# Equality in the Spacetime Positive Mass Theorem

## TL;DR

This paper proves the rigidity part of the spacetime positive mass theorem in dimensions less than eight, showing that zero energy-momentum implies flat spacetime under certain conditions, extending previous spin manifold results.

## Contribution

It extends the rigidity theorem to non-spin manifolds in dimensions less than eight, removing the previous restriction to spin manifolds.

## Key findings

- Proves the rigidity conjecture for dimensions <8.
- Shows that E=|P|=0 implies flat spacetime.
- Results hold under dominant energy condition and asymptotic flatness.

## Abstract

We affirm the rigidity conjecture of the spacetime positive mass theorem in dimensions less than eight. Namely, if an asymptotically flat initial data set satisfies the dominant energy condition and has $E=|P|$, then $E=|P|=0$, where $(E, P)$ is the ADM energy-momentum vector. The dimensional restriction can be removed if we assume the positive mass inequality holds. Previously the result was only known for spin manifolds.