Sectional Curvature Bounds in Gravity: Regularisation of the Schwarzschild Singularity

TL;DR

This paper introduces a geometric framework for gravity theories with sectional curvature bounds, leading to regularized black hole solutions that exclude spacelike singularities, differing significantly from classical Schwarzschild solutions.

Contribution

It develops a universal geometric scheme for constructing gravity theories with curvature bounds, resulting in singularity-free solutions in static, spherically symmetric spacetimes.

Findings

Excludes spacelike singularities in black hole solutions.

Provides a new regularisation mechanism for gravitational singularities.

Shows significant deviations from classical Schwarzschild solutions.

Abstract

A general geometrical scheme is presented for the construction of novel classical gravity theories whose solutions obey two-sided bounds on the sectional curvatures along certain subvarieties of the Grassmannian of two-planes. The motivation to study sectional curvature bounds comes from their equivalence to bounds on the acceleration between nearby geodesics. A universal minimal length scale is a necessary ingredient of the construction, and an application of the kinematical framework to static, spherically symmetric spacetimes shows drastic differences to the Schwarzschild solution of general relativity by the exclusion of spacelike singularities.