Narrow Results

We show how the motion of a charged particle near the horizon of an extreme Reissner–Nordström black hole can lead to different forms of conformal mechanics, depending on the choice of the time coordinate.

We investigate dynamics of probe particles moving in the near-horizon limit of (2N + 1)-dimensional extremal Myers–Perry black hole (in the cases of N = 3, 4, 5) with arbitrary rotation parameters. Very recently it has been shown in [T. Hakobyan, A. Nersessian and M. M. Sheikh-Jabbari, Phys. Lett. B772, 586 (2017)] that in the most general cases with non-equal nonvanishing rotational parameters the system admits separation of variables in N-dimensional ellipsoidal coordinates. We wrote down the explicit expressions of Liouville integrals of motion, given in the above-mentioned reference in ellipsoidal coordinates, in initial “Cartesian” coordinates in seven, nine and eleven dimensions, and found that these expressions hold in any dimension. Then, taking the limit where all of the rotational parameters are equal, we reveal that each of these N − 1 integrals of motion results in the Hamiltonian of the spherical mechanics of a (2N + 1)-dimensional MP black hole with equal nonvanishing rotational parameters.

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.

We consider the grand canonical ensemble of the static and extremal black holes, when the equivalence of the electric charge and mass of individual black hole is postulated. Assuming uniform distribution of black holes in space, we are finding the effective mass of test particle and mean time dilation at the admissible points of space, taking into account the gravitational action of surrounding black holes. Having specified the statistics that governs extremal black holes, we study its effect on those quantities. Here, the role of statistics is to assign a statistical weight to the configurations of certain fixed number of black holes. We borrow these weights from Bose–Einstein, Fermi–Dirac, classical and infinite statistics. Using mean field approximation, the aforementioned characteristics are calculated and visualized, which permits us to draw the conclusions on visible effect of each statistics.

We test whether static charged dilaton black holes in $(2+1)$ dimensions can be turned into naked singularities by sending in test particles from infinity. We derive that overcharging is possible and generic for both extremal and nearly extremal black holes. Our analysis also implies that nearly extremal charged dilaton black holes can be continuously driven to extremality and beyond, unlike nearly extremal Ban̆ados–Teitelboim–Zanelli, Kerr and Reissner–Nordström black holes which are overspun or overcharged by a discrete jump. Thus, the weak form of the cosmic censorship conjecture and the third law of black hole thermodynamics are both violated in the interaction of charged dilaton black holes in $(2+1)$ dimensions, with test particles. We also derive that there exist no points, where the heat capacity vanishes or diverges in the transition from black holes to naked singularities. The phase transitions that could potentially prevent the formation of naked singularities do not occur.

We define an algebraic characterization of half supersymmetric branes in supergravity theories with different amount of supersymmetry. We furthermore illustrate how this classification can be used as starting point to explain the orbits stratification for extremal black holes.