The square of the Weyl tensor can be negative

TL;DR

This paper demonstrates that the square of the Weyl tensor, a measure of spacetime curvature, can take negative values by providing a specific example, challenging previous assumptions about its positivity.

Contribution

It provides the first explicit example showing the Weyl tensor squared can be negative, which was previously thought to be non-negative.

Findings

Weyl tensor squared can be negative in certain spacetimes

Explicit example constructed to demonstrate negativity

Challenges assumptions about positivity of curvature invariants

Abstract

We show that the square of the Weyl tensor can be negative by giving an example.