Narrow Results

Combination of both quantum field theory (QFT) and string theory in curved backgrounds in a consistent framework, the string analogue model, allows us to provide a full picture of the Kerr–Newman black hole and its evaporation going beyond the current picture. We compute the quantum emission cross-section of strings by a Kerr–Newman black hole (KNbh). It shows the black hole emission at the Hawking temperature T_sem in the early stage of evaporation and the new string emission featuring a Hagedorn transition into a string state of temperature T_s at the last stages. New bounds on J and Q emerge in the quantum string regime (besides the known ones of the classical/semiclassical QFT regime). The last state of evaporation of a semiclassical Kerr–Newman black hole with mass M > m_Pl, angular momentum J and charge Q is a string state of temperature T_s, string mass M_s, J = 0 and Q = 0, decaying as usual quantum strings do into all kinds of particles. (Naturally, in this framework, there is no loss of information, (there is no paradox at all).) We compute the string entropy S_s(m, j) from the microscopic string density of states of mass m and spin mode j, ρ(m, j). (Besides the Hagedorn transition at T_s) we find for high j (extremal string states j → m²α′c), a new phase transition at a temperature , higher than T_s. By precisely identifying the semiclassical and quantum (string) gravity regimes, we find a new formula for the Kerr black hole entropy S_sem(M, J), as a function of the usual Bekenstein–Hawking entropy . For M ≫ m_Pl and J < GM²/c, is the leading term, but for high angular momentum, (nearly extremal case J = GM²/c), a gravitational phase transition operates and the whole entropy S_sem is drastically different from the Bekenstein–Hawking entropy . This new extremal black hole transition occurs at a temperature T_{sem J} = (J/ℏ)T_sem, higher than the Hawking temperature T_sem.

The report considers the interaction of scalar particles, photons and fermions with the gravitational and electromagnetic Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman fields. The behavior of effective potentials in the relativistic Schrödinger-type second-order equations is analyzed. It was found that the quantum theory is incompatible with the hypothesis of the existence of classical black holes with event horizons of zero thickness that were predicted based on solutions of the general relativity (GR) with zero and non-zero cosmological constant $\mathrm{\Lambda }$. The alternative may be presented by compound systems, i.e., collapsars with fermions in stationary bound states.

We investigate null geodesics impinging parallel to the rotation axis of a Kerr–Newman black hole, and show that the absorption cross section for a massless scalar field in the eikonal limit can be described in terms of the photon orbit parameters. We compare our sinc and low-frequency approximations with numerical results, showing that they are in excellent agreement.

We have recently proposed a new action principle for combining Einstein equations and the Dirac equation for a point mass. We used a length scale $L_{\mathrm{\text{CS}}}$, dubbed the Compton–Schwarzschild length, to which the Compton wavelength and Schwarzschild radius are small mass and large mass approximations, respectively. Here, we write down the field equations which follow from this action. We argue that the large mass limit yields Einstein equations, provided we assume the wave function collapse and localization for large masses. The small mass limit yields the Dirac equation. We explain why the Kerr–Newman black hole has the same gyromagnetic ratio as the Dirac electron, both being twice the classical value. The small mass limit also provides compelling reasons for introducing torsion, which is sourced by the spin density of the Dirac field. There is thus a symmetry between torsion and gravity: torsion couples to quantum objects through Planck’s constant $\hslash$ (but not $G$) and is important in the microscopic limit. Whereas gravity couples to classical matter, as usual, through Newton’s gravitational constant $G$ (but not $\hslash$), and is important in the macroscopic limit. We construct the Einstein–Cartan–Dirac equations which include the length $L_{\mathrm{\text{CS}}}$. We find a potentially significant change in the coupling constant of the torsion driven cubic nonlinear self-interaction term in the Dirac–Hehl–Datta equation. We speculate on the possibility that gravity is not a fundamental interaction, but emerges as a consequence of wave function collapse, and that the gravitational constant maybe expressible in terms of Planck’s constant and the parameters of dynamical collapse models.

In this paper, we study the superradiant instability of slowly rotating Kerr–Newman (sKN) black holes under a charged massive scalar perturbation. These black holes resemble closer the Reissner–Nordström black holes than the Kerr–Newman black holes. From the scalar potential analysis, we find that the superradiant instability is not allowed in the sKN black holes because the condition for a trapping well is not compatible with the superradiance condition. However, the rate of energy extraction might grow exponentially if the sKN black hole is placed inside a reflecting cavity. Finally, we obtain two conditions for the trapping well to possess quasibound states in the sKN black holes by analyzing asymptotic scalar potential and far-region wave functions.