Matching of the Vaidya and Robertson-Walker metric

Abstract

The authors give the necessary conditions for the matching of a general Robertson-Walker geometry to general spherically symmetric radiating metric. They also found the conditions for the matching of a Vaidya metric (1951) to a general Robertson-Walker metric. The possible applications of the results to the stellar collapse and to the study of local inhomogeneities in a cosmological context are considered. An alternative interpretation of the energy-momentum tensor of the Robertson-Walker part of spacetime is given in such a way that the physical processes can be better understood.

Interiors of Vaidya's radiating metric: Gravitational collapse

“…Of course, this is a very natural result. On the other hand, (21) informs us that the total normal pressure must vanish on the matching surface, which again is a very satisfactory result and generalizes similar properties in the static case. In fact, (21) is strictly equivalent to the matching condition (10).…”

“…On the other hand, (21) informs us that the total normal pressure must vanish on the matching surface, which again is a very satisfactory result and generalizes similar properties in the static case. In fact, (21) is strictly equivalent to the matching condition (10). In order to prove this, let us note that (21) is generated by which via Einstein's equations can be rewritten in terms of the Einstein tensor GI,, as Now, by using (A81, ( 1 11, and (AI)-(A4), it is straightforward to show that this last relation, and therefore (21), leads exactly to the matching condition (10).…”

Gravitational Collapse without a Remnant

“…which has been studied extensively [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]24]. In particular, the gravitational collapse of a radiating spherical star with heat flow has been studied in an isotropic coordinate system [17][18][19] …”

“…In Sect. 4, as examples, several numerical solutions are presented. The concluding remarks are given in Sect.…”

Gravitational collapse of quantum matter

“…This was followed some years later by the Vaidya solution [2] which describes the collapse of pressureless null dust to a Schwarzschild black hole. Models of this type have been much studied in various contexts [3][4][5][6][7] There is a generalization of the Vaidya solution to a null dust with pressure, with equation of state P = kρ [8], which gives the Reissner-Nordstrum charged black hole for k = 1, and a more general class of hairy black holes for k > 1 as the end point of collapse. Although these solutions are analytic, they describe purely ingoing (or outgoing) matter in spherical symmetry.…”