Vacuum fluctuation force on a rigid Casimir cavity in de Sitter and Schwarzschild-de Sitter spacetime

TL;DR

This paper analyzes the vacuum fluctuation forces on a rigid Casimir cavity in various curved spacetimes, revealing how gravitational fields and horizons influence the force's magnitude and direction, with potential implications for understanding universe geometry.

Contribution

It provides a detailed analysis of Casimir forces in de Sitter and Schwarzschild-de Sitter spacetimes, including the effects of weak and strong gravitational fields, and the behavior near black hole horizons.

Findings

Force follows inverse square law in de Sitter spacetime but is too weak to measure.

Weak gravitational fields split the force into gravitational and spacetime structure parts.

Near black hole horizons, the force becomes observable and switches from repulsive to attractive.

Abstract

We investigate the net force on a rigid Casimir cavity generated by vacuum fluctuations of electromagnetic field in three cases, de Sitter spacetime, de Sitter spacetime with weak gravitational field and Schwarzschild-de Sitter spacetime. In de Sitter spacetime the resulting net force follows the square inverse law but unfortunately it is too weak to be measurable due to the large universe radius. By introducing a weak gravitational field into the de Sitter spacetime, we find the net force now can be splited into two parts, one is the gravitational force due to the induced effective mass between the two plates, the other one is generated by the metric structure of de Sitter spacetime. In order to investigate the vacuum fluctuation force on the rigid cavity under strong gravitational field, we perform the similar analysis in Schwarzschild-de Sitter spacetime, results are obtained in three different limits. The most interesting one is when the cavity gets closer to the horizon of a blackhole, square inverse law is recovered and the repulsive force due to negative energy/mass of the cavity now has an observable strength. More important the force changes from being repulsive to attractive when the cavity crosses the event horizon, so that the energy/mass of the cavity switches the sign which suggests the unusual time direction inside the event horizon. %A possible way in verifying whether our universe is in a de Sitter or Minkowski spacetime is discussed.