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Cited by 52Cosmology and Gravitation TheoriesPulsars and Gravitational Waves ResearchRelativity and Gravitational Theory

Brans-Dicke theory in Bondi-Sachs form: Asymptotically flat solutions, asymptotic symmetries, and gravitational-wave memory effects

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Tahura, Shammi, Nichols, David A., Saffer, Alexander, Stein, Leo C., Yagi, Kent·2021·Physical Review D
DOI 10.1103/physrevd.103.104026
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Abstract

Gravitational-wave memory effects are identified by their distinctive effects on families of freely falling observers: after a burst of waves pass by their locations, memory effects can cause lasting relative displacements of the observers. These effects are closely related to the infrared properties of gravity, including its asymptotic symmetries and conserved quantities. In this paper, we investigate the connection between memory effects, symmetries, and conserved quantities in Brans-Dicke theory. We compute the field equations in Bondi coordinates, and we define a set of boundary conditions that represent asymptotically flat solutions in this context. Next, we derive the asymptotic symmetry group of these spacetimes, and we find that it is the same as the Bondi-Metzner-Sachs group in general relativity. Because there is an additional polarization of gravitational waves in Brans-Dicke theory, we compute the memory effects associated with this extra polarization (the so-called ``breathing'' mode). This breathing mode produces a uniform expansion (or contraction) of a ring of freely falling observers. After these breathing gravitational waves pass by the observers' locations, there are two additional memory effects that depend on their initial displacements and relative velocities. Neither of these additional memory effects seems to be related to asymptotic symmetries or conserved quantities; rather, they are determined by the properties of the nonradiative region before and after the bursts of the scalar field and the gravitational waves. We discuss the properties of these regions necessary to support nontrivial breathing-mode-type memory effects.

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  • An Einstein frame observer is insensitive to the overall breathing mode.

    “Thus the Einstein news tensor is equivalent to the trace-free Bondi news tensor - an Einstein frame observer is insensitive to the overall breathing mode as we expect [24].”

    From Gravitational memory and compact extra dimensions (2022) · cites this paper as [24]

    The Introduction (p. 2) says test particles in the Einstein frame accelerate in response to scalar-field gradients; it does not describe them as insensitive to the scalar mode. It also says physical predictions, including gravitational-wave memory effects, are conformal-frame invariant. The paper’s description of the breathing mode as an expansion or contraction of freely falling observers (p. 1) further contradicts the claimed physical insensitivity. (LLM, conf=0.82)

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  • The Einstein news tensor is equivalent to the trace-free Bondi news tensor.

    “Thus the Einstein news tensor is equivalent to the trace-free Bondi news tensor - an Einstein frame observer is insensitive to the overall breathing mode as we expect [24].”

    From Gravitational memory and compact extra dimensions (2022) · cites this paper as [24]

    The asymptotically flat solutions section (pp. 7–9) defines the Bondi news tensor as the time derivative of a trace-free tensor and treats scalar-field radiation separately. The passages from our copy do not establish that this tensor is equivalent to an Einstein-frame news tensor; the frame-to-frame equivalence is the unsupported part. (LLM, conf=0.76)

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Sorted by citations

Authors
Tahura, S., Nichols, D. A., Saffer, A., Stein, L. C., & Yagi, K.
Affiliations
  • University of Virginia (US)
  • University of Mississippi (US)
ORCID
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
2021-05-14
Volume
103
Issue
10
ISSN
  • 2470-0010 (ISSN-L)
  • 2470-0029
DOI
10.1103/physrevd.103.104026
OpenAlex
W3045975136
Cited by
52
References
4
Citations by year
2026: 5 · 2025: 11 · 2024: 7 · 2023: 8 · 2022: 12 · 2021: 8 · 2013: 1
FWCI
4.53
Type
journal article
Language
en
Open access
Licence
Locations
  • Physical review. D/Physical review. D. (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (PHY-1806776, PHY-2011784)
  • National Aeronautics and Space Administration (80NSSC20K0523)
  • Alfred P. Sloan Foundation
  • European Cooperation in Science and Technology (CA16104)
  • Japan Society for the Promotion of Science (JP17H06358)
  • Owens Innovation Fund
Topics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Pulsars and Gravitational Waves Research
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
Keywords
Brans-Dicke theory, asymptotic symmetries, Bondi-Metzner-Sachs group, asymptotically flat spacetimes, breathing mode, scalar-tensor gravity, first integrals, freely falling observers, scalar field

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