Search results for "Schwarzschild coordinates"
showing 3 items of 3 documents
Flat synchronizations in spherically symmetric space-times
2010
It is well known that the Schwarzschild space-time admits a spacelike slicing by flat instants and that the metric is regular at the horizon in the associated adapted coordinates (Painleve-Gullstrand metric form). We consider this type of flat slicings in an arbitrary spherically symmetric space-time. The condition ensuring its existence is analyzed, and then, we prove that, for any spherically symmetric flat slicing, the densities of the Weinberg momenta vanish. Finally, we deduce the Schwarzschild solution in the extended Painleve-Gullstrand-Lemaitre metric form by considering the coordinate decomposition of the vacuum Einstein equations with respect to a flat spacelike slicing.
Schwarzschild Interior in Conformally Flat Form
2004
A unified conformally flat form of the static Schwarzschild interior space–times is provided. A new parameter that allows us to analyze the symmetry (spherical, plane or hyperbolic) of the three well known classes of metrics is introduced. In the spherically symmetric case, this parameter is related to the historical limit value of the mass to radius ratio found by Schwarzschild for a sphere of incompressible fluid.
An intrinsic characterization of the Schwarzschild metric
1998
An intrinsic algorithm that exclusively involves conditions on the metric tensor and its differential concomitants is presented to identify every type-D static vacuum solution. In particular, the necessary and sufficient explicit and intrinsic conditions are given for a Lorentzian metric to be the Schwarzschild solution.