The Experts below are selected from a list of 288 Experts worldwide ranked by ideXlab platform
Philippe Tchamitchian - One of the best experts on this subject based on the ideXlab platform.
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On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
Classical and Quantum Gravity, 2013Co-Authors: Ricardo E. Gamboa Saravi, Marcela Sanmartino, Philippe TchamitchianAbstract:We give simple conditions implying the well-posedness of the Cauchy problem for the propagation of classical scalar fields in general (n + 2)-dimensional static and spherically symmetric spacetimes. They are related to the properties of the underlying Spatial Part of the wave operator, one of which being the standard essentially self-adjointness. However, in many examples the Spatial Part of the wave operator turns out to be not essentially self-adjoint, but it does satisfy a weaker property that we call here quasi-essentially self-adjointness, which is enough to ensure the desired well-posedness. This is why we also characterize this second property. We state abstract results, then general results for a class of operators encompassing many examples in the literature, and we finish with the explicit analysis of some of them.
Ricardo E. Gamboa Saravi - One of the best experts on this subject based on the ideXlab platform.
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On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
Classical and Quantum Gravity, 2013Co-Authors: Ricardo E. Gamboa Saravi, Marcela Sanmartino, Philippe TchamitchianAbstract:We give simple conditions implying the well-posedness of the Cauchy problem for the propagation of classical scalar fields in general (n + 2)-dimensional static and spherically symmetric spacetimes. They are related to the properties of the underlying Spatial Part of the wave operator, one of which being the standard essentially self-adjointness. However, in many examples the Spatial Part of the wave operator turns out to be not essentially self-adjoint, but it does satisfy a weaker property that we call here quasi-essentially self-adjointness, which is enough to ensure the desired well-posedness. This is why we also characterize this second property. We state abstract results, then general results for a class of operators encompassing many examples in the literature, and we finish with the explicit analysis of some of them.
Othmar Brodbeck - One of the best experts on this subject based on the ideXlab platform.
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Self-adjoint wave equations for dynamical perturbations of self-gravitating fields
Physical Review D, 2001Co-Authors: Olivier Sarbach, Markus Heusler, Othmar BrodbeckAbstract:It is shown that the dynamical evolution of linear perturbations on a static space-time is governed by a constrained wave equation for the extrinsic curvature tensor. The Spatial Part of the wave operator is manifestly elliptic and self-adjoint. In contrast with metric formulations, the curvature-based approach to gravitational perturbation theory generalizes in a natural way to self-gravitating matter fields. It is also demonstrated how to obtain symmetric pulsation equations for self-gravitating non-Abelian gauge fields, Higgs fields and perfect fluids. For vacuum fluctuations on a vacuum space-time, the Regge-Wheeler and Zerilli equations are re-derived.
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Generalization of the regge-wheeler equation for self-gravitating matter fields
Physical review letters, 2000Co-Authors: Othmar Brodbeck, Markus Heusler, Olivier SarbachAbstract:It is shown that the dynamical evolution of perturbations on a static spacetime is governed by a standard pulsation equation for the extrinsic curvature tensor. The centerpiece of the pulsation equation is a wave operator whose Spatial Part is manifestly self-adjoint. In contrast to metric formulations, the curvature-based approach to perturbation theory generalizes in a natural way to self-gravitating matter fields, including non-Abelian gauge fields and perfect fluids. As an example, the pulsation equations for self-gravitating, non-Abelian gauge fields are explicitly shown to be symmetric.
Olivier Sarbach - One of the best experts on this subject based on the ideXlab platform.
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Self-adjoint wave equations for dynamical perturbations of self-gravitating fields
Physical Review D, 2001Co-Authors: Olivier Sarbach, Markus Heusler, Othmar BrodbeckAbstract:It is shown that the dynamical evolution of linear perturbations on a static space-time is governed by a constrained wave equation for the extrinsic curvature tensor. The Spatial Part of the wave operator is manifestly elliptic and self-adjoint. In contrast with metric formulations, the curvature-based approach to gravitational perturbation theory generalizes in a natural way to self-gravitating matter fields. It is also demonstrated how to obtain symmetric pulsation equations for self-gravitating non-Abelian gauge fields, Higgs fields and perfect fluids. For vacuum fluctuations on a vacuum space-time, the Regge-Wheeler and Zerilli equations are re-derived.
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Generalization of the regge-wheeler equation for self-gravitating matter fields
Physical review letters, 2000Co-Authors: Othmar Brodbeck, Markus Heusler, Olivier SarbachAbstract:It is shown that the dynamical evolution of perturbations on a static spacetime is governed by a standard pulsation equation for the extrinsic curvature tensor. The centerpiece of the pulsation equation is a wave operator whose Spatial Part is manifestly self-adjoint. In contrast to metric formulations, the curvature-based approach to perturbation theory generalizes in a natural way to self-gravitating matter fields, including non-Abelian gauge fields and perfect fluids. As an example, the pulsation equations for self-gravitating, non-Abelian gauge fields are explicitly shown to be symmetric.
Marcela Sanmartino - One of the best experts on this subject based on the ideXlab platform.
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On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
Classical and Quantum Gravity, 2013Co-Authors: Ricardo E. Gamboa Saravi, Marcela Sanmartino, Philippe TchamitchianAbstract:We give simple conditions implying the well-posedness of the Cauchy problem for the propagation of classical scalar fields in general (n + 2)-dimensional static and spherically symmetric spacetimes. They are related to the properties of the underlying Spatial Part of the wave operator, one of which being the standard essentially self-adjointness. However, in many examples the Spatial Part of the wave operator turns out to be not essentially self-adjoint, but it does satisfy a weaker property that we call here quasi-essentially self-adjointness, which is enough to ensure the desired well-posedness. This is why we also characterize this second property. We state abstract results, then general results for a class of operators encompassing many examples in the literature, and we finish with the explicit analysis of some of them.
