Electromagnetic Modes in Schwarzschild Geometry in an Annular Region

Physics

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Scientific paper

The fundamental electromagnetic modes in a spherical annular cavity with perfectly conducting walls at $r = a$ and $r = b$ are calculated, in the presence of a weak Schwarzschild gravitational field. Explicit expressions are given for the case of a ``thin" shell, $(b - a)/a \ll 1$. The modified angular frequency for mode $\ell , m$ can be written as $\omega =\omega_0\{ 1-(GM/a) [2-\ell (\ell +1)/(\omega_0 a)^2]$ where $\omega_0$ is the nongravitational frequency. This formula (being independent of $m$) holds for the magnetic as well as for the electric modes.

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