Singular vacuum solutions as singular matter solutions: Where do spacetime singularities come from?

Abstract

A direct evidence for the existence of spacetime singularities is the existence of singularities in vacuum solutions of the Einstein equation. A singular vacuum solution implies that spacetime itself may have singularities. In this paper, we exemplify that a singular vacuum solution can also serve as a non-vacuum solution of the Einstein equation with a singular matter source. If so, we may be able to think that there is no singularity in a vacuum spacetime; the singularity comes from an artificial singular matter source.

Cylindrical Gravitational Wave: Source and Resonance

“…That is, there is a Dirac delta source (charge) Q at the singularity r = 0 [34]. In Reference [35], we show that there is a Dirac delta source at r = 0 in the Schwarzschild spacetime.…”

“…We use the standard mathematical analysis to calculate the energy-momentum tensor at ρ = 0. More details of this method can be found in our previous work [35]. By replacing ρ by ρ 2 + 2 in Equations ( 12) and ( 13) and substituting the metric (1) into Equations ( 2)-( 5) by the Einstein equation G µν = 8πT µν , we obtain the following.…”

Cylindrical gravitational waves: radiation and resonance

“…We use a standard mathematical analysis method to calculate the energy-momentum tensor at ρ = 0. More details of this method can be found in our previous work [27]. Replacing ρ by ρ 2 + ǫ 2 in eqs.…”