A spherical mass shell as a `total reflector' for gravitational waves

Details A spherical mass shell as a `total reflector' for gravitational waves A spherical mass shell as a `total reflector' for gravitational waves

Aug 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996cqgra..13.2267p&link_type=abstract

Classical and Quantum Gravity, Volume 13, Issue 8, pp. 2267-2277 (1996).

Computer Science

2

Scientific paper

For normal bulk material the reflection coefficient for gravitational waves is usually much smaller than 1. Therefore, a spherical mass shell (mass M, radius R) can serve as a `container' for gravitational radiation at most in the extreme case R = 2M. If, however, the shell material is especially adapted to the properties of the wave, total reflection can occur due to interference effects, i.e. suitable mass shells can totally reflect weak gravitational waves of arbitrary frequency 0264-9381/13/8/019/img1 and angular momentum l coming from the outside; for waves inside the shell total reflection is only possible for a series of discrete 0264-9381/13/8/019/img1-values, dependent on R and l. This is proven by first-order perturbation theory on the basis of the Schwarzschild mass shell. Perturbation of the exterior Schwarzschild metric is treated in Regge - Wheeler gauge. Connection of this exterior metric to a (suitably transformed) flat interior metric at r = R according to Israel's method leads to a unique relation between the amplitudes of the ingoing and outgoing wave (total reflection!). For 0264-9381/13/8/019/img3, the shell material fulfils the dominant energy condition. The logarithmic phase of the asymptotic gravitational wave (in radiation gauge) compares nicely with the phase in relativistic Coulomb scattering: different sign of the logarithmic term due to gravitational attraction, and a factor 2 due to the spin of the `graviton'.

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