We explore, within the framework of linearized quantum gravity, the Casimir-Polder (CP)–like quantum gravitational interaction between an excited nonpointlike object and a gravitational Dirichlet boundary based on perturbation theory. Our result shows that, the gravitational Casimir-Polder interaction potential for an excited object decreases as $z^{-5}$ in the near regime where the distance between the object and the boundary is smaller than the characteristic transition wavelength of the object, while it oscillates as $z^{-1}$ in the far regime where the distance is larger than the characteristic transition wavelength, with $z$ denoting the object-boundary distance. Compared to the gravitational CP force between a ground-state object and a gravitational Dirichlet boundary, which is repulsive in both the near and far regimes, the present interaction can be either attractive or repulsive in the far zone, depending on the object-boundary distance and the transition wavelength of the object. Moreover, the far-region behavior of an excited object decays as $z^{-1}$, which is significantly slower than the $z^{-6}$ dependence observed for a ground-state object. This suggests that the gravitational CP interaction can be enhanced or modulated by altering the initial state of the nonpointlike object.

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• Casimir effect
• Gauge-gravity dualities
• General relativity
• Quantum gravity