# Spontaneous tensorization from curvature coupling and beyond

## TL;DR

This paper extends scalar-tensor-Gauss-Bonnet theories to include spontaneous growth of nonscalar fields like vectors, enriching the phenomenology of spontaneous tensorization and its implications for strong gravity tests.

## Contribution

It introduces a broader class of theories allowing spontaneous tensorization beyond scalars, including vectors, and discusses their theoretical properties and phenomenological implications.

## Key findings

- Theories can produce large signals in strong gravity regimes.
- Spontaneous tensorization can occur for vector fields.
- Derivative couplings may introduce higher derivatives in equations.

## Abstract

We generalize the recently introduced extended scalar-tensor-Gauss-Bonnet (ESTGB) theories and their close relatives to include spontaneous growth of nonscalar fields such as vectors. This is analogous to the program that developed spontaneous tensorization from the original spontaneous scalarization theory of Damour and Esposito-Far\`ese (DEF). The new larger family of theories conserves the appeal of the DEF theory in terms of conforming to weak-field tests and also providing large signals in strong gravity. Moreover, they provide a much richer phenomenology including spontaneous tensorization of black holes as in ESTGB. These theories, together with other possible future extensions that we discuss, testify to the ubiquity of spontaneous growth in gravity. We also note that theories with derivative coupling require special attention since they can lead to potentially problematic higher derivatives in the equations of motion.