Degenerate wormholes defined by vanishing metric determinant g at the throat are exact vacuum solutions to g²-modified Einstein equations, unifying Einstein-Rosen bridge and Klinkhamer wormholes as limits of non-degenerate cases with exotic matter.
Topology Change in Classical General Relativity
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abstract
This paper clarifies some aspects of Lorentzian topology change, and it extends to a wider class of spacetimes previous results of Geroch and Tipler that show that topology change is only to be had at a price. The scenarios studied here are ones in which an initial spacelike surface is joined by a connected ``interpolating spacetime'' to a final spacelike surface, possibly of different topology. The interpolating spacetime is required to obey a condition called causal compactness, a condition satisfied in a very wide range of situations. No assumption is made about the dimension of spacetime. First, it is stressed that topology change is kinematically possible; i.e., if a field equation is not imposed, it is possible to construct topology-changing spacetimes with non-singular Lorentz metrics. Simple 2-dimensional examples of this are shown. Next, it is shown that there are problems in such spacetimes: Geroch's closed-universe argument is applied to causally compact spacetimes to show that even in this wider class of spacetimes there are causality violations associated with topology change. It follows from this result that there will be causality violations if the initial (or the final) surface is not connected, even when there is no topology change. Further, it is shown that in dimensions $\geq 3$ causally compact topology-changing spacetimes cannot satisfy Einstein's equation (with a reasonable source); i.e., there are severe dynamical obstructions to topology change. This result extends a previous one due to Tipler. Like Tipler's result, it makes no assumptions about geodesic completeness; i.e., it does not permit topology change even at the price of singularities (of the standard incomplete-geodesic variety). Brief discussions are also given of ways in which the results of this paper might be circumvented.
verdicts
UNVERDICTED 4representative citing papers
Wormhole nucleation is achieved via 0-surgery yielding a singular cobordism, resolved by connected sum with CP² to produce a nonsingular Lorentzian metric with closed timelike curves and violated energy conditions.
A new metric-affine gravity toy model dynamically generates a global time function via projective invariance breaking to enforce stable causality, recovering mimetic gravity and yielding a broader dark sector.
Using an extended equivalence principle on the Klinkhamer metric, the radial dynamics of a degenerate wormhole reduce to test-particle fall in Schwarzschild spacetime, proving collapse of bound traversable states into Einstein-Rosen wormholes with a long lifetime estimate.
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Non-degenerate and degenerate wormholes: a unified approach
Degenerate wormholes defined by vanishing metric determinant g at the throat are exact vacuum solutions to g²-modified Einstein equations, unifying Einstein-Rosen bridge and Klinkhamer wormholes as limits of non-degenerate cases with exotic matter.
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Wormhole Nucleation via Topological Surgery in Lorentzian Geometry
Wormhole nucleation is achieved via 0-surgery yielding a singular cobordism, resolved by connected sum with CP² to produce a nonsingular Lorentzian metric with closed timelike curves and violated energy conditions.
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Metric affine gravity with dynamical chronology protection
A new metric-affine gravity toy model dynamically generates a global time function via projective invariance breaking to enforce stable causality, recovering mimetic gravity and yielding a broader dark sector.
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Matter-free gravitational collapse and the equivalence principle
Using an extended equivalence principle on the Klinkhamer metric, the radial dynamics of a degenerate wormhole reduce to test-particle fall in Schwarzschild spacetime, proving collapse of bound traversable states into Einstein-Rosen wormholes with a long lifetime estimate.