Abstract
Nonstationary, spherically symmetric solutions of the coupled field equationsR μυ=2φ,μφ,υ and □φ=0, in which the coupling polarity is opposite to the orthodox, are derived. The basic solution, termed the evolving, flowless drainhole manifold, has these properties: (1) geodesic completeness; (2) a topological hole that shrinks to a point at a singular event and immediately begins to expand back to infinite size; (3) multiple branching of geodesics that arrive at the singular event; (4) asymptotic flatness at spatial infinity, luminal infinity, and temporal infinity; (5) isometric symmetry under time reversal and under space reflection through the drainhole; (6) conformal symmetry under space-time dilatations that leave the singular event fixed, and also under space-time inversions that interchange the singular event and a point at infinity. An earlier, static drainhole solution of the same equations was able to represent an ordinary star's external field or to serve as a model of a simple gravitating or nongravitating particle, replacing in these capacities the Kruskal-Fronsdal-Schwarzschild black-hole manifolds. The evolving, flowless drainhole can be thought of as modeling the death and rebirth of a scalar particle that is infinitely large in the infinite past and the infinite future. This particle does not gravitate, for the “ether flow” whose spatial variations in the static drainhole solution are identified with gravitation is removed from consideration in the evolving, flowless drainhole solution by being turned off at the outset. What is left is space alone, evolving dynamically in accordance with the field equations.
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Ellis, H.G. The evolving, flowless drainhole: A nongravitating-particle model in general relativity theory. Gen Relat Gravit 10, 105–123 (1979). https://doi.org/10.1007/BF00756794
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DOI: https://doi.org/10.1007/BF00756794