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85038992479
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The gauge-invariant variables are computed from (Formula presented) In the linear order, (Formula presented) The linearized Einstein equation for (Formula presented) in our formulation
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The gauge-invariant variables are computed from (Formula presented) In the linear order, (Formula presented) The linearized Einstein equation for (Formula presented) in our formulation 1619 is (Formula presented)If the Hamiltonian constraint in the linear level is satisfied, (Formula presented) Then, the solution of (Formula presented) is (Formula presented) and consequently, the gauge-invariant variables do not contain (Formula presented) However, if the Hamiltonian constraint is violated, the effects of (Formula presented) are contained in the gauge-invariant variables. In the present work, we found that its effect is small, and hence we ignore it.
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39
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85039028831
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In
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In 15, a three-dimensional simulation for an oscillating and nonrotating star which is almost the same as model S1 was performed. They computed approximate gravitational waveforms in a near zone (Formula presented) and derived the period for the fundamental quadrupole mode as (Formula presented) This value agrees with ours in (Formula presented) error.
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