The Imaginary Universe

Abstract

Imaginary dimensions in physics require an imaginary set of base Planck units and some negative parameter $c_n$ corresponding to the speed of light in vacuum $c$. The second, negative fine-structure constant $\alpha_2^{-1} \approx -140.178$ is present in Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene, leading to these imaginary Planck units, and it establishes $c_n \approx -3.06 \times 10^8~\text{[m/s]}$. It follows that electric charges are the same in real and imaginary dimensions. We model neutron stars and white dwarfs, emitting perfect black-body radiation, as objects having energy exceeding their mass-energy equivalence ratios. We define complex energies in terms of real and imaginary Planck units. Their imaginary parts, inaccessible for direct observation, store the excess of these energies. It follows that black holes are fundamentally uncharged, charged micro neutron stars and white dwarfs with masses lower than $5.7275 \times 10^{-10}~[\text{kg}]$ are inaccessible for direct observation, and the radii of white dwarfs' cores are limited to $R_{\text{WD}} < 6.7933~G M_{\text{WD}}/c^2$. It is conjectured that the maximum atomic number $Z=238$. A black-body object is in the equilibrium of complex energies of masses, charges, and photons if its radius $R_\text{eq} \approx 2.7665~G M_{\text{BBO}}/c^2$, which corrects the value of the photon sphere radius $R_{\text{ps}}=3G M/c^2$, by taking into account the value(s) of the fine-structure constant(s), which is otherwise neglected in general relativity. Complex Newton’s law of universal gravitation, based on complex energies, leads to the black-body object's surface gravity and the generalized Hawking radiation temperature, which includes its charge. The proposed model explains the registered (GWOSC) high masses of neutron stars' mergers without resorting to any hypothetical types of exotic stellar objects.