Constant scalar curvature hypersurfaces in extended Schwarzschild space-time

TL;DR

This paper introduces a class of spherically symmetric hypersurfaces with constant negative scalar curvature in the Kruskal extension of Schwarzschild space-time, highlighting their hyperboloidal nature in asymptotically flat regions.

Contribution

It constructs and analyzes hyperboloidal hypersurfaces with constant negative scalar curvature in Schwarzschild space-time's Kruskal extension, a novel geometric class.

Findings

Hypersurfaces are spherically symmetric and hyperboloidal.

They have constant negative scalar curvature.

Applicable in asymptotically flat regions of space-time.

Abstract

We present a class of spherically symmetric hypersurfaces in the Kruskal extension of the Schwarzschild space-time. The hypersurfaces have constant negative scalar curvature, so they are hyperboloidal in the regions of space-time which are asymptotically flat.