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arxiv: 2605.26743 · v1 · pith:5MW336TMnew · submitted 2026-05-26 · ✦ hep-th · gr-qc· quant-ph

Thermal Casimir Effect in A Schwarzschild-like Wormhole Spacetime

Arista Romadani , Apriadi Salim Adam , Ar Rohim , Bintoro Anang Subagyo , Agus Purwanto This is my paper

Pith reviewed 2026-06-29 16:15 UTC · model grok-4.3

classification ✦ hep-th gr-qcquant-ph
keywords Casimir effectwormhole spacetimethermal correctionscalar fieldfinite temperaturerenormalized free energyDirichlet boundary conditionsthermodynamic quantities
0
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The pith

In a Schwarzschild-like wormhole the thermal correction to the Casimir free energy becomes independent of geometry in the comoving frame.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper computes the finite-temperature Casimir effect for a massless scalar field between parallel plates obeying Dirichlet conditions inside a Schwarzschild-like wormhole spacetime. It reports that the thermal correction to the renormalized free energy decreases steadily as temperature rises and eventually loses all dependence on the details of the background metric when evaluated in the comoving frame. From this free energy the authors extract the renormalized entropy, internal energy, and heat capacity at constant volume, all of which display characteristic temperature profiles that match ordinary thermodynamic expectations at low temperature.

Core claim

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.

What carries the argument

The renormalized Casimir free energy for the massless scalar field evaluated in the comoving frame of the Schwarzschild-like wormhole metric.

If this is right

  • Thermodynamic quantities derived from the free energy exhibit distinct temperature dependence.
  • At low temperatures the entropy, internal energy, and heat capacity recover the expected thermodynamic limits.
  • The calculation supplies a compact framework for studying quantum vacuum forces in gravitational backgrounds.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the comoving frame is the physically relevant one, gravitational corrections to thermal Casimir energies can be suppressed by frame choice alone.
  • The same loss of geometry dependence may occur for other static curved backgrounds when the same frame is used.
  • The low-temperature thermodynamic recovery indicates that the regularization preserves the third law.

Load-bearing premise

The spacetime is taken to be a specific Schwarzschild-like wormhole metric and the plates are analyzed in the comoving frame.

What would settle it

An explicit recalculation of the same free energy in a non-comoving frame or in a different wormhole metric that retains geometry dependence at high temperature would falsify the reported independence.

Figures

Figures reproduced from arXiv: 2605.26743 by Agus Purwanto, Apriadi Salim Adam, Arista Romadani, Ar Rohim, Bintoro Anang Subagyo.

Figure 1
Figure 1. Figure 1: Casimir cavity orbiting around Schwarzschild-like wormhole [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Plot of L3 S ∆TF ren as a function of dimensionless parameter, 1/β˜. We perform the summation over m up to 1000. being an angular velocity and a proper surface of the plate Sp defined as Sp ≡ S √ ∆/r−1 3 . Those two quantities will determine the geometry of plates. In contrast, our expression for the thermal corrections does not have such scaled quantity as the spacetime background of our Casimir cavity … view at source ↗
Figure 3
Figure 3. Figure 3: Plot of thermodynamics quantities: L2 S ∆T S ren , L3 S ∆TU ren and L2 S ∆T CV ren as a function of dimensionless parameter, 1/β˜. The black-solid, blue-dotted, and red-dashed lines correspond to the thermal correction of the renormalized Casimir entropy, internal energy, and heat capacity at constant volume, respectively. For each quantity, we perform the summation over m up to 1000. to other terms in Eq.… view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript examines the finite-temperature Casimir effect for a massless scalar field between two parallel plates in a Schwarzschild-like wormhole spacetime. Using Dirichlet boundary conditions in the comoving frame, the authors compute the renormalized Casimir free energy and find that its thermal correction decreases with temperature and becomes independent of the background geometry. They also analyze the associated thermodynamic quantities (entropy, internal energy, heat capacity), which exhibit expected low-temperature behavior consistent with thermodynamics.

