Darwin-Riemann Problems in General Relativity

Bonazzola, S.; Gourgoulhon, Éric; Grandclément, Philippe; Marck, J. A.

doi:10.1143/ptps.136.216

Cited by 3 publications

(3 citation statements)

References 21 publications

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“…While quasi-equilibrium NS-NS binary models (the so-called Darwin-Riemann problems) have been successfully constructed in general relativity (see Bonazzola et al 1999aBonazzola et al , 1999b for a review), only Newtonian models of NS-BH binaries have been studied so far (see Uryu & Eriguchi 1999). The semianalytic Roche-Riemann models studied in this paper provide useful insight on the relativistic tidal e †ects in coalescing NS-BH and WD-BH binaries.…”

Section: Discussionmentioning

confidence: 99%

“…This implies that o c the tidal Ðeld stabilizes the star against collapse. Physically, this stabilization arises from that fact that the self-gravity of a distorted object is weaker, and the star expands in order to satisfy hydrostatic equilibrium (see, e.g., Lai 1996 ; LRS1 ; Brady & Hughes 1997 ;Wiseman 1997 ;Baumgarte et al 1998 ;Thorne 1998 ;Flanagan 1998 ;Bonazzola et al 1999a ;Bonazzola, Gourgoulhon, & Marck 1999b).…”

Section: Roche-riemann Model : Irrotational Equilibriummentioning

confidence: 99%

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Tidal Interaction between a Fluid Star and a Kerr Black Hole in Circular Orbit

Wiggins

Lai

2000

ApJ

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We present a semianalytic study of the equilibrium models of close binary systems containing a Newtonian Ñuid star (mass m and radius and a Kerr black hole (mass M) in a circular orbit. We consider R 0 ) the limit M ? m where spacetime is described by the Kerr metric. The tidally deformed star is approximated by an ellipsoid and satisÐes the polytropic equation of state. The models also include Ñuid motion in the stellar interior, allowing binary models with nonsynchronized stellar spin (as expected for coalescing neutron starÈblack hole binaries) to be constructed. Our relativistic, compressible RocheRiemann model is a generalization of the incompressible, corotating Roche model studied earlier by Fishbone. Tidal disruption occurs at orbital radius but the dimensionless ratio r tide D R 0 (M/m)1@3, rü tide \ depends on the spin parameter of the black hole as well as on the equation of state r tide /[R 0 (M/m)1@3] and the internal rotation of the star. We Ðnd that the general relativistic tidal Ðeld disrupts the star at a larger than the Newtonian tide ; the di †erence is particularly prominent if the disruption occurs in rü tide the vicinity of the black holeÏs horizon. In general, is smaller for a (prograde rotating) Kerr black rü tide hole than for a Schwarzschild black hole. We apply our results to coalescing black holeÈneutron star and black holeÈwhite dwarf binaries. The tidal disruption limit is important for characterizing the expected gravitational wave signals and is relevant for determining the energetics of gamma-ray bursts that may result from such disruptions.

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Section: Discussionmentioning

confidence: 99%

Section: Roche-riemann Model : Irrotational Equilibriummentioning

confidence: 99%

Tidal Interaction between a Fluid Star and a Kerr Black Hole in Circular Orbit

Wiggins

Lai

2000

ApJ

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“…Recently Bonazzola, Gourgoulhon and Marck have numerically studied the irrotational binary neutron stars in general relativity with the conformally flat condition [18][19][20]. More recently, Uryū and Eriguchi have also numerically solved the same problem as that of Bonazzola, Gourgoulhon and Marck [21].…”

Section: Introductionmentioning

confidence: 99%

Equilibrium sequences of irrotational binary polytropic stars: The case of double polytropic stars

Taniguchi¹,

Nakamura²

2000

Phys. Rev. D

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Solutions to equilibrium sequences of irrotational binary polytropic stars in Newtonian gravity are expanded in a power of = a0/R, where R and a0 are the orbital separation of the binary system and the radius of each star for R = ∞. For each order of , we should solve ordinary differential equations for arbitrary polytropic indices n. We show solutions for polytropic indices n = 0.5, 1, 1.5 and 2 up to 6 orders. Our semi-analytic solutions can be used to check the validity of numerical solutions. PACS number(s): 04.30. Db, 04.25.Dm, 97.80.Fk

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Post-Newtonian Expansion of Gravitational Radiation

Blanchet

1999

Prog. Theor. Phys. Suppl.

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The post-Newtonian expansion appears to be a relevant tool for predicting the gravitational waveforms generated by some astrophysical systems such as binaries. In particular, inspiralling compact binaries are well-modelled by a system of two point-particles moving on a quasi-circular orbit whose decay by emission of gravitational radiation is described by a post-Newtonian expansion. In this paper we summarize the basics of the computation by means of a series of multipole moments of the exterior field generated by an isolated source in the post-Newtonian approximation. This computation relies on an ansatz of matching the exterior multipolar field to the inner field of a slowly-moving source. The formalism can be applied to point-particles at the price of a further ansatz, that the infinite self-field of point-particles can be regularized in a certain way. As it turns out, the concept of point-particle requires a precise definition in high post-Newtonian approximations of general relativity.

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Darwin-Riemann Problems in General Relativity

Abstract: A review is given of recent results about the computation of irrotational Darwin-Riemann configurations in general relativity. Such configurations are expected to represent fairly well the late stages of inspiralling binary neutron stars. typeset using PTPT E X.sty

Cited by 3 publications

References 21 publications

Tidal Interaction between a Fluid Star and a Kerr Black Hole in Circular Orbit

Tidal Interaction between a Fluid Star and a Kerr Black Hole in Circular Orbit

Equilibrium sequences of irrotational binary polytropic stars: The case of double polytropic stars

Post-Newtonian Expansion of Gravitational Radiation

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