The N-body problem in general relativity

Spyrou, N.

doi:10.1086/153562

Cited by 25 publications

(23 citation statements)

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“…However, vanishing of all terms depending on the second order rotational moment of inertia in general relativity is in disagreement with calculations of Brumberg [127], Spyrou [128], Dallas [152] and Vincent [153] who came to the conclusion that the general relativistic Lagrangian for the system of N spherically-symmetric bodies must depend on the second-order moments of inertia of these bodies, I…”

Section: Translational Equations Of Motionmentioning

confidence: 92%

“…These definitions were used by Fock [48], Papapetrou [49], Petrova [140], Brumberg [131], and some other researchers (see, e.g., [128,129,141,142] and references therein) for derivation of the post-Newtonian equations of translational motion of extended, spherically-symmetric bodies. Physical intuition tells us that equations of motion of such bodies, in principle, have to depend only on masses of the bodies which are supposed to be the only parameters characterizing the magnitude of their internal gravitational field.…”

Section: Introductionmentioning

confidence: 99%

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Parametrized post-Newtonian theory of reference frames, multipolar expansions and equations of motion in the N-body problem

2004

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Section: Translational Equations Of Motionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Parametrized post-Newtonian theory of reference frames, multipolar expansions and equations of motion in the N-body problem

2004

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“…It is clear that, generally, in the interior of a continuous perfect fluid source the hydrodynamic flow differs from the geodesic motion. In this case, dynamical equivalence rests in the fact of the functional similarity between the corresponding (covariantly expressed) differential equations of motion (Spyrou 1999). Accordingly, the spaces of the solutions of these equations are isomorphic.…”

Section: Introductionmentioning

confidence: 99%

Geodesic motions versus hydrodynamic flows in a gravitating perfect fluid: dynamical equivalence and consequences

Kleidis¹,

Spyrou²

2000

Class. Quantum Grav.

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Stimulated by the methods applied for the observational determination of masses in the central regions of the AGNs, we examine the conditions under which, in the interior of a gravitating perfect fluid source, the geodesic motions and the general relativistic hydrodynamic flows are dynamically equivalent to each other. Dynamical equivalence rests on the functional similarity between the corresponding (covariantly expressed) differential equations of motion and is obtained by conformal transformations. In this case, the spaces of the solutions of these two kinds of motion are isomorphic. In other words, given a solution to the problem hydrodynamic flow in a gravitating perfect fluid, one can always construct a solution formally equivalent to the problem geodesic motion of a fluid element and vice versa. Accordingly, we show that, the observationally determined nuclear mass of the AGNs is being overestimated with respect to the real, physical one. We evaluate the corresponding mass-excess and show that it is not always negligible with respect to the mass of the central dark object, while, under circumstances, can be even larger than the rest-mass of the circumnuclear gas involved.

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“…However normal values were reached only progressively after the intervention: 2.1 + 0.8, 2.3 _+ 0.7 and 3.1 _+ 0.9 ml/min/g, at 24 hours, 1 week and 3 months respectively. In a recent preliminary report, identical observations were made following complete revascularization by CABG [48]. The perfusion reserve of the whole heart was 1 _+ 0.2 ml/min/g before surgery, 1.7 _+ 0.6 one month after and 2.3 +_ 0.4 at 6 months.…”

Section: Effect Of Therapeutic Interventionsmentioning

confidence: 52%

The value of quantitative myocardial perfusion imaging with Positron Emission Tomography in coronary artery disease

Wijns

Camici

1997

Herz

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Positron Emission Tomography (PET) is the only available technique that permits quantification of regional myocardial perfusion in humans. To this end, tracer kinetic models and appropriate tracers such as 13N-Ammonia and 15O labeled water are required. Quantification is possible because accurate radioactivity quantities can be measured externally, both for the vascular and myocardial compartments. Normal value for baseline and maximal perfusion after pharmacologically induced vasodilatation of the resistance microcirculatory vessels are age-dependent. The functional hemodynamic significance of epicardial stenoses can be estimated from the progressive reduction in coronary perfusion reserve, which decreases progressively when stenosis severity reaches 40% in diameter. The effect of revascularization procedures such as CABG and PTCA can be objectively measured. In addition, there is increasing evidence from PET studies that resistive vessel dysfunction (probably through endothelial factors) contributes to the reduced perfusion reserve in patients with epicardial coronary artery disease. Therefore quantification of myocardial perfusion with PET appears an ideally suited endpoint for primary and secondary prevention trials.

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The N-body problem in general relativity

Cited by 25 publications

References 0 publications

Parametrized post-Newtonian theory of reference frames, multipolar expansions and equations of motion in the N-body problem

Parametrized post-Newtonian theory of reference frames, multipolar expansions and equations of motion in the N-body problem

Geodesic motions versus hydrodynamic flows in a gravitating perfect fluid: dynamical equivalence and consequences

The value of quantitative myocardial perfusion imaging with Positron Emission Tomography in coronary artery disease

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