Binary Inspirals in Nordstr\"om's Second Theory

TL;DR

This paper explores Nordstr"om's second theory of gravitation through numerical simulations of inspiraling binary stars, comparing results with semi-analytic predictions, and demonstrating the potential of these methods for modeling long binary inspirals.

Contribution

It develops numerical techniques for Nordstr"om's gravity theory and validates them against semi-analytic models, advancing methods for simulating binary inspirals.

Findings

Inspiral closely follows the 1/4 power law profile.

Eccentric binaries circularize and precess as expected.

Methods show promise for long binary inspiral modeling in relativity.

Abstract

We investigate Nordstr\"om's second theory of gravitation, with a focus on utilizing it as a testbed for developing techniques in numerical relativity. Numerical simulations of inspiraling compact star binaries are performed for this theory, and compared to the predictions of semi-analytic calculations (which are similar to Peters and Mathews' results for GR). The simulations are based on a co-rotating spherical coordinate system, where both finite difference and pseudo-spectral methods are used. We also adopt the "Hydro without Hydro" approximation, and the Weak Radiation Reaction approximation when the orbital motion is quasi-circular. We evolve a binary with quasi-circular initial data for hundreds of orbits and find that the resulting inspiral closely matches the 1/4 power law profile given by the semi-analytical calculations. We additionally find that an eccentric binary circularizes and precesses at the expected rates. The methods investigated thus provide a promising line of attack for the numerical modeling of long binary inspirals in general relativity.