Dynamical Casimir effect under the action of gravitational waves

Several nontrivial phenomena emerge when a quantum field is subjected to dynamical perturbations, with prominent examples including the Hawking and Unruh effects, as well as the dynamical Casimir effect. In this work, we compute the number of particles produced via the dynamical Casimir effect in an ideal cavity, where one of the mirrors is allowed to move under the influence of a gravitational wave. Assuming an oscillatory mirror motion and a plane gravitational wave, we identify the resonance conditions that lead to an exponential increase in the number of created particles through parametric amplification.

💡 Research Summary

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The paper investigates how a classical gravitational wave (GW) influences particle creation via the dynamical Casimir effect (DCE) in an ideal three‑dimensional cavity with one movable mirror. Starting from a mass‑less real scalar field on a curved background, the authors linearise the metric around flat spacetime, introduce a small perturbation (h_{\mu\nu}) in the transverse‑traceless (TT) gauge, and consider a plane GW propagating along the (z)‑axis with plus and cross polarizations. The field equation becomes (\Box\Phi-\bar h_{ij}\partial_i\partial_j\Phi=0), where the GW couples to spatial derivatives of the field.

The cavity is defined as a rectangular box (\Sigma(t)) with Dirichlet boundary conditions on all walls; the mirror at (z=L_z(t)) moves according to a prescribed law while the opposite wall remains fixed. The authors construct instantaneous mode functions (\phi_{\mathbf k}(\mathbf x;L_z(t))) that satisfy the modified Helmholtz equation including the GW term, and obtain the time‑dependent eigenfrequencies \