Sectional curvature bounds in gravity: regularisation of the Schwarzschild singularity

2004/03/12 by Frederic P. Schuller, F. Schüller, Mattias N. R. Wohlfarth · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2004.07.040

published as Nucl.Phys. B698 (2004) 319 · 20 pages, 1 figure, REVTeX4, updated references

arxiv created 2004/03/12 · openalex publication_date 2004/08/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Spacetime singularities in string theory
• Non-linear electrodynamics from quantized strings

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