# More than the sum of its parts: combining parameterized tests of extreme gravity

## TL;DR

This paper links two formalisms describing deviations from general relativity in neutron stars and gravitational waves, showing how strong-field deformations affect gravitational wave signals and enabling constraints on alternative gravity theories using GW170817.

## Contribution

It introduces a framework connecting strong-field and radiative regime formalisms, allowing combined tests of gravity with neutron star and gravitational wave data.

## Key findings

- Deformations in neutron star exterior metrics influence gravitational wave phases.
- GW170817 data constrains post-Tolman-Oppenheimer-Volkoff parameters.
- The approach enables theory-independent tests of gravity.

## Abstract

We connect two formalisms that describe deformations away from general relativity, one valid in the strong-field regime of neutrons stars and another valid in the radiative regime of gravitational waves: the post-Tolman-Oppenheimer-Volkoff and the parametrized-post-Einsteinian formalisms respectively. We find that post-Tolman-Oppenheimer-Volkoff deformations of the exterior metric of an isolated neutron star induce deformations in the orbital binding energy of a neutron star binary. Such a modification to the binding energy then percolates into the gravitational waves emitted by such a binary, with the leading-order post-Tolman-Oppenheimer-Volkoff modifications introducing a second post-Newtonian order correction to the gravitational wave phase. The lack of support in gravitational wave data for general relativity deformations at this post-Newtonian order can then be used to place constraints post-Tolman-Oppenheimer-Volkoff parameters. As an application, we use the binary neutron star merger event GW170817 to place the constraint $-2.4 \leq \chi \leq 44$ (at 90% credibility) on a combination of post-Tolman-Oppenheimer-Volkoff parameters. We also explore the implications of this result to the possible deformations of the mass-radius relation of neutron stars allowed within this formalism. This work opens the path towards theory-independent tests of gravity, combining astronomical observations of neutron stars and gravitational wave observations.