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arXiv · 2512.15610

Stefan-Boltzmann Law and Thermal Casimir Effect in Neutron Star Spacetime via Thermo Field Dynamics

K. E. L. de Farias·M. A. Anacleto·Rafael A. Batista·Iver Brevik·F. A. Brito·E. Passos·Amilcar R. Queiroz·Lázaro L. Sales
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Abstract

We investigate the thermal Casimir effect for a massless scalar field in the curved spacetime of a neutron star within the Thermo Field Dynamics (TFD) formalism. Starting from the renormalized energy-momentum tensor, we generalize the Stefan-Boltzmann law to include gravitational redshift and curvature corrections governed by the Tolman-Oppenheimer-Volkoff (TOV) metric. Finite temperature and spatial compactification are introduced simultaneously, allowing a unified and consistent treatment of both vacuum and thermal contributions inside and outside the star. Analytical expressions are derived for the high- and low-temperature limits, showing explicitly how curvature and redshift modify the characteristic $T^4$ dependence of thermal radiation. The results reveal that strong gravity significantly alters the local energy density and pressure, demonstrating the nontrivial interplay between quantum vacuum fluctuations and compact astrophysical geometries. A polytropic model is considered to perform numerical analyses, highlighting the influence of the spacetime background on vacuum fluctuations.

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K. E. L. de Farias, M. A. Anacleto, Rafael A. Batista, Iver Brevik, F. A. Brito, E. Passos, Amilcar R. Queiroz, Lázaro L. Sales. 2025-12-17. Stefan-Boltzmann Law and Thermal Casimir Effect in Neutron Star Spacetime via Thermo Field Dynamics. https://arxiv.org/abs/2512.15610

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