Stability of giant Fabry-Perot cavities of interferometric gravitational-wave detectors

We consider the coupling of the thermoelastic mirror deformations to the resonance of giant cavities involved in interferometric detectors of gravitational waves. As this problem is coupled and nonlinear, instabilities could occur a priori. We analytically solve the coupled problem of thermoelastic deformations and their effect on the laser field, perturbatively, and we show that within the realm of our (physically reasonable) assumptions there are no instabilities that can simulate a false event in the observational frequency range of 1 Hz to 1 kHz.