The regularity of static spherically cylindrically and plane symmetric spacetimes at the origin

Lake, Kayll; Musgrave, Peter

doi:10.1007/bf02107148

Cited by 22 publications

(32 citation statements)

References 2 publications

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“…Recently, it has been presented different algorithms based on the choice of a single monotone function in order to generate all regular static spherically symmetric perfect fluid solutions of Einstein's equations in 3 + 1 dimensions [5]. The procedure to obtain the exact solutions of the Einstein equations in 2 + 1 dimensions, corresponding to static circularly symmetric spacetime coupled to perfect fluids, is straightforward via integration of the Einstein equations with cosmological constant as it was realized by García et al [6].…”

Section: Introductionmentioning

confidence: 99%

Static circularly symmetric perfect fluid solutions with an exterior BTZ metric

2005

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In this work we study static perfect fluid stars in 2 + 1 dimensions with an exterior BTZ spacetime. We found the general expression for the metric coefficients as a function of the density and pressure of the fluid. We found the conditions to have regularity at the origin throughout the analysis of a set of linearly independent invariants. We also obtain an exact solution of the Einstein equations, with the corresponding equation of state p = p(ρ), which is regular at the origin.

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Section: Introductionmentioning

confidence: 99%

Static circularly symmetric perfect fluid solutions with an exterior BTZ metric

2005

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“…We have also examined the other Ricci and Weyl invariant for the rotating metric (1) [39][40][41][42]; they can be obtained with Mathematica or Maple. It will be necessary to introduce the trace-free Ricci tensor defined by…”

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confidence: 99%

“…b is the Ricci tensor [39][40][41][42]. The non-zero Ricci invariant for the rotating metric (1) reads Not surprisingly they are also regular everywhere.…”

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confidence: 99%

A nonsingular rotating black hole

2015

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The spacetime singularities in classical general relativity are inevitable, as predicated by the celebrated singularity theorems. However, it is a general belief that singularities do not exist in Nature and that they are the limitations of the general relativity. In the absence of a welldefined quantum gravity, models of regular black holes have been studied. We employ a probability distribution inspired mass function m(r ) to replace the Kerr black hole mass M to represent a nonsingular rotating black hole that is identified asymptotically (r k, k > 0 constant) exactly as the KerrNewman black hole, and as the Kerr black hole when k = 0. The radiating counterpart renders a nonsingular generalization of Carmeli's spacetime as well as Vaidya's spacetime, in the appropriate limits. The exponential correction factor changing the geometry of the classical black hole to remove the curvature singularity can also be motivated by quantum arguments. The regular rotating spacetime can also be understood as a black hole of general relativity coupled to nonlinear electrodynamics.The celebrated theorems of Penrose and Hawking [1] state that under some circumstances singularities are inevitable in general relativity. For the Kerr solution these singularities have the shape of a ring, this case is timelike. The Kerr metric [2] is undoubtedly the most remarkable exact solution in the Einstein theory of general relativity, which represents the prototypical black hole that can arise from gravitational collapse, which contains an event horizon [3]. Thanks to the no-hair theorem, the vacuum region outside a stationary black hole has a Kerr geometry. It is believed that spacetime singularities do not exist in Nature; they are a creation of general relativity. It turns out that we need to ask to what extent a singularity in general relativity could be adequately explained by some other theory, say, quantum gravity. However, we are yet afar from a specific theory of quantum gravity. So a suitable course of action is to understand the inside of a black hole and resolve its singularity by carrying out research of a

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“…In fact, Lake and Musgrave [22] have takenthe set of fourteen independent second-order curvature invariants found by Carminati and McLenaghan [23] and worked out the necessary and sufficient conditions for them to be finite at the origin of certain static space-times; for the cylindrically symmetric case the conditions are, in our coordinate system, those deduced above, namely…”

Section: The Field Equationsmentioning

confidence: 99%

“…Equations (21) may be taken as defining the constants A, B and C; in (22) there are three conditions for the two constants σ and k, but since…”

Section: Solutions With a Boundarymentioning

confidence: 99%

Perfect-fluid cylinders and walls - sources for the Levi-Civita spacetime

Philbin

1996

Class. Quantum Grav.

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The diagonal metric tensor whose components are functions of one spatial coordinate is considered. Einstein's field equations for a perfect-fluid source are reduced to quadratures once a generating function, equal to the product of two of the metric components, is chosen. The solutions are either static fluid cylinders or walls depending on whether or not one of the spatial coordinates is periodic. Cylinder and wall sources are generated and matched to the vacuum (LeviCivita) space-time. A match to a cylinder source is achieved for − 1 2 < σ < 1 2 , where σ is the mass per unit length in the Newtonian limit σ → 0, and a match to a wall source is possible for |σ| > 1 2 , this case being without a Newtonian limit; the positive (negative) values of σ correspond to a positive (negative) fluid density. The range of σ for which a source has previously been matched to the Levi-Civita metric is 0 ≤ σ < 1 2 for a cylinder source.

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The regularity of static spherically cylindrically and plane symmetric spacetimes at the origin

Cited by 22 publications

References 2 publications

Static circularly symmetric perfect fluid solutions with an exterior BTZ metric

Static circularly symmetric perfect fluid solutions with an exterior BTZ metric

A nonsingular rotating black hole

Perfect-fluid cylinders and walls - sources for the Levi-Civita spacetime

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