Alexei J. Nurmagambetov

Introduction/Objective: The main objective of this study is to develop a generalization of the Kerr metric that can be used to model the initial or intermediate stage of the formation of a rotating black hole. The end result of this process may involve either the complete absorption of matter by the black hole or the formation of a quasi-stable black-hole configuration with an accretion disk consisting of external matter. Methods: Solving the aforementioned tasks involves the use of well-established methods in theoretical physics, based on finding solutions to systems of differential equations, analyzing symmetries, and applying various criteria to describe the dynamics of test particles in the vicinity of massive astrophysical objects. Results: As a result of our research, we derived a series of solutions for a rotating Kerr-type black hole with non-trivial matter on a flat and (A)dS background. Symmetry arguments and singularity analysis in the proposed black hole models allowed us to fix the free parameters of the solutions, while the study of popular energy conditions enabled us to impose constraints on the configuration and field content of the external matter. The resulting spacetime geometry exhibits a singularity of a special type in the directions of the north and south poles, which may be responsible for a bipolar outflow of particles from the black holes. As a step toward constructing a solution for a nonstationary rotating black hole in the presence of matter, we investigated the zero angular momentum limit of the constructed metrics. The use of the Eddington–Finkelstein coordinates allowed us to generalize the proposed construction to a Vaidya-type black hole. Finally, using the Newman–Janis algorithm, we found the corresponding generalization of the solution for the Kerr–Vaidya black hole. Discussion: It is important to note that the general nature of our analysis does not require a specific definition of the fields of matter; it is sufficient that they be described by the standard energymomentum tensor of relativistic matter. A key point in the construction is the connection between the generalization of spacetime geometry proposed here and the original Kerr solution, which implies keeping the fundamental characteristics of the Kerr metric. Conclusion: Our findings represent necessary and important steps toward solving the problem of the formation and evolution of Kerr black holes. Given their importance in astrophysics, these results open new perspectives on the study of compact rotating astrophysical objects, provide new insights into the possible composition of accretion disks, and suggest new ways to explain the mechanisms of formation of ultra-high-energy particle jets from rotating black holes. PACS: 04.70.-s, 04.70.Bw, 04.20.Jb.

Supersymmetry is one of the most important and indispensable ingredients of modern theoretical physics. However, the absence, at least at the time of publishing this review, of experimental verification of supersymmetry in elementary particle/high-energy physics casts doubt on the viability of this concept at the energies achievable at the LHC. The more unexpected are either already experimentally verified or proposed for verification manifestations of supersymmetry at the level of low (condensed matter physics, quantum optics) and medium (nuclear physics) energies where standard quantum mechanics works. Using examples of various systems from completely different areas of physics, we discuss the isospectrality of quantum Hamiltonians, hidden and explicit supersymmetry, the advantages of the supersymmetric quantum mechanics approach and its role in quantum engineering.

Supersymmetry is one of the most important and indispensable ingredients of modern theoretical physics. However, the absence, at least at the time of publishing this review, of experimental verification of supersymmetry in elementary particle/high-energy physics casts doubt on the viability of this concept at the energies achievable at the LHC. The more unexpected are either already experimentally verified or proposed for verification manifestations of supersymmetry at the level of low (condensed matter physics, quantum optics) and medium (nuclear physics) energies where standard quantum mechanics works. Using examples of various systems from completely different areas of physics, we discuss the isospectrality of quantum Hamiltonians, hidden and explicit supersymmetry, the advantages of the supersymmetric quantum mechanics approach and its role in quantum engineering.

We consider subtleties of the horizon (null-hypersurface) limit in the Parikh-Wilczek Membrane Approach to Black Holes. Specifically, we refine the correspondence between the projected Einstein equations of gravity with matter and the Raychaudhuri-Damour-Navier-Stokes (RDNS) equations of relativistic hydrodynamics. For a general configuration of gravity with matter we obtain additional terms in the hydrodynamic equations, which include very specific combinations of the contracted logarithmic derivatives of a parameter (the regularization function) determining the proximity of a stretