THE TOPOLOGY OF SCHWARZSCHILD'S SOLUTION
AND THE KRUSKAL METRIC
SALVATORE ANTOCI AND DIERCK-EKKEHARD LIEBSCHER
Abstract. Kruskal's extension solves the problem of the arrow of time
of the "Schwarzschild solution" through combining two Hilbert mani-
folds by a singular coordinate transformation. We discuss the implica-
tions for the singularity problem and the definition of the mass point.
The analogy set by Rindler between the Kruskal metric and the
Minkowski spacetime is investigated anew. The question is answered,
whether this analogy is limited to a similarity of the chosen "Bildršaume",
or can be given a deeper, intrinsic meaning. The conclusion is reached by
observing a usually neglected difference: the left and right quadrants of
Kruskal's metric are endowed with worldlines of absolute rest, uniquely
defined through each event by the manifold itself, while such worldlines
obviously do not exist in the Minkowski spacetime.
1. Introduction: Kruskal's extension of the Schwarzschild
solution and the arrow of time
In general, a manifold cannot be covered by a single coordinate system.
An atlas of coordinate systems is required, and it reflects the global prop-