# Neutron star sensitivities in Ho\v{r}ava gravity after GW170817

## TL;DR

This paper investigates neutron star sensitivities within Hořava gravity, finding that under certain conditions, violations of the strong equivalence principle are absent at leading post-Newtonian order, limiting observational constraints on the theory.

## Contribution

It demonstrates that neutron star sensitivities vanish for specific parameter choices in Hořava gravity, indicating no strong equivalence principle violations at leading order.

## Key findings

- Neutron star sensitivities are zero for $eta=0$ and $ ext{generic }
eq0$ in Hořava gravity.
- No violations of the strong equivalence principle occur at leading post-Newtonian order.
- Binary pulsar and gravitational wave data are unlikely to constrain $ ext{lambda}$ in this parameter regime.

## Abstract

Ho\v{r}ava gravity breaks boost invariance in the gravitational sector by introducing a preferred time foliation. The dynamics of this preferred slicing is governed, in the low-energy limit suitable for most astrophysical applications, by three dimensionless parameters $\alpha$, $\beta$ and $\lambda$. The first two of these parameters are tightly bound by solar system and gravitational wave propagation experiments, but $\lambda$ remains relatively unconstrained ($0\leq\lambda\lesssim 0.01-0.1$). We restrict here to the parameter space region defined by $\alpha=\beta=0$ (with $\lambda$ kept generic), which in a previous paper we showed to be the only one where black hole solutions are non-pathological at the universal horizon, and we focus on possible violations of the strong equivalence principle in systems involving neutron stars. We compute neutron star 'sensitivities', which parametrize violations of the strong equivalence principle at the leading post-Newtonian order, and find that they vanish identically, like in the black hole case, for $\alpha=\beta=0$ and generic $\lambda\neq0$. This implies that no violations of the strong equivalence principle (neither in the conservative sector nor in gravitational wave fluxes) can occur at the leading post-Newtonian order in binaries of compact objects, and that data from binary pulsars and gravitational interferometers are unlikely to further constrain $\lambda$.