The charged dust solution of Ruban: matching to Reissner–Nordström and shell crossings

Krasiński, Andrzej; Giono, Gabriel

doi:10.1007/s10714-011-1274-7

Cited by 3 publications

(2 citation statements)

References 20 publications

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“…Several papers look at models of spherical collapse to Reissner-Nordström, such as [14][15][16]. Most papers considering collapsing models focus on the interior of the collapsing star.…”

Section: Previous Workmentioning

confidence: 99%

The scattering map on collapsing charged spherically symmetric spacetimes

Alford

2024

Class. Quantum Grav.

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In this paper we generalise our previous results [1] concerning scattering on the exterior of collapsing dust clouds to the charged case, including in particular the extremal case. We analyse the energy boundedness of solutions $\phi$ to the wave equation on the exterior of collapsing spherically symmetric charged matter clouds. We then proceed to define the scattering map on this spacetime, and look at the implications of our boundedness results on this map. More specifically, we first construct a class of spherically symmetric charged collapsing matter cloud exteriors, and then consider solutions to the wave equation with Dirichlet (reflective) boundary conditions on the surface of these clouds. We then show that the energy of $\phi$ remains uniformly bounded going forwards or backwards in time, and that the scattering map is bounded going forwards but not backwards. Therefore, the scattering map is not surjective onto the space of finite energy on $\mathcal{I}^+\cup\mathcal{H}^+$. Thus there does not exist a backwards scattering map from finite energy radiation fields on $\mathcal{I}^+\cup\mathcal{H}^+$ to finite energy radiation fields on $\mathcal{I}^-$ for these models.These results will be used to give a treatment of Hawking radiation in a companion paper [2].

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“…Several papers look at models of spherical collapse to Reissner-Nordström, such as [14][15][16]. Most papers considering collapsing models focus on the interior of the collapsing star.…”

Section: Previous Workmentioning

confidence: 99%

The scattering map on collapsing charged spherically symmetric spacetimes

Alford

2024

Class. Quantum Grav.

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“…it can be proved that, for any shell, quantities R [R min (a)] and R [R max (a)] have opposite signs and, consequently, R [R(a, T )] vanishes for some R between R min (a) and R max (a); hence, for β = 1 the use of comoving coordinates numbering shells is not a good choice to fully describe the internal shells collapse. A similar situation it is analyzed in [17] and [24] for a spherically symmetric charged dust collapse, and also in [25] where the charged dust solution of Ruban [26], a generalisation of the Datt [27] solution for a non-charged dust is considered. It can be found in [28] that, in spite of the inclusion of a positive cosmological constant, this repulsion does not prevent the shell crossings.…”

Section: Shell Crossingsmentioning

confidence: 99%

Spherical symmetric dust collapse in vector-tensor gravity

Dale

Sáez

2018

Phys. Rev. D

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There is a viable vector-tensor gravity (VTG) theory, whose vector field produces repulsive forces leading to important effects. In the background universe, the effect of these forces is an accelerated expansion identical to that produced by vacuum energy (cosmological constant). Here, we prove that another of these effects arises for great enough collapsing masses which lead to Schwarzschild black holes and singularities in general relativity (GR). For these masses, pressure becomes negligible against gravitational attraction and the complete collapse cannot be stopped in the context of GR; however, in VTG, a strong gravitational repulsion could stop the falling of the shells towards the symmetry center. A certain study of a collapsing dust cloud is then developed and, in order to undertake this task, the VTG equations in comoving coordinates are written. In this sense and, as it happens in general relativity for a pressureless dust ball, three different solutions are found. These three situations are analyzed and the problem of the shell crossings is approached. The apparent horizons and trapped surfaces, whose analysis will lead to diverse situations, depending on certain theory characteristic parameter value, are also examined. I. INTRODUCTION Any vector-tensor theory of gravitation involves the metric tensor g µν and a vector field A µ. These fields are coupled to build up an appropriate action leading to the basic equations via variational calculations. There are many actions and vector-tensor theories [1, 2], but one of them has been extensively studied to conclude that: (i) it has not either classical or quantum instabilities and, (ii) it explains-as well as general relativity (GR)-both cosmological and solar system observations [3-7]; hence, new applications of this viable and promising theory are worthwhile. Since there are opposite gravitational forces, this theory will be hereafter called AR-VTG (attractive-repulsive vector-tensor gravity). As it was shown in [6], for appropriate values of the AR-VTG parameters (see below), there are black hole event horizons with admissible radii which are a little smaller than those of GR; nevertheless, for other values of these parameters, there are no horizons of this kind.

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New classes of spherically symmetric, inhomogeneous cosmological models

Gürses

Heydarzade

2019

Phys. Rev. D

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We present two classes of inhomogeneous, spherically symmetric solutions of the Einstein-Maxwell-Perfect Fluid field equations with cosmological constant generalizing the Vaidya-Shah solution. Some special limits of our solution reduce to the known inhomogeneous charged perfect fluid solutions of the Einstein field equations and under some other limits we obtain new charged and uncharged solutions with cosmological constant. Uncharged solutions in particular represent cosmological models where the universe oscillates between two Friedman-Robertson-Walker universes with different spatial curvatures. We show that there exist some spacelike surfaces where the pressure and mass density of the fluid distribution diverge. We study the behavior of our new solutions in their general form as the radial distance goes to zero and infinity. Finally, we briefly address the null geodesics and apparent horizons associated to the obtained solutions. *

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The charged dust solution of Ruban: matching to Reissner–Nordström and shell crossings

Cited by 3 publications

References 20 publications

The scattering map on collapsing charged spherically symmetric spacetimes

The scattering map on collapsing charged spherically symmetric spacetimes

Spherical symmetric dust collapse in vector-tensor gravity

New classes of spherically symmetric, inhomogeneous cosmological models

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