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In this paper we discuss the Casimir effect in a small cavity, freely fallingfrom spatial infinity in spacetime geometry outside of a Schwarzschild blackhole. Our main goal is to search for possible changes in the vacuum energy, aswell as particle creation inside the falling cavity, with respect to a comovingobserver. Working in the Lema\^itre chart and assuming a cavity size $L$ muchsmaller than the Schwarzschild radius ($L/r_g\ll 1$), we solve the Klein-Gordonequation for a massless scalar field confined within the cavity in thereference frame of the comoving observer. We follow Schwinger's proper timeapproach, evaluating the one-loop effective action for the field in the fallingcavity hence evaluating the corrections to the vacuum energy. We find a smallreduction in the absolute value of Casimir energy as the cavity approaches theblack hole horizon due to the changing spacetime geometry. Since the spacetimegeometry for the cavity changes dynamically, we further find the energy densityof the created particles due to the dynamical Casimir effect. These dynamicalcontributions exactly match the deficit to the static Casimir energy. Combined,the observer measures a net increase in energy within the cavity as she falls.

Casimir effect in free-fall towards a Schwarzschild black hole