HIGH-FREQUENCY INTERACTING GRAVITATIONAL AND MAGNETOSONIC WAVES

The interaction of high-frequency asymptotic waves in general relativi stic magnetohydrodynamics will be investigated. It shall be proved tha t an order-one magnetosonic wave generates a gravitational wave of ord er three (theorem 1), and an order-two gravitational wave generates a magnetosonic wave of the same order (theorem 2). If the fluid satisfie s the limit state equation e(p)' = 1, then a magnetosonic and a gravit ational wave of same phase and of the same order can coexist and inter act, each one acting as a source for the other (theorem 3).