Erratum: Avoidance of singularities in spherically symmetric charged dust [Phys. Rev. D73, 124033 (2006)]

Abstract

In spherically symmetric charged dust, just like in neutral dust, two kinds of singularity may be present: the Big Bang/Crunch (BB/BC) singularity, and shell crossings. Quite unlike in neutral dust, the BB/BC singularity may be avoided.When the charge density ρ e and the mass-energy density ǫ obey |ρ e | < D e def = √ Gǫ/c 2 , the conditions that allow the model to avoid the BB/BC singularity necessarily lead to shell crossings. However, when |ρ e | → D e at the center of symmetry while |ρ e | < D e elsewhere, both kinds of singularity may be avoided for a sufficiently long period that a body of charged dust may go through the tunnel between the singularities in the maximally extended Reissner -Nordström spacetime, to emerge into another asymptotically flat region. An explicit example of such a configuration is presented and discussed. It does not contradict any astrophysical constraints. Spherically symmetric dust in electromagnetic fieldFor the spherically symmetric spacetimes in the comoving coordinates, the metric can be put in the formThe case R, r = 0 requires separate consideration. In this case, a solution of the Einstein equations for electrically neutral dust was found by Datt [1] and then derived and interpreted by Ruban [2,3]; the corresponding Einstein-Maxwell equations were systematically derived and solved by Ruban [4,5,6]. We will discuss the solutions of the Einstein-Maxwell equations in the generic case R, r = 0. Most of the material of Sections 2 to 7 has been known for a long time, but a few points were overlooked by some of the earlier authors. That material is reviewed here in order to introduce the framework and notation, and to fill in the few little gaps. New results are reported in Sections 8 and following.

Collapse of spherical charged anisotropic fluid spacetimes

“…However the avoidance of shell focusing singularities -up to spacetime extension as said before -already found in [10] remains true for this wider class of (generally anisotropic) solutions, giving a first answer (in the negative) to the conjecture raised in [10] that the occurence of shell crossing singularities was determined by the vanishing of the pressure spatial gradient. It emerges that electromagnetic charge completely changes the final state of the collapsing star in this anisitropic case.…”

“…Therefore, one can say that the process of solution charging is -under a mathematical point of viewinternal to the class of models considered, i.e. those determined by the state function (10). Although the charged solution does not satisfy all the regularity properties of the original one, however it is possible to explicitly derive the metric and then to study its properties.…”

“…carrying a non-vanishing electric charge density ρ e . We introduce the skew-symmetrc Maxwell tensor F µν and, due to spherical symmetry and the absence of magnetic monopole [10,12], the only nonzero component is F 01 . From the Maxwell's equations…”

“…In [10] the charged spherical dust cloud collapse was studied to find that shell focusing singularities are avoided in general, obtaining either shell crossing singularities or completely regular solutions, depending on mass-to-charge ratio. In the same paper it was conjectured that shell crossing effects could be averted if spatial gradient of pressure remains nonzero.…”

Gravitational collapse of spherically symmetric plasmas in Einstein-Maxwell spacetimes

“…The role of EM fields in fully relativistic gravitational collapse has been the topic of much interest over recent years [2,3,4]. Of particular interest is the formation of naked singularities [5,6,7], the formation and evolution of charged neutron stars within the context of full general relativity [8,9,10], and the collapse of charged shells of matter * Electronic address: paul.lasky@sci.monash.edu.au † Electronic address: anthony.lun@sci.monash.edu.au onto existing black holes [11]. We utilize a formalism which puts general, spherically symmetric charged fluids into an initial value setting on a spacelike hypersurface such that all of these issues can be discussed either analytically or numerically.…”