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For example, S. L. Shapiro and S. A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars (Wiley Interscience, New York, 1983).
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For example, K. S. Thorne, in Proceeding of Snowmass 95 Summer Study on Particle and Nuclear Astrophysics and Cosmology, edited by E. W. Kolb and R. Peccei (World Scientific, Singapore, 1995), p. 398, and references therein.
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K. Oohara and T. Nakamura, in Relativistic Gravitation and Gravitational Radiation, edited by J.-P. Lasota and J.-A. Marck (Cambridge University Press, Cambridge, England, 1997), p. 309.
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K. Uryū and Y. Eriguchi (unpublished)
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K. Uryū and Y. Eriguchi (unpublished).
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47
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85037182627
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The equation for the Hamiltonian constraint is written in the form (Formula presented) where (Formula presented) and (Formula presented) are the Laplacian with respect to (Formula presented) and a function of (Formula presented) (Formula presented) (Formula presented) (Formula presented) P and (Formula presented) We define a function (Formula presented) for measuring the violation of the Hamiltonian constraint. We have found that (Formula presented) is typically less than (Formula presented) for a region in which (Formula presented) is larger than (Formula presented) For the less dense region, however, (Formula presented) often becomes (Formula presented) because such a low density region is not well resolved in our finite differencing scheme for the hydrodynamic equations
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The equation for the Hamiltonian constraint is written in the form (Formula presented) where (Formula presented) and (Formula presented) are the Laplacian with respect to (Formula presented) and a function of (Formula presented) (Formula presented) (Formula presented) (Formula presented) P and (Formula presented) We define a function (Formula presented) for measuring the violation of the Hamiltonian constraint. We have found that (Formula presented) is typically less than (Formula presented) for a region in which (Formula presented) is larger than (Formula presented) For the less dense region, however, (Formula presented) often becomes (Formula presented) because such a low density region is not well resolved in our finite differencing scheme for the hydrodynamic equations.
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48
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85037255991
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The rest mass is conserved because of no mass ejection. The angular momentum decreases by 5–10 % in the whole evolution, and the total amount of the decrease roughly agrees with the angular momentum emission in gravitational waves within (Formula presented) error [see Eq. (4.2)]
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The rest mass is conserved because of no mass ejection. The angular momentum decreases by 5–10 % in the whole evolution, and the total amount of the decrease roughly agrees with the angular momentum emission in gravitational waves within (Formula presented) error [see Eq. (4.2)].
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50
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85037178114
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The definition of differential rotation depends on the coordinate condition. Strictly speaking, we have found that the new massive neutron star is differentially rotating in our present gauge, and the rotation law found in this paper could change slightly if it is defined in the stationary axisymmetric gauge used in
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The definition of differential rotation depends on the coordinate condition. Strictly speaking, we have found that the new massive neutron star is differentially rotating in our present gauge, and the rotation law found in this paper could change slightly if it is defined in the stationary axisymmetric gauge used in 4.
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51
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85037199275
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Note that we recompute the constraint equations whenever we modify the initial quasiequilibrium configurations
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Note that we recompute the constraint equations whenever we modify the initial quasiequilibrium configurations.
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52
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0000201414
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T. W. Baumgarte, G. B. Cook, M. A. Scheel, S. L. Shapiro, and S. A. Teukolsky, Phys. Rev. D 57, 6181 (1998).
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53
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For example, M. Shibata, Phys. Rev. D 58, 024012 (1998), and references therein.
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54
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85037223759
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Actually, it is possible to construct differentially rotating neutron stars of such a large mass, which are dynamically (but not always secularly) stable against gravitational collapse and bar mode deformation 5;M. Shibata, T. W. Baumgarte, and S. L. Shapiro (in preparation).
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Shibata, M.1
Baumgarte, T.W.2
Shapiro, S.L.3
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56
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85037245345
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The new, massive neutron stars may be secularly unstable to becoming a black hole on a long time scale even if the effect of gravitational radiation is small. The reason is that they are differentially rotating and supramassive, which implies if we take into account the effects of viscosity or magnetic fields, angular momentum will be transported outward or dissipated, and eventually they may become unstable to gravitational collapse. See also
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The new, massive neutron stars may be secularly unstable to becoming a black hole on a long time scale even if the effect of gravitational radiation is small. The reason is that they are differentially rotating and supramassive, which implies if we take into account the effects of viscosity or magnetic fields, angular momentum will be transported outward or dissipated, and eventually they may become unstable to gravitational collapse. See also 5.
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59
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85037177781
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If the time duration is fairly long, we may be able to observe a peak around the oscillation frequency in the Fourier spectrum of gravitational waves as pointed out in
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If the time duration is fairly long, we may be able to observe a peak around the oscillation frequency in the Fourier spectrum of gravitational waves as pointed out in 15. On the other hand, we will not find the peak if the time duration is short. Thus, we may say that the amplitude of the peak in the Fourier space also provides important information.
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Blanchet, L.1
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Wiseman, A.G.4
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