On the possibility of a complex 4-dimensional space-time manifold

According to traditional theory, it is believed that Fermions do not exhibit superradiation. However, when predetermined boundary conditions are in place, there is a possibility of combining the wave function of coupled Fermions, which can result in the emergence of superradiation phenomena. This article presents a novel perspective, proposing that Fermions have the potential to display superradiation phenomena. This implies that there is a broader scope for investigating superradiation and its relationship with boundary conditions.

physics.gen-ph↗

arXiv2026

All About the Galilean Group SGal(3)

We consider the Galilean group of affine transformations that preserve absolute time intervals between events in spacetime, as well as spatial distances between simultaneous events. The special Galilean group, SGal(3), is a 10-dimensional Lie group; we examine the structure of the group and its Lie algebra and discuss the representation of uncertainty on the group manifold. We also derive closed-form expressions for the $\LieGroupSGal{3}$ exponential and logarithmic maps, the Cayley and inverse Cayley maps, and the left Jacobian and its inverse. Along the way, we mention other groups, including the special orthogonal group, the special Euclidean group, and the group of extended poses, all of which are proper subgroups of the special Galilean group. We describe the role of time in Galilean relativity and touch on the relationship between temporal and spatial uncertainty.

physics.gen-ph↗

arXiv2026

Constraints on Rastall gravity from current observational data

We study the cosmological features of Rastall gravity, where the covariant energy-momentum conservation is modified to $\nabla_μT^μ_ν=λ\nabla_νR$ in curved spacetime. For this purpose, we obtain the modified field equations of Rastall model to linear order of perturbations, and then inspect the evolutionary behavior of cosmological observables, chiefly the matter power spectrum and the Hubble parameter, within the context of Rastall gravity. We also compare Rastall model with cosmological probes, namely cosmic microwave background, weak lensing, supernovae, baryon acoustic oscillations, and redshift-space distortions data. According to our numerical results, Rastall gravity prefers lower growth of structures compared to the $Λ$CDM model, which indicates consistency with low-redshift large-scale structure probes. Moreover, numerical analysis reveals that Rastall gravity with a cosmological constant as the dark energy component suffers from the Hubble tension, like the $Λ$CDM model.

physics.gen-ph↗