# Gravitational-wave memory effects in Brans-Dicke theory: Waveforms and effects in the post-Newtonian approximation

**Authors:** Shammi Tahura, David A. Nichols, Kent Yagi  
**arXiv:** [2107.02208](https://arxiv.org/abs/2107.02208)  
**Date:** 2021-07-05  
**Summary page:** https://www.summarizepaper.com/en/paper/2107.02208v1/

## Key points

- Shammi Tahura, David A. Nichols, and Kent Yagi study gravitational-wave (GW) memory effects in Brans-Dicke theory
- Focus on tensor GW memory effect at Newtonian order in nonprecessing binaries
- Analysis reveals nonlinear components of displacement and spin GW memory effects during inspiral phase
- Study explores how modifications to general relativity theories impact gravitational-wave phenomena
- Comprehensive analysis includes calculating asymptotically flat solutions, symmetries, conserved quantities, and GW memory effects within Brans-Dicke theory
- Utilization of post-Newtonian approximation to compute GW memories from compact binaries
- Energy and angular momentum losses through scalar radiation considered negligible compared to losses through tensor GWs
- Corrections introduced due to energy radiated through scalar dipole moment at -1 PN order-effect
- Scalar radiation at Newtonian order results in distinct sky pattern for memory effect compared to GR scenarios

## Summary

In their study, Shammi Tahura, David A. Nichols, and Kent Yagi delve into the intricate realm of gravitational-wave (GW) memory effects within the framework of Brans-Dicke theory. Specifically focusing on the tensor GW memory effect at Newtonian order, they explore the nonlinear components of both displacement and spin GW memory effects generated during the inspiral phase of quasicircular nonprecessing binaries in Brans-Dicke theory. This detailed analysis sheds light on how modifications to general relativity (GR) theories influence gravitational-wave phenomena and provides valuable insights into understanding complex gravitational interactions within alternative theoretical frameworks. The researchers conducted a comprehensive analysis, calculating asymptotically flat solutions, symmetries, conserved quantities, and GW memory effects specifically within Brans-Dicke theory. Building upon this groundwork, they utilized the post-Newtonian (PN) approximation to compute GW memories arising from compact binaries. They considered energy and angular momentum losses through scalar radiation to be negligible compared to losses through tensor GWs. While our understanding of GW memory effects in GR is well-established, exploring these phenomena in modified theories poses a significant challenge. The appearance of energy radiated through the scalar dipole moment as a -1 PN order-effect introduces certain corrections such as logarithmic dependence on PN parameters for displacement memory and relative -1 PN-order correction for spin memory; however, these corrections remain minimal as they are tied to total energy and angular momentum radiated in the scalar field. Notably, at Newtonian order, scalar radiation introduces a distinct sky pattern for the memory effect around an isolated source compared to that observed in GR scenarios. This highlights the importance of considering alternative theoretical frameworks when studying gravitational-wave phenomena. , , , , and .