Black holes and neutron stars in the generalized tensor-vector-scalar theory

TL;DR

This paper develops strong-field solutions for a generalized TeVeS theory, exploring neutron stars and black holes, and finds their solutions match those of the original theory under parameter mappings, with implications for stability and constraints.

Contribution

It introduces a generalized TeVeS framework with Einstein-Aether action and demonstrates that neutron star and black hole solutions are equivalent to the original TeVeS solutions under parameter mappings.

Findings

Solutions match original TeVeS solutions under parameter mapping

Provides constraints on coupling constants based on solution equivalence

Discusses stability and generalizations of these solutions

Abstract

Bekenstein's Tensor-Vector-Scalar (TeVeS) theory has had considerable success as a relativistic theory of Modified Newtonian Dynamics (MoND). However, recent work suggests that the dynamics of the theory are fundamentally flawed and numerous authors have subsequently begun to consider a generalization of TeVeS where the vector field is given by an Einstein-Aether action. Herein, I develop strong-field solutions of the generalized TeVeS theory, in particular exploring neutron stars as well as neutral and charged black holes. I find that the solutions are identical to the neutron star and black hole solutions of the original TeVeS theory, given a mapping between the parameters of the two theories, and hence provide constraints on these values of the coupling constants. I discuss the consequences of these results in detail including the stability of such spacetimes as well as generalizations to more complicated geometries.