The ghost of vector fields in compact stars

TL;DR

This paper investigates whether spontaneous vectorization can occur in compact stars, finding that ghost instabilities prevent straightforward generalization of scalarization mechanisms to vector fields.

Contribution

The study performs a perturbative analysis of vector field models in compact stars, revealing ghost instabilities that hinder spontaneous vectorization.

Findings

Ghost instabilities arise when effective mass squared becomes negative.

Spontaneous scalarization does not straightforwardly extend to vector fields.

Obstacles to vectorization challenge alternative gravity theories.

Abstract

Spontaneous scalarization is a mechanism that allows a scalar field to go undetected in weak gravity environments and yet develop a nontrivial configuration in strongly gravitating systems. At the perturbative level it manifests as a tachyonic instability around spacetimes that solve Einstein's equations. The endpoint of this instability is a nontrivial scalar field configuration that can significantly modify a compact object's structure and can produce observational signatures of the scalar field's presence. Does such a mechanism exists for vector fields? Here we revisit the model that constitutes the most straightforward generalization of the original scalarization model to a vector field and perform a perturbative analysis. We show that a ghost appears as soon as the square of the naive effective mass squared becomes negative anywhere. This result poses a serious obstacle in generalizing spontaneous scalarization to vector fields.