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arXiv:2605.26743

Thermal Casimir Effect in A Schwarzschild-like Wormhole Spacetime

Arista Romadani, Apriadi Salim Adam, Ar Rohim, Bintoro Anang Subagyo, Agus Purwanto

hep-thgr-qcquant-phSubmitted May 26, 2026• Announced May 27, 2026• Revised Sep 23, 2026 (v2)
v1 · May 26, 2026v2 · Sep 23, 2026
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Abstract

We study the finite-temperature Casimir effect for a massless scalar field confined between two parallel plates in a Schwarzschild-like wormhole spacetime. Imposing Dirichlet boundary conditions, we compute the renormalized Casimir free energy in the comoving frame. We find that the thermal correction to the renormalized Casimir free energy decreases gradually with the temperature and becomes independent of the background geometry in this frame. Thermodynamic quantities derived from the Casimir free energy, namely, the renormalized Casimir entropy, internal energy, and heat capacity at constant volume, exhibit distinct temperature dependence. At low temperatures, all thermodynamic quantities recover the expected behavior, consistent with the fundamental laws of thermodynamics. These results provide a compact framework for analyzing quantum vacuum forces in gravitational backgrounds.

Comments
24 pages, 4 figures, a new subsection is added, subsections 2.3 and 2.4 are slightly modified, one figure is added, comments are welcome

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We study the finite-temperature Casimir effect for a massless scalar field confined between two parallel plates in a Schwarzschild-like wormhole spacetime. Imposing Dirichlet boundary conditions, we compute the renormalized Casimir free energy in the comoving frame. We find that the thermal correction to the renormalized Casimir free energy decreases gradually with the temperature and becomes independent of the background geometry in this frame. Thermodynamic quantities derived from the Casimir free energy, namely, the renormalized Casimir entropy, internal energy, and heat capacity at constant volume, exhibit distinct temperature dependence. At low temperatures, all thermodynamic quantities recover the expected behavior, consistent with the fundamental laws of thermodynamics. These results provide a compact framework for analyzing quantum vacuum forces in gravitational backgrounds.
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Considering the Casimir effect due to phononic excitations of a weakly interacting dilute Bose–Einstein condensate (BEC), we derive a renormalized expression for the zero-temperature Casimir energy of a BEC confined to a parallel plate geometry with periodic boundary conditions. Our expression is formally equivalent to the free energy of a bosonic field at finite temperature, with a nontrivial density of modes that we compute analytically. As a function of the interaction strength, smoothly describes the transition from the weakly interacting Bogoliubov regime to the non-interacting ideal BEC. For the weakly interacting case, reduces to leading order to the Casimir energy due to zero-point fluctuations of massless phonon modes. In the limit of an ideal Bose gas, our result correctly describes the Casimir energy going to zero.
We investigate the Casimir effect for a massive real scalar field confined between two perfectly reflecting parallel plates in the presence of a position-dependent effective mass, a mechanism for coupling a scalar background to a scalar field. Exact normal modes are obtained by solving the corresponding Klein-Gordon equation, leading to a transverse energy spectrum that exhibits a characteristic Landau-like structure despite the absence of an external magnetic field. Upon quantization of the field, the vacuum energy is evaluated by means of generalized zeta-function regularization together with an appropriate renormalization procedure. The renormalized vacuum energy naturally separates into a Landau-like contribution and an additional term induced by the spatial dependence of the effective mass. We show analytically and numerically that both contributions are exponentially suppressed in the strong-coupling regime. In the opposite limit, the Landau-like contribution smoothly reproduces the standard vacuum energy for a massive scalar field confined between parallel plates, whereas the additional contribution becomes singular owing to the restricted domain of validity of the exact spectrum. Except in the vicinity of this singular limit, the vacuum energy is shown to be dominated by the Landau-like sector. Our results establish a direct connection between position-dependent effective masses and boundary-induced quantum vacuum phenomena, providing a new exactly solvable framework for the investigation of Casimir effects in spatially inhomogeneous relativistic systems.
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Extending the analysis in our previous paper, we construct the entanglement thermodynamics for a massless scalar field on Schwarzschild spacetime. Contrary to the flat case, the entanglement energy Eent{E}_{\mathrm{ent}}Eent​ turns out to be proportional to the area radius of the boundary if it is near the horizon. This peculiar behavior of Eent{E}_{\mathrm{ent}}Eent​ can be understood by the redshift effect caused by the curved background. Combined with the behavior of the entanglement entropy, this result yields, quite surprisingly, the entanglement thermodynamics of the same structure as black hole thermodynamics. On the basis of these results, we discuss the relevance of the concept of entanglement as the microscopic origin of black hole thermodynamics.