Generalized disformal coupling leads to spontaneous tensorization

TL;DR

This paper explores how disformal metric transformations in gravity theories can cause spontaneous growth of vector fields, leading to potential observable deviations from general relativity in strong gravity regimes.

Contribution

It extends the concept of spontaneous tensorization to disformal couplings involving vectors and analyzes the absence of such effects for spinor fields.

Findings

Vector disformal couplings induce spontaneous vectorization.

Spontaneous growth is not observed for spinor fields.

Results are relevant for gravitational wave observations.

Abstract

We show that gravity theories involving disformally transformed metrics in their matter coupling lead to spontaneous growth of various fields in a similar fashion to the spontaneous scalarization scenario in scalar-tensor theories. Scalar-dependent disformal transformations have been investigated in this context, and our focus is understanding the transformations that depend on more general fields. We show that vector-dependent disformal couplings can be obtained in various different ways, each leading to spontaneous vectorization as indicated by the instabilities in linearized equations of motion. However, we also show that spontaneous growth is not evident beyond vectors. For example, we could not identify a spontaneous growth mechanism for a spinor field through disformal transformations, even though there is a known example for conformal transformations. This invites further work on the fundamental differences between the two types of metric transformations. We argue that our results are relevant for observations in strong gravity such as gravitational wave detections due to their promise of large deviations from general relativity in this regime.