The Imaginary Universe

Abstract

Maxwell’s equations in vacuum provide the negative speed of light $-c$, which leads to imaginary Planck units. However, the second, negative fine-structure constant $\alpha_2^{-1} \approx -140.178$, present in the Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene, establishes the different, negative speed of light in vacuum $c_2 \approx -3.06 \times 10^8~\text{[m/s]}$, which introduces imaginary Planck units different in magnitude from those parametrized with $c$. 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 \textit{objects} having energy exceeding their mass-energy equivalence ratios. We define complex energies in terms of real and imaginary natural units. Their imaginary parts, inaccessible for direct observation, store the excess of these energies. It follows that black holes are fundamentally uncharged, masses of charged neutron stars and white dwarfs satisfy $M \lesssim 5.7275 \times 10^{-10}~[\text{kg}]$, and the radii of white dwarfs' cores are limited to $R_{\text{WD}} \lesssim 3.3967~R_{\text{BH}}$, where $R_{\text{BH}}$ is the Schwarzschild radius of a white dwarf mass. It is conjectured that the maximum atomic number $Z=238$. A black-body \textit{object} is in the equilibrium of complex energies if its radius $R_\text{eq} \approx 1.3833~R_{\text{BH}}$, which is close to the photon sphere radius $R_{\text{ps}}=1.5~R_{\text{BH}}$, and marginally greater than a locally negative energy density bound of $4/3~R_{\text{BH}}$. 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 takes into account the value(s) of the fine-structure constant(s), which is/are otherwise neglected in general relativity, and explains the registered (GWOSC) high masses of neutron stars' mergers and the associated fast radio bursts (CHIME) without resorting to any hypothetical types of exotic stellar \textit{objects}.