Tensor-multi-scalar theories: relativistic stars and 3+1 decomposition

TL;DR

This paper explores tensor-multi-scalar theories with two scalar fields, analyzing their effects on relativistic stars and providing a 3+1 decomposition of the field equations for future numerical simulations.

Contribution

It introduces a simple two-scalar-field model with a maximally symmetric target space and investigates spontaneous scalarization in relativistic stars.

Findings

Scalarization threshold depends on eigenvalues of the coupling matrix.

Strongly scalarized stars are influenced by target-space curvature.

Provides a 3+1 decomposition for tensor-multi-scalar theories.

Abstract

Gravitational theories with multiple scalar fields coupled to the metric and each other --- a natural extension of the well studied single-scalar-tensor theories --- are interesting phenomenological frameworks to describe deviations from general relativity in the strong-field regime. In these theories, the $N$-tuple of scalar fields takes values in a coordinate patch of an $N$-dimensional Riemannian target-space manifold whose properties are poorly constrained by weak-field observations. Here we introduce for simplicity a non-trivial model with two scalar fields and a maximally symmetric target-space manifold. Within this model we present a preliminary investigation of spontaneous scalarization for relativistic, perfect fluid stellar models in spherical symmetry. We find that the scalarization threshold is determined by the eigenvalues of a symmetric scalar-matter coupling matrix, and that the properties of strongly scalarized stellar configurations additionally depend on the target-space curvature radius. In preparation for numerical relativity simulations, we also write down the $3+1$ decomposition of the field equations for generic tensor-multi-scalar theories.