General static plane-symmetric solutions of the Einstein-Maxwell equations

Amundsen, Per Amund; Grøn, Øyvind

doi:10.1103/physrevd.27.1731

Cited by 36 publications

(47 citation statements)

References 60 publications

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“…In the plane-symmetric four-dimensional case, considered here, we deal with an essentially two-dimensional problem, and the appropriate Newtonian force law implies κΣ ≡ −2k z where Σ is the gravitational mass per area of the plane. The factor of two is included because the gravitational acceleration is half the mass per area in the planar symmetric case (in the reflection symmetric case [45,51] one finds that the acceleration on both sides is a quarter of the mass density). In the same spirit as the compact spherically symmetric case, Eq.…”

Section: Tolman's Mass Per Areamentioning

confidence: 99%

Local and global gravitational aspects of domain wall space-times

1993

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Local and global gravitational effects induced by eternal vacuum domain walls are studied. We concentrate on thin walls between non-equal and non-positive cosmological constants on each side of the wall. The assumption of homogeneity, isotropy, and geodesic completenes of the space-time intrinsic to the wall as described in the comoving coordinate system and the constraint that the same symmetries hold in hypersurfaces parallel to the wall, yield a general Ansatz for the lineelement of space-time. We restrict the problem further by demanding that the wall's surface energy density, σ, is positive and by requiring that the infinitely thin wall represents a thin wall limit of a kink-like scalar field configuration. These vacuum domain walls fall in three classes depending on the value of their σ: (1) extreme walls with σ = σext are planar, static walls corresponding to supersymmetric configurations, (2) non-extreme walls with σ = σnon > σext correspond to expanding bubbles with observers on either side of the wall being inside the bubble, and (3) ultra-extreme walls with σ = σ ultra < σext represent the bubbles of false vacuum decay. On the sides with less negative cosmological constant, the extreme, non-extreme, and ultra-extreme walls exhibit no, repulsive, and attractive effective "gravitational forces," respectively. These "gravitational forces" are global effects not caused by local curvature. Since the non-extreme wall encloses observers on both sides, the supersymmetric system has the lowest gravitational mass accessable to outside observers. It is conjectured that similar positive mass protection occurs in all physical systems and that no finite negative mass object can exist inside the universe. We also discuss the global space-time structure of these singularity free space-times and point out intriguing analogies with the causal structure of black holes.

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Section: Tolman's Mass Per Areamentioning

confidence: 99%

Local and global gravitational aspects of domain wall space-times

1993

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“…A discussion and an extensive list of references on this subject can be found in Ref. 1. None of these solutions has the correct matter configuration for an infinite plane, namely ͑z͒ ϰ ␦͑z͒ as in Eq.…”

Section: Introductionmentioning

confidence: 99%

The general relativistic infinite plane

Jones

Muñoz

Ragsdale

et al. 2008

American Journal of Physics

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Uniform fields are one of the simplest and most pedagogically useful examples in introductory courses on electrostatics or Newtonian gravity. In general relativity there have been several proposals as to what constitutes a uniform field. In this article we examine two metrics that can be considered the general relativistic version of the infinite plane with finite mass per unit area. The first metric is the 4D version of the 5D "brane" world models which are the starting point for many current research papers. The second case is the cosmological domain wall metric. We examine to what extent these different metrics match or deviate from our Newtonian intuition about the gravitational field of an infinite plane. These solutions provide the beginning student in general relativity both computational practice and conceptual insight into Einstein's field equations. In addition they do this by introducing the student to material that is at the forefront of current research.Comment: Accepted for publication in the American Journal of Physic

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“…(24), (25). There is no problem of gravitation singularity in the considering approximation, because the criterion of its applicability coincides with the condition of a gravitation collapse of the disk.…”

Section: Discussion and Summarymentioning

confidence: 99%

Quasi-uniform gravitational field of a disk revisited

Silenko

Tsalkou

2019

Int. J. Mod. Phys. A

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We calculate the quasi-uniform gravitational field of a disk in the weak-field approximation and demonstrate an inappropriateness of preceding results. The Riemann tensor of this field is determined. A nonexistence of the uniform gravitational field is proven. It is shown that a difference between equations of a particle motion and a spin rotation in the accelerated frame and in the quasi-uniform gravitational field of a disk does not violate the Einstein equivalence principle.

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General static plane-symmetric solutions of the Einstein-Maxwell equations

Cited by 36 publications

References 60 publications

Local and global gravitational aspects of domain wall space-times

Local and global gravitational aspects of domain wall space-times

The general relativistic infinite plane

Quasi-uniform gravitational field of a disk revisited

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