Exact solutions for the massless plane symmetric scalar field in general relativity, with cosmological constant

Vuille, Chris

doi:10.1007/s10714-007-0411-9

Cited by 11 publications

(16 citation statements)

References 11 publications

(12 reference statements)

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“…In four dimensions we can mention the existence of a particular plane-symmetric solution with nonzero cosmological constant (of arbitrary sign) given in [28]. Finally, a particular solution to the problem in d dimensions with a flat base manifold was found in [15].…”

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confidence: 90%

Anti-de Sitter massless scalar field spacetimes in arbitrary dimensions

García-Sáenz

Martínez

2012

Phys. Rev. D

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We consider $d$-dimensional static spacetimes in Einstein gravity with a cosmological constant in the presence of a minimally coupled massless scalar field. The spacetimes have a $(d-2)$-dimensional base manifold given by an Einstein space and the massless scalar field depends only on the radial coordinate. The field equations are decoupled in the general case, and can be solved exactly for the cases when either the cosmological constant vanishes or the base manifold is Ricci flat. We focus on the case of a negative cosmological constant and a Ricci-flat base manifold. The solution has a curvature singularity located at the origin, where also the scalar field diverges. Since there is no event horizon surrounding this singularity, the solution describes a naked singularity dressed with a nontrivial scalar field. This spacetime is an asymptotically locally anti-de Sitter one when the Ricci-flat base manifold is locally flat. The asymptotic solution for an arbitrary Einstein base manifold is found and the corresponding mass, calculated through the canonical generator of the time-translation invariance, is shown to be finite. The contribution to the mass from the scalar field at infinity is also discussed.Comment: 14 pages, 1 figure. Typos correcte

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confidence: 90%

Anti-de Sitter massless scalar field spacetimes in arbitrary dimensions

García-Sáenz

Martínez

2012

Phys. Rev. D

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“…Now we investigate the stability of the field equations (3,4) under small pertubations.First we note that instead of working with the system (3,4) we can treat the (6,8) as the field equations.in linear approximation (6) becomes…”

Section: About the Stability Of The Field Equationsmentioning

confidence: 99%

Cylindrically Symmetric Scalar Field and it’s Lyapunov stability in General Relativity

Rezazadeh

2010

Int J Theor Phys

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In this paper we found an Exact solution for massless scalar field with cosmological constant.This exact solution generalized the Levi-Civita vacuum solution[8] to a massless scalar field,with a cosmological constant term.This solution in the absence of the Cosmological constant recovers the spacetime of a massless scalar field with cylindrical symmetry (Buchdahl metric[2]).Also if the scalar field disappears, the spacetime is a representation of de-Sitter space.We prove that the form of the metric's function which was purposed in [1] is valid even if we assume a general form.Too we show that in which conditions this solution satisfies energy conditions. Finally the validity of focusing theorem is proved.

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“…Finally, a generalization of the Singh's solution with the presence of a massless plane symmetric scalar field and a cosmological constant was recently found by Vuille. [9] One particular solution which leads to the above potential in the Newtonian limit is the Rohrlich [10] solution that actually describes flat spacetime in a special coordinate system. On the other hand, in this article, we will consider the metric first found by Horský [11] which represents a truly curved spacetime.…”

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confidence: 99%

Propagation of Scalar Fields in a Plane Symmetric Spacetime

2016

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The present article deals with solutions for a minimally coupled scalar field propagating in a static plane symmetric spacetime. The considered metric describes the curvature outside a massive infinity plate and exhibits an intrinsic naked singularity (a singular plane) that makes the accessible universe finite in extension. This solution can be interpreted as describing the spacetime of static domain walls. In this context, a first solution is given in terms of zero order Bessel functions of the first and second kind and presents a stationary pattern which is interpreted as a result of the reflection of the scalar waves at the singular plane. This is an evidence, at least for the massless scalar field, of an old interpretation given by Amundsen and Grøn regarding the behaviour of test particles near the singularity. A second solution is obtained in the limit of a weak gravitational field which is valid only far from the singularity. In this limit, it was possible to find out an analytic solution

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Exact solutions for the massless plane symmetric scalar field in general relativity, with cosmological constant

Cited by 11 publications

References 11 publications

Anti-de Sitter massless scalar field spacetimes in arbitrary dimensions

Anti-de Sitter massless scalar field spacetimes in arbitrary dimensions

Cylindrically Symmetric Scalar Field and it’s Lyapunov stability in General Relativity

Propagation of Scalar Fields in a Plane Symmetric Spacetime

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