Geodesic completeness from string T-duality
Kimet Jusufi, Piero Nicolini
TL;DR
This paper investigates geodesic completeness in a quantum-gravity–corrected spacetime inspired by string T-duality, using a static, spherically symmetric metric with a zero-point length $l_0$ that distributes mass over a finite region. By applying the Raychaudhuri equation in Painlevé–Gullstrand coordinates, it shows that the expansion $\Theta$ remains negative but finite and that the focusing term $d\Theta/d\tau$ is bounded and reaches a finite minimum, with a region where the strong energy condition is violated, allowing a smooth transition to a de Sitter core. The results demonstrate that gravity becomes repulsive at short distances, effectively screening the classical attraction and ensuring geodesic completeness ($\tau\to\infty$ as $r\to0$) for negative initial $\Theta$, while preserving Schwarzschild behavior at large $r$. Moreover, these conclusions hold model-independently for a broad class of regular black-hole metrics with $m(r)\sim r^\alpha$, $\alpha\ge3$, highlighting a local, universal quantum-gravity feature rather than a global spacetime property. Overall, the work argues that quantum gravity effects can avert curvature singularities via short-scale screening, reinterpreting classical gravity as an emergent, large-distance phenomenon.
Abstract
By studying the Raychaudhuri equation for the gravitational force resulting from a string T-duality modified propagator, we present an analysis of the geodesic compression beyond the conventional classical limit. The result is that gravity on short length scales is subject to a screening effect similar to the Debye screening in electrostatics, which prevents the formation of curvature singularities. Using model-independent arguments, we conclude that the conventional attractive nature of gravity is only a low-energy effect.