Static plane symmetric relativistic fluids and empty repelling singular boundaries

Saraví, R. E. Gamboa

doi:10.1088/0264-9381/25/4/045005

Cited by 9 publications

(7 citation statements)

References 9 publications

(20 reference statements)

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“…In the literature, the perfect fluid ǫ = 0 is most studied ( [7] , [8], [9], [10], [11], [12], [2]sec. 15.7.1), followed by the Einstein-Maxwell system of a charged infinite plane ( [3], [13] ), where γ = 0 and ǫ = −1.…”

Section: Applications To Simple Fluidsmentioning

confidence: 99%

“…For a constant γ, we have the Collins solutions ( [11,12]). In this case matter obeys the equation of state p 1 ( ) g r = -.…”

Section: Exact Solutionsmentioning

confidence: 99%

“…To define specific values of γ, the reader might consult the rich literature on the subject ([2] Section 15.7.1, [7][8][9][10]). In the following, we exemplify our approach in two distinct examples: the Collins solutions ( [11,12]) and the Tabensky-Taub solution ( [8]).…”

Section: Exact Solutionsmentioning

confidence: 99%

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On the local form of static plane symmetric spacetimes in the presence of matter

Gomes¹

2015

Class. Quantum Grav.

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For any configuration of a static plane-symmetric distribution of matter along spacetime, there are coordinates where the metric can be put explicitly as a functional of the energy density and pressures. It satisfies Einstein equations as far as we require the conservation of the energy-momentum tensor, which is the single ODE for selfgravitating hydrostatic equilibrium. As a direct application, a general solution is given when the pressures are linearly related to the energy density, recovering, as special cases, most of known solutions of static plane-symmetric Einstein equations.

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Section: Applications To Simple Fluidsmentioning

confidence: 99%

“…For a constant γ, we have the Collins solutions ( [11,12]). In this case matter obeys the equation of state p 1 ( ) g r = -.…”

Section: Exact Solutionsmentioning

confidence: 99%

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On the local form of static plane symmetric spacetimes in the presence of matter

Gomes¹

2015

Class. Quantum Grav.

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“…In such a case, the singularities are not the sources of the fields, but they arise owing to the attraction of distant matter. We call them empty repelling singular boundaries (see also [12]).…”

Section: Geometric Settingmentioning

confidence: 99%

An alternative well-posedness property and static spacetimes with naked singularities

Saraví¹,

Sanmartino²,

Tchamitchian³

2010

Class. Quantum Grav.

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In the first part of this paper, we show that the Cauchy problem for wave propagation in some static spacetimes presenting a singular timelike boundary is well-posed, if we only require the waves to have finite energy, although no boundary condition is required. This feature does not come from essential self-adjointness, which is false in these cases, but from a different phenomenon that we call the alternative well-posedness property, whose origin is due to the degeneracy of the metric components near the boundary. Beyond these examples, in the second part, we characterize the type of degeneracy which leads to this phenomenon.

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“…This corresponds to setting γ = β 0 + 7 in the metric (30). Such solutions have been studied at least from the 1950's ( [12]) and are still matter of interest ( [9]). For more references, the reader could consult [13], [2], [3] and [10].…”

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confidence: 99%

General Solutions to Static Plane Symmetric Einstein's Equations

Gomes¹

2013

Preprint

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A general formula for the metric as an explicit function of the generic energymomentum tensor is given which satisfies static plane symmetric Einstein's equations with cosmological constant Λ. In order to illustrate it, the solutions for the vacuum with cosmological constant, the perfect fluid with a linear equation of state and the electrically charged plane are derived and compared with known results. The general solution with a linear relation among the energy-momentum tensor components is also obtained.

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Static plane symmetric relativistic fluids and empty repelling singular boundaries

Cited by 9 publications

References 9 publications

On the local form of static plane symmetric spacetimes in the presence of matter

On the local form of static plane symmetric spacetimes in the presence of matter

An alternative well-posedness property and static spacetimes with naked singularities

General Solutions to Static Plane Symmetric Einstein's Equations

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