Nonexistence of Generalized Apparent Horizons in Minkowski Space

TL;DR

This paper proves that generalized apparent horizons do not exist in Minkowski space, addressing a question about the presence of such horizons in flat spacetime.

Contribution

It establishes a Positive Mass Theorem for Einstein initial data with generalized trapped surfaces, solving a specific open problem about horizons in Minkowski space.

Findings

No generalized apparent horizons in Minkowski space.

Positive Mass Theorem applies to initial data with trapped surfaces.

Answers a question posed by R. Wald.

Abstract

We establish a Positive Mass Theorem for initial data sets of the Einstein equations having generalized trapped surface boundary. In particular we answer a question posed by R. Wald concerning the existence of generalized apparent horizons in Minkowski space.