A no-go on strictly stationary spacetimes in four/higher dimensions

TL;DR

This paper proves that strictly stationary spacetimes in four or higher dimensions cannot support non-trivial form or scalar fields, implying such fields only exist in trivial Minkowski or anti-de Sitter backgrounds.

Contribution

It establishes a no-go theorem showing the incompatibility of non-trivial form and scalar fields with strictly stationary spacetimes in higher dimensions.

Findings

Strictly stationary spacetimes cannot support non-trivial form or scalar fields.

Such spacetimes are limited to Minkowski or anti-de Sitter geometries.

Self-gravitating complex scalar and form fields are forbidden in these settings.

Abstract

We show that strictly stationary spacetimes cannot have non-trivial configurations of form fields/complex scalar fields and then the spacetime should be exactly Minkowski or anti-deSitter spacetimes depending on the presence of negative cosmological constant. That is, self-gravitating complex scalar fields and form fields cannot exist.