Topic
Harmonic coordinate condition
About: Harmonic coordinate condition is a research topic. Over the lifetime, 9 publications have been published within this topic receiving 296 citations. The topic is also known as: de Donder gauge.
Papers
TL;DR: In this paper, the geometry of a typical quantum universe was studied using computer simulations, i.e., the geometry one might expect before a possible period of inflation, using coordinates defined by means of four classical scalar fields satisfying the Laplace equation with nontrivial boundary conditions.
Abstract: Using computer simulations, we study the geometry of a typical quantum universe, i.e., the geometry one might expect before a possible period of inflation. We display it using coordinates defined by means of four classical scalar fields satisfying the Laplace equation with nontrivial boundary conditions. They are a close analogue of the harmonic coordinate condition used in the context of GR (Kuchar and Torre in Phys Rev D 43:419–441, 1991). It is highly nontrivial that these ideas can be applied to understand the structures which appear in very irregular and fluctuating geometries. The field configurations reveal cosmic web structures surprisingly similar to the ones observed in the present-day universe.
8 citations
TL;DR: In this article, the authors separate the linearized general fourth-order field equation into three second-order normal equations and use the normal harmonic coordinate condition for the special case of a static spherically symmetric mass distribution.
Abstract: The authors separate the linearized general fourth-order field equation into three second-order normal equations. The special coordinate condition of Teyssandier (1988) is not used; rather the normal harmonic coordinate condition is used. As an example, the special case of a static spherically symmetric mass distribution is discussed in detail. The resulting metric gii is obtained in a different gauge from that in Teyssandier. Some conclusions are also discussed.
4 citations
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TL;DR: In this paper, the authors prove a global existence theorem in the direction of cosmological expansion for sufficiently small perturbations of a family of spatially compact variants of the Friedmann-Robertson--Walker vacuum spacetime.
Abstract: In this paper we prove a global existence theorem, in the direction of cosmological expansion, for sufficiently small perturbations of a family of spatially compact variants of the $k=-1$ Friedmann--Robertson--Walker vacuum spacetime. We use a special gauge defined by constant mean curvature slicing and a spatial harmonic coordinate condition, and develop energy estimates through the use of the Bel-Robinson energy and its higher order generalizations. In addition to the smallness condition on the data, we need a topological constraint on the spatial manifold to exclude the possibility of a non--trivial moduli space of flat spacetime perturbations, since the latter could not be controlled by curvature--based energies such as those of Bel--Robinson type. Our results also demonstrate causal geodesic completeness of the perturbed spacetimes (in the expanding direction) and establish precise rates of decay towards the background solution which serves as an attractor asymptotically.
2 citations
TL;DR: In this article, the vacuum field equations of general projective relativity have been solved for Liouville space-time and harmonic coordinate condition and singular behaviour of Kretschmann scalar for the solution is discussed.
Abstract: Vacuum field equations of general projective relativity have been solved for Liouville space-time. Finally harmonic coordinate condition and singular behaviour of Kretschmann scalar for the solution is discussed.
1 citations
TL;DR: In a recent paper devoted to the linearized field equations in R+R2 gravitational theories, Xu and Ellis (1991) have attempted to determine the metric of a static spherically symmetric body in harmonic coordinates.
Abstract: In a recent paper devoted to the linearized field equations in R+R2 gravitational theories, Xu and Ellis (1991) have attempted to determine the metric of a static spherically symmetric body in harmonic coordinates. The author points out that their result is erroneous and he exhibits the correct solution. The form of this solution shows that the harmonic coordinate condition is not convenient in linearized R+R2 gravity.
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2004 | 1 |
| 2003 | 2 |
| 1992 | 2 |
| 1991 | 1 |
| 1990 | 1 |