Geodesic Incompleteness and Partially Covariant Gravity

Universe

Spiros Cotsakis¹  Ignatios Antoniadis² 

[1] Institute of Gravitation and Cosmology, RUDN University, ul. Miklukho-Maklaya 6, 117198 Moscow, Russia;Laboratoire de Physique Théorique et Hautes Energies—LPTHE, Sorbonne Université, CNRS 4 Place Jussieu, 75005 Paris, France;

关键词: Hořava–Lifshitz gravity;    geodesic incompleteness;    geometric flows;   

DOI  :  10.3390/universe7050126

来源: DOAJ

【 摘 要 】

We study the issue of length renormalization in the context of fully covariant gravity theories as well as non-relativistic ones such as Hořava–Lifshitz gravity. The difference in their symmetry groups implies a relation among the lengths of paths in spacetime in the two types of theory. Provided that certain asymptotic conditions hold, this relation allows us to transfer analytic criteria for the standard spacetime length to be finite and the Perelman length to be likewise finite, and therefore formulate conditions for geodesic incompleteness in partially covariant theories. We also discuss implications of this result for the issue of singularities in the context of such theories.

【 授权许可】

Unknown