Significance. Should the reported geometry independence of the thermal correction hold after detailed verification, the result would be significant for the study of quantum vacuum effects in curved spacetimes with non-trivial topology. It suggests that thermal effects can dominate and erase geometric dependence in the comoving frame, offering a compact framework for such analyses. The consistency with thermodynamic laws at low T provides a necessary check.

major comments (3)
  1. [Abstract] The central claim of geometry independence for the thermal correction (stated in the abstract) requires that the mode sum after Dirichlet conditions and the subsequent renormalization fully erase metric dependence. No derivation steps, explicit mode frequencies, or renormalization procedure are supplied, preventing verification that curvature effects are removed without residual dependence.
  2. [Setup of plates (likely §2)] The plate positions are not specified as fixed proper distance or fixed coordinate separation. If plates are placed at fixed coordinate r while the redshift or shape function varies, the proper distance between plates changes with the metric parameters, so the Casimir scale itself retains geometry dependence and the independence claim does not follow.
  3. [Renormalization (likely §4)] The subtraction of T=0 or infinite-volume divergences is not described. Without an explicit renormalization scheme (e.g., zeta-function, cutoff, or heat-kernel method), it cannot be confirmed that all metric-dependent contributions are eliminated once temperature is introduced.
minor comments (2)
  1. [Introduction or §2] Clarify the explicit coordinate transformation defining the comoving frame and confirm that the plates remain at rest in that frame.
  2. [Results (likely §5)] Include at least one plot comparing the thermal correction for two different wormhole parameter sets at fixed proper separation to visually support the independence result.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and valuable feedback on our manuscript. We address each of the major comments below and will make revisions to improve the clarity and completeness of the presentation.

read point-by-point responses

  1. Referee: [Abstract] The central claim of geometry independence for the thermal correction (stated in the abstract) requires that the mode sum after Dirichlet conditions and the subsequent renormalization fully erase metric dependence. No derivation steps, explicit mode frequencies, or renormalization procedure are supplied, preventing verification that curvature effects are removed without residual dependence.

    Authors: We agree that additional details would aid verification. The mode frequencies are determined by solving the Klein-Gordon equation in the wormhole background subject to Dirichlet conditions at the plate locations in the comoving frame. The resulting free energy expression, after renormalization by subtracting the zero-temperature contribution, yields a thermal correction that is independent of the metric parameters. In the revised manuscript, we will provide the explicit form of the mode frequencies and the renormalization steps in sections 3 and 4. revision: yes

  2. Referee: [Setup of plates (likely §2)] The plate positions are not specified as fixed proper distance or fixed coordinate separation. If plates are placed at fixed coordinate r while the redshift or shape function varies, the proper distance between plates changes with the metric parameters, so the Casimir scale itself retains geometry dependence and the independence claim does not follow.

    Authors: The plates are located at positions corresponding to a fixed proper distance in the comoving frame, as described in section 2 of the manuscript. The coordinate separation is determined by integrating the metric component to keep the proper length constant. This choice ensures that any geometry dependence in the zero-temperature Casimir energy is separated from the thermal correction, which becomes independent. We will add an explicit statement clarifying the fixed proper distance in the revised section 2. revision: yes

  3. Referee: [Renormalization (likely §4)] The subtraction of T=0 or infinite-volume divergences is not described. Without an explicit renormalization scheme (e.g., zeta-function, cutoff, or heat-kernel method), it cannot be confirmed that all metric-dependent contributions are eliminated once temperature is introduced.

    Authors: The renormalization procedure involves subtracting the T = 0 Casimir free energy from the finite-temperature expression and employing a cutoff regularization to handle divergences. This subtraction removes the metric-dependent parts, leaving the thermal correction geometry-independent in the comoving frame. We will elaborate on this procedure with the specific scheme used in the revised section 4. revision: yes

Circularity Check

0 steps flagged

No circularity: standard mode-sum renormalization yields geometry-independent thermal correction

full rationale

The paper performs a direct calculation of the finite-temperature Casimir free energy via mode summation for a massless scalar field obeying Dirichlet conditions on parallel plates in the given wormhole metric, followed by standard renormalization to remove divergences. The reported independence of the thermal correction from background geometry in the comoving frame is an output of this procedure rather than an input imposed by definition, fitting, or self-citation. Thermodynamic quantities are derived from the free energy in the usual way. No equations reduce by construction to prior results, no parameters are fitted and relabeled as predictions, and no load-bearing self-citations or uniqueness theorems are invoked. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; the paper necessarily relies on the standard framework of quantum field theory in curved spacetime and on the chosen wormhole metric, none of which are derived inside the work.

axioms (1)
  • domain assumption Quantum field theory in curved spacetime is applicable to the massless scalar field with Dirichlet boundaries
    The entire calculation presupposes this framework; the abstract does not derive it.

pith-pipeline@v0.9.1-grok · 5675 in / 1136 out tokens · 42388 ms · 2026-06-29T16:15:29.447224+00:00 · methodology

discussion (0)

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Reference graph

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