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To this day, the nature of dark matter (DM) remains elusive despite all our efforts. This type of matter has not been directly observed, so we infer its gravitational effect. Since galaxies and supermassive objects like these are most likely to contain DM, we assume that dense objects such as neutron stars (NSs) are also likely to host DM. The NS is considered the best natural laboratory for testing theories and collecting observational data. We mainly focus on two types of DM particles, fermions and bosons, with a mass range of [0.01–1.5] GeV and repulsive interactions of about [10−4–10−1] MeV−1. Using a two-fluid model to solve the TOV equations, we find stable configurations that span hundreds of kilometers and weigh tens or even hundreds of solar masses. To visualize results, we think of a giant invisible compact DM object and the NS in the center as the core, the only visible part. Stability criteria are met for these configurations, so collapsing into a black hole is unlikely. We go further and use this work for smaller formations that exist inside the mysterious Mass Gap. We also find stable configurations of 3–4 solar masses, with NS-DM mixing capable of describing the mass gap. Regardless, the present theoretical prediction, if combined with corresponding observations, could shed light on the existence of DM and even more on its fundamental properties.

To this day, the nature of dark matter (DM) remains elusive despite all our efforts. This type of matter has not been directly observed, so we infer its gravitational effect. Since galaxies and supermassive objects like these are most likely to contain DM, we assume that dense objects such as neutron stars (NSs) are also likely to host DM. The NS is considered the best natural laboratory for testing theories and collecting observational data. We mainly focus on two types of DM particles, fermions and bosons, with a mass range of [0.01–1.5] GeV and repulsive interactions of about [ 10 − 4 – 10 − 1 ] MeV − 1 . Using a two-fluid model to solve the TOV equations, we find stable configurations that span hundreds of kilometers and weigh tens or even hundreds of solar masses. To visualize results, we think of a giant invisible compact DM object and the NS in the center as the core, the only visible part. Stability criteria are met for these configurations, so collapsing into a black hole is unlikely. We go further and use this work for smaller formations that exist inside the mysterious Mass Gap. We also find stable configurations of 3–4 solar masses, with NS-DM mixing capable of describing the mass gap. Regardless, the present theoretical prediction, if combined with corresponding observations, could shed light on the existence of DM and even more on its fundamental properties. [ABSTRACT FROM AUTHOR]

Snyder's quantum space‐time which is Lorentz invariant is investigated. It is found that the quanta of space‐time have a positive mass that is interpreted as a positive real mass gap of space‐time. This mass gap is related to the minimal length of measurement which is provided by Snyder's algebra. Several reasons to consider the space‐time quanta as a 24‐cell are discussed. Geometric reasons include its self‐duality property and its 24 vertices that may represent the standard model of elementary particles. The 24‐cell symmetry group is the Weyl/Coxeter group of the F4$F_4$ group which was found recently to generate the gauge group of the standard model. It is found that 24‐cell may provide a geometric interpretation of the mass generation, Avogadro number, color confinement, and the flatness of the observable universe. The phenomenology and consistency with measurements is discussed. Snyder's quantum space‐time which is Lorentz invariant is investigated. It is found that the quanta of space‐time have a positive mass that is interpreted as a positive real mass gap of space‐time. This mass gap is related to the minimal length of measurement which is provided by Snyder's algebra. Several reasons to consider the space‐time quanta as a 24‐cell are discussed. Geometric reasons include its self‐duality property and its 24 vertices that may represent the standard model of elementary particles. The 24‐cell symmetry group is the Weyl/Coxeter group of the F4 group which was found recently to generate the gauge group of the standard model. It is found that 24‐cell may provide a geometric interpretation of the mass generation, Avogadro number, color confinement, and the flatness of the observable universe. The phenomenology and consistency with measurements is discussed. [ABSTRACT FROM AUTHOR]

The Casimir–Polder force between spherical nanoparticles and a graphene-coated silica plate is investigated in situations out of thermal equilibrium, i.e., with broken time-reversal symmetry. The response of the graphene coating to the electromagnetic field is described on the basis of first principles of quantum electrodynamics at nonzero temperature using the formalism of the polarization tensor in the framework of the Dirac model. The nonequilibrium Casimir–Polder force is calculated as a function of the mass-gap parameter, the chemical potential of graphene, and the temperature of the graphene-coated plate, which can be both higher or lower than that of the environment. It is shown that the force value increases with the increasing chemical potential, and this increase is more pronounced when the temperature of a graphene-coated plate is lower than that of the environment. The nonequilibrium force also increases with increasing temperature of the graphene-coated plate. This increase is larger when the plate is hotter than the environment. The effect is revealed that the combined impact of the chemical potential, μ , and mass gap, Δ , of the graphene coating depends on the relationship between Δ and 2 μ. If 2 μ > Δ , the magnitude of the nonequilibrium force between nanoparticles and a cooled graphene-coated plate becomes much larger than for a graphene coating with μ = 0 . The physical reasons explaining this effect are elucidated. Possible applications of the obtained results are discussed. [ABSTRACT FROM AUTHOR]

The Casimir–Polder force between spherical nanoparticles and a graphene-coated silica plate is investigated in situations out of thermal equilibrium, i.e., with broken time-reversal symmetry. The response of the graphene coating to the electromagnetic field is described on the basis of first principles of quantum electrodynamics at nonzero temperature using the formalism of the polarization tensor in the framework of the Dirac model. The nonequilibrium Casimir–Polder force is calculated as a function of the mass-gap parameter, the chemical potential of graphene, and the temperature of the graphene-coated plate, which can be both higher or lower than that of the environment. It is shown that the force value increases with the increasing chemical potential, and this increase is more pronounced when the temperature of a graphene-coated plate is lower than that of the environment. The nonequilibrium force also increases with increasing temperature of the graphene-coated plate. This increase is larger when the plate is hotter than the environment. The effect is revealed that the combined impact of the chemical potential, μ, and mass gap, Δ, of the graphene coating depends on the relationship between Δ and 2μ. If 2μ>Δ, the magnitude of the nonequilibrium force between nanoparticles and a cooled graphene-coated plate becomes much larger than for a graphene coating with μ=0. The physical reasons explaining this effect are elucidated. Possible applications of the obtained results are discussed.