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In the Kaluza–Klein theory, one extra spatial dimension is added to usual spacetime. On one hand, particles moving in it gain excitations leading to a mass spectrum, which can be associated with hadronic states. Neutron stars are modelled using the equation of state of an extra-dimensional interacting zero-temperature Fermi gas. Macroscopic observables are calculated, compared to astronomical data, and a range of extra dimension sizes with the possibility of detection is given [1].
On the other hand, the extra dimension introduces a scalar field into the theory, which modifies the curvature of spacetime. On a curved background, the uncertainty relation of particles is modified, resulting in a modified dispersion relation and thermodynamics. Such effects become significant near the horizon of black holes, where even gravity induced particle decay is possible [2].
[1] A. Horváth, E. Forgács-Dajka, G.G. Barnaföldi: "Application of Kaluza-Klein Theory in Modeling Compact Stars: Exploring Extra Dimensions", MNRAS https://doi.org/10.1093/mnras/stae2637 (2024)
[2] A. Horváth, A. Wojnar, GG. Barnaföldi: "Modified Dispersion Relation in Kaluza–Klein Theory". Particles. 2026; 9(3):87. https://doi.org/10.3390/particles9030087