# Compact binary systems in scalar-tensor gravity: Equations of motion to 2.5 post-Newtonian order

**Authors:** Saeed Mirshekari, Clifford M. Will  
**arXiv:** [1301.4680](https://arxiv.org/abs/1301.4680)  
**Date:** 2013-01-20  
**Summary page:** https://www.summarizepaper.com/en/paper/1301.4680v1/

## Key points

- Saeed Mirshekari and Clifford M. Will study scalar-tensor theories of gravity focusing on non-spinning compact objects up to 2.5 post-Newtonian order.
- They use the DIRE formalism tailored to scalar-tensor theory and Eardley's method for internal gravity within self-gravitating bodies.
- The researchers derive the two-body Lagrangian, determine conserved energy and momentum up to second post-Newtonian order for conservative motion.
- Their investigation includes exploring 1.5 post-Newtonian and 2.5 post-Newtonian contributions to gravitational radiation reaction, particularly dipole gravitational radiation effects.
- Findings align with previous energy flux calculations, validating their approach.
- Motion up to 2.5 post-Newtonian order in binary black hole systems matches general relativity predictions.
- Deviations from general relativity occur in mixed black hole-neutron star binary configurations beyond the first post-Newtonian order due to dipole gravitational radiation influences.
- Deviations in mixed system motion are governed by a singular parameter dependent on the scalar-tensor coupling constant and neutron star structure.
- This parameter's influence remains consistent across various scalar-tensor theories similar to pure Brans-Dicke theory, advancing understanding of gravitational dynamics in such frameworks.

## Summary

In their study, Saeed Mirshekari and Clifford M. Will delve into the realm of scalar-tensor theories of gravity to analyze the explicit equations of motion for non-spinning compact objects up to 2.5 post-Newtonian order. By employing the DIRE formalism tailored to scalar-tensor theory and incorporating Eardley's method for accounting for internal gravity within compact self-gravitating bodies, the researchers make significant strides in understanding the dynamics of gravitational interactions. Through meticulous calculations, they derive the two-body Lagrangian and determine conserved energy and momentum up to second post-Newtonian order for the conservative component of motion. Their investigation extends to exploring 1.5 post-Newtonian and 2.5 post-Newtonian contributions to gravitational radiation reaction with a specific focus on dipole gravitational radiation effects. Remarkably, their findings align with previous assessments of energy flux calculations validating the accuracy of their approach. The researchers also shed light on binary black hole systems demonstrating that motion up to 2.5 post-Newtonian order mirrors predictions made by general relativity. However, when examining mixed black hole-neutron star binary configurations deviations from general relativity manifest beyond the first post-Newtonian order due in part to dipole gravitational radiation influences. Notably, through rigorous analysis extending to 2.5 post-Newtonian order Mirshekari and Will reveal that these deviations in mixed system motion are governed by a singular parameter dependent solely on the scalar-tensor coupling constant and neutron star structure. Intriguingly this parameter's influence remains consistent across a broad spectrum of scalar-tensor theories akin to pure Brans-Dicke theory. This comprehensive exploration not only advances our comprehension of gravitational dynamics within scalar-tensor frameworks but also underscores the intricate interplay between theoretical models and observational data in elucidating complex astrophysical phenomena involving compact binary systems.