philosophical Society, 2005
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Annales Henri Poincaré, 2007
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Advances in Theoretical and Mathematical Physics, 2011
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We revisit and generalize, to the Einstein-Yang-Mills-Higgs system, previous results of D. Christ... more We revisit and generalize, to the Einstein-Yang-Mills-Higgs system, previous results of D. Christodoulou and D. Chae concerning global solutions for the Einstein-scalar field and the Einstein-Maxwell-Higgs equations. The novelty of the present work is twofold. For one thing the assumption on the self-interaction potential is improved. For another thing explanation is furnished why the solutions obtained here and those proved by Chae for the Einstein-Maxwell-Higgs decay more slowly than those established by Christodoulou in the case of self-gravitating scalar fields. Actually this latter phenomenon stems from the non-vanishing local charge in Einstein-Maxwell-Higgs and Einstein-Yang-Mills-Higgs models.
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Structure of solutions near the initial singularity
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Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
The Einstein-Vlasov system describes a self-gravitating, collision-less gas within the framework ... more The Einstein-Vlasov system describes a self-gravitating, collision-less gas within the framework of general relativity. We investigate the initial value problem in a cosmological setting with surface symmetry and a non-zero cosmological constant and prove local existence and continuation criteria in both time directions. The continuation criterion says that as long as the maximum velocity remains bounded and the lapse function remains bounded then the solution can be continued. This applies to either time direction.
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
We prove a local in time existence theorem for the Cauchy problem for the Yang-Mills system in te... more We prove a local in time existence theorem for the Cauchy problem for the Yang-Mills system in temporal gauge, with current generated both by a distribution function that satisfies the Vlasov equation, and an unknown Yang-Mills charge density, subject to a conservation equation. We prove a global in time existence theorem in the case of massless particles.
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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012
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Journal of Hyperbolic Differential Equations, Sep 1, 2008
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Proceedings of the Royal Society of London a Mathematical Physical and Engineering Sciences, Aug 8, 2002
Bookmarks Related papers MentionsView impact