# Measuring scalar charge with compact binaries: High accuracy modelling with self-force

**Authors:** Andrew Spiers, Andrea Maselli, Thomas P. Sotiriou  
**arXiv:** [2310.02315](https://arxiv.org/abs/2310.02315)  
**Date:** 2023-10-03  
**Summary page:** https://www.summarizepaper.com/en/paper/2310.02315v1/

## Key points

- Mathews, Pound, and Wardell (2022) present a high-accuracy formalism for modeling compact binaries in theories with a massless scalar field non-minimally coupled to gravity.
- They focus on the case of a non-spinning compact body with no scalar dipole.
- The authors derive first- and second-order perturbative field equations and equations of motion for the secondary compact object.
- The goal is to produce waveform templates accurate enough for precision measurements of the scalar charge of the secondary using data from extreme-mass-ratio inspirals collected by LISA.
- The formalism is consistent with almost all general scalar-tensor theories of gravity.
- It can be integrated into existing models in General Relativity using the two-timescale formalism used in self-force models.
- Implementing this approach is not significantly more challenging than computing first post adiabatic waveforms in General Relativity.
- Future work will address spinning and scalar dipole cases.
- References to related studies are provided for further context.

## Summary

In their recent work, Mathews, Pound, and Wardell (2022) present a high-accuracy formalism for modeling compact binaries in theories with a massless scalar field non-minimally coupled to gravity. They employ the self-force approach and focus on the case of a non-spinning compact body with no scalar dipole. The authors derive first- and second-order perturbative field equations and equations of motion for the secondary compact object by introducing an ansatz for the scalar charged point particle action. The main goal of this formalism is to produce waveform templates that are sufficiently accurate for precision measurements of the scalar charge of the secondary using data from extreme-mass-ratio inspirals collected by the Laser Interferometer Space Antenna (LISA). The authors emphasize that their formalism is consistent with almost all general scalar-tensor theories of gravity. To incorporate their formalism into existing models in General Relativity, Mathews et al. show that it can be straightforwardly integrated into the two-timescale formalism used in self-force models. They highlight that implementing their approach does not pose significantly more challenging barriers than computing first post adiabatic waveforms in General Relativity. It is worth noting that while this work focuses on non-spinning compact bodies without scalar dipoles, Mathews et al. mention they plan to address spinning and scalar dipole cases in an upcoming paper. Additionally, they provide references to related studies by Drummond and Hughes (2022a,b), Drummond et al. (2023), Sotiriou et al. (2019), Hawking (1972), Faraoni et al. (2012), Hui and Nicolis (2013), Zhou et al. (2014), Thaalba et al. (2021), Antoniou et al. (2023), Kanti et al. (1996), Maselli et al. (2022), Barsanti et al. (2022) and Thaalba et al. (2020) for further context. Overall, this work by Mathews, Pound, and Wardell presents a promising formalism for accurately modeling compact binaries in theories with a massless scalar field non-minimally coupled to gravity.