The Imaginary Universe

Three Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene establish three complementary fine-structure constants, two of which are negative. Each introduces its own specific set of Planck units. Hence, two sets of basic Planck units are real, and two are imaginary. The elementary charge is the same in all those sets of Planck units, establishing equality between the products of each fine-structure constant and the speed of light it is associated with. All fine-structure constants are related to each other through the constant of \( \pi \), which indicates that they do not vary over time. The negative complementary fine-structure constant inferred from graphene reflectance is dual to the fine-structure constant. The assumption of universality of the black hole entropy formula to the remaining two stellar objects emitting perfect black-body radiation, less dense than a black hole (neutron stars and white dwarfs), renders their energies exceeding their mass-energy equivalence. To accommodate this unphysical result, we introduced an imaginary mass, and we defined three complex energies in terms of real and imaginary Planck units, storing the surplus energy in their imaginary parts. It follows that black holes are fundamentally uncharged and have a vanishing imaginary mass. We have derived the lower bound on the mass of a charged black-body object, the upper bound on the radius of a white dwarf, and the equilibrium density for all three complex energies. The complex force between real masses and imaginary charges leads to the complex black-body object's surface gravity and generalized Hawking radiation complex temperature. Furthermore, based on the Bohr model for the hydrogen atom, we show that complex conjugates of this force represent atoms and antiatoms. The proposed model considers the value(s) of the fine-structure constant(s), which are otherwise neglected in general relativity.