Near spacetime singularities, Synge's world function and van Vleck determinant exhibit drastically altered scaling that reveals non-trivial geodesic flow structures.
Minimal Length and Small Scale Structure of Spacetime
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abstract
Many generic arguments support the existence of a minimum spacetime interval $L_0$. Such a "zero-point" length can be naturally introduced in a locally Lorentz invariant manner via Synge's world function bi-scalar $\Omega(p,P)$ which measures squared geodesic interval between spacetime events $p$ and $P$. I show that there exists a \emph{non-local} deformation of spacetime geometry given by a \emph{disformal} coupling of metric to the bi-scalar $\Omega(p,P)$, which yields a geodesic interval of $L_0$ in the limit $p \rightarrow P$. Locality is recovered when $\Omega(p,P) >> L_0^2/2$. I discuss several conceptual implications of the resultant small-scale structure of spacetime for QFT propagators as well as spacetime singularities.
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UNVERDICTED 2representative citing papers
O(ℓ²) corrections to Padmanabhan's duality-invariant propagator are realized by a free massive scalar field in Euclidean R^{D+2}.
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Geodesic structure of spacetime near singularities
Near spacetime singularities, Synge's world function and van Vleck determinant exhibit drastically altered scaling that reveals non-trivial geodesic flow structures.
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On Padmanabhan's duality invariance and the quantum of length
O(ℓ²) corrections to Padmanabhan's duality-invariant propagator are realized by a free massive scalar field in Euclidean R^{D+2}.