An Unpublished Letter of M.A. Bakunin to R.Solger

Cutler, Robert M.

doi:10.1017/s0020859000008749

Cited by 2 publications

(4 citation statements)

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“…(0.1). Analytic [15,16] and Monte Carlo [17] calculations show that (i) the "chirp mass" M c ≡ µ 3/5 M 2/5 [which governs the Newtonian part of (0.1)] will typically be measured to 0.1 per cent, and (ii) if we somehow knew that the spins were small, then the reduced mass µ would be measured to ∼ 1 per cent for NS/NS and NS/BH binaries, and ∼ 3 per cent for BH/BH binaries. (Here and below NS means a ∼ 1.4M ⊙ neutron star and BH means a ∼ 10M ⊙ black hole.)…”

mentioning

confidence: 99%

“…(0.1) are not sufficiently different to give a clean separation between µ and the spins. Preliminary estimates [17], in which the S.O. term in Eq.…”

mentioning

confidence: 99%

“…The highest accuracy parameter information will come from low frequencies where most of the waves' cycles are located [15][16][17]. (It thus is important that the interferometers achieve good low-frequency performance).…”

mentioning

confidence: 99%

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The last three minutes: Issues in gravitational-wave measurements of coalescing compact binaries

et al. 1993

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Gravitational-wave interferometers are expected to monitor the last three minutes of inspiral and final coalescence of neutron star and black hole binaries at distances approaching cosmological, where the event rate may be many per year. Because the binary's accumulated orbital phase can be measured to a fractional accuracy <^C 10~3 and relativistic effects are large, the wave forms will be far more complex and carry more information than has been expected. Improved wave form modeling is needed as a foundation for extracting the waves' information, but is not necessary for wave detection.

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mentioning

confidence: 99%

“…(0.1) are not sufficiently different to give a clean separation between µ and the spins. Preliminary estimates [17], in which the S.O. term in Eq.…”

mentioning

confidence: 99%

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The last three minutes: Issues in gravitational-wave measurements of coalescing compact binaries

et al. 1993

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“…By noting that the governing equation remains invariant to the addition of terms represented by constant gradients to Φ (so-called Galilean invariance), Hui et al [41] suggested that the influence of a distant mass on a local system could be approximated by first solving for the local system in isolation and then adding the linearized potential of the field of the distant mass. For an axisymmetric two-body problem, an analytic perturbation expansion based on this assumption has been developed [42]. To achieve higher accuracy for the twobody problem or to solve complex systems containing many bodies or non-spherical masses, it becomes necessary to turn to numerical solution techniques.…”

Section: Scalar Potential Solution For the Axisymmetric Sun-earth And 3dmentioning

confidence: 99%

Robust numerical computation of the 3D scalar potential field of the cubic Galileon gravity model at solar system scales

White,

Troian,

Jewell

et al. 2020

Preprint

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Direct detection of dark energy or modified gravity may finally be within reach due to ultrasensitive instrumentation such as atom interferometry capable of detecting incredibly small scale accelerations. Forecasts, constraints and measurement bounds can now too perhaps be estimated from accurate numerical simulations of the fifth force and its Laplacian field at solar system scales. The cubic Galileon gravity scalar field model (CGG), which derives from the DGP braneworld model, describes modified gravity incorporating a Vainshtein screening mechanism. The nonlinear derivative interactions in the CGG equation suppress the field near regions of high density, thereby restoring general relativity (GR) while far from such regions, field enhancement is comparable to GR and the equation is dominated by a linear term. This feature of the governing PDE poses some numerical challenges for computation of the scalar potential, force and Laplacian fields even under stationary conditions. Here we present a numerical method based on finite differences for solution of the static CGG scalar field for a 2D axisymmetric Sun-Earth system and a 3D Cartesian Sun-Earth-Moon system. The method relies on gradient descent of an integrated residual based on the normal attractive branch of the CGG equation. The algorithm is shown to be stable, accurate and rapidly convergent toward the global minimum state. We hope this numerical study, which can easily be extended to include smaller bodies such as detection satellites, will prove useful to future measurement of modified gravity force fields at solar system scales.

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An Unpublished Letter of M.A. Bakunin to R.Solger

Cited by 2 publications

References 1 publication

The last three minutes: Issues in gravitational-wave measurements of coalescing compact binaries

The last three minutes: Issues in gravitational-wave measurements of coalescing compact binaries

Robust numerical computation of the 3D scalar potential field of the cubic Galileon gravity model at solar system scales

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