Abstract
Descriptions are presented of two different analyses in which systems which radiate gravitational waves are damped.
The first analysis shows how the back-reaction of gravitational radiation can be incorporated with ease into any slow-motion expansion of general relativity. This analysis reveals that the dominant effects of general-relativistic radiation resistance can be incorporated into the Newtonian theory of gravity by a simple change in the boundary condition on the Newtonian potential at r = ∞. The rate of energy loss from a radiating system, as calculated by this analysis, agrees with the power carried in the gravitational waves, as calculated by the Isaacson stress-energy tensor or the Landau-Lifschitz pseudotensor.
The second analysis treats the small-amplitude, nonradial pulsations of fully relativistic stellar models, which may be arbitrarily close to their Schwarzschild radii. The slow-motion and weak-field approximations, which are crucial to the first analysis, are not made here. As a consequence, the radiation damping appears at first order in the amplitude of pulsation. This analysis reveals that a neutron star formed by gravitational collapse should emit a burst of gravitational waves with frequencies of ~ 103 hz, energy ~ 1052 ergs, and damping time ~ 1 second.
In the slow-motion, weak-field limit, the second analysis reduces to the first.
Supported in part by the National Science Foundation [GP-9433, GP-9114] and the Office of Naval Research [Nonr-220(47)].
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Burke, W.L., Thorne, K.S. (1970). Gravitational Radiation Damping. In: Carmeli, M., Fickler, S.I., Witten, L. (eds) Relativity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-0721-1_12
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DOI: https://doi.org/10.1007/978-1-4684-0721-1_12
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