492 research outputs found
Post-Newtonian Hydrodynamic Equations Using the (3+1) Formalism in General Relativity
Using the (3+1) formalism in general relativity, we perform the
post-Newtonian(PN) approximation to clarify what sort of gauge condition is
suitable for numerical analysis of coalescing compact binary neutron stars and
gravitational waves from them. We adopt a kind of transverse gauge condition to
determine the shift vector. On the other hand, for determination of the time
slice, we adopt three slice conditions(conformal slice, maximal slice and
harmonic slice) and discuss their properties. Using these conditions, the PN
hydrodynamic equations are obtained up through the 2.5PN order including the
quadrupole gravitational radiation reaction. In particular, we describe methods
to solve the 2PN tensor potential which arises from the spatial 3-metric. It is
found that the conformal slice seems appropriate for analysis of gravitational
waves in the wave zone and the maximal slice will be useful for describing the
equilibrium configurations. The PN approximation in the (3+1) formalism will be
also useful to perform numerical simulations using various slice conditions
and, as a result, to provide an initial data for the final merging phase of
coalescing binary neutron stars which can be treated only by fully general
relativistic simulations.Comment: 40 pages, TeX file using phyzzx, no figures, to appear in Prog.
Theor. Phy
Irrotational and Incompressible Ellipsoids in the First Post-Newtonian Approximation of General Relativity
First post-Newtonian (1PN) hydrostatic equations for an irrotational fluid
which have been recently derived are solved for an incompressible star. The 1PN
configurations are expressed as a deformation of the Newtonian irrotational
Riemann ellipsoid using Lagrangian displacement vectors introduced by
Chandrasekhar. For the 1PN solutions, we also calculate the luminosity of
gravitational waves in the 1PN approximation using the Blanchet-Damour
formalism. It is found that the solutions of the 1PN equations exhibit
singularities at points where the axial ratios of semi-axes are 1:0.5244:0.6579
and 1:0.2374:0.2963, and the singularities seem to show that at the points, the
irrotational Riemann ellipsoid is unstable to the deformation induced by the
effect of general relativity. For stable cases (a_2/a_1 > 0.5244, where a_1 and
a_2 are the semi-major and minor axes, respectively) we find that when
increasing the 1PN correction, the angular velocity and total angular momentum
increase, while the total energy and luminosity of gravitational waves
decrease. These 1PN solutions will be useful when examining the accuracy of
numerical code for obtaining relativistic irrotational stars.
We also investigate the validity of an ellipsoidal approximation, in which a
1PN solution is obtained assuming an ellipsoidal figure and neglecting the
deformation. It is found that for , the ellipsoidal
approximation gives a fairly accurate result for the energy, angular momentum,
and angular velocity, although in the approximation we cannot find the
singularities.Comment: 33 pages with 3 figures, ptptex, corrected some typos, tables and
figure
The Criticism of Modern Society and Labor: One Aspect of the Difference between Marx and Hegel
Ohta, Kohtaro:On the Preface of Hegel’s Phenomenology: The birth of “mediation.” (Chapter 7 of Ohta, Kotaro. 2018. Hegel no Baikai Shiso [Hegel on Mediation]. Hiroshima: Keisui Sha)
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