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

Abstract

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 targetspace 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.

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