On singular Yamabe obstructions

TL;DR

This paper investigates the singular Yamabe obstruction  in four-dimensional hypersurfaces, deriving explicit formulas and relating them to existing literature using elementary proofs.

Contribution

It provides new explicit formulas for the singular Yamabe obstruction  and connects these to prior results with straightforward proofs.

Findings

Explicit formulas for  derived

Connections made to existing literature

Elementary proofs provided

Abstract

We discuss the singular Yamabe obstruction $\mathcal{B}_3$ of a hypersurface in a four-dimensional general background. We derive various explicit formula for $\mathcal{B}_3$ from the original definition. We relate these formulas to corresponding formulas in the literature. The proofs are elementary.