ELECTROMAGNETIC MODES IN SCHWARZSCHILD GEOMETRY IN AN ANNULAR REGION

The fundamental electromagnetic modes in a spherical annular cavity wi th perfectly conducting walls at r = a and r = b are calculated, in th e presence of a weak Schwarzschild gravitational field. Explicit expre ssions are given for the case of a ''thin'' shell, (b - a)la << 1. The modified angular frequency for mode l, m can be written as w = w(0){1 -(GM/a)[2-l(l+1)/(w(0)a)(2)] where w(0) is the nongravitational freque ncy. This formula (being independent of m) holds for the magnetic as w ell as for the electric modes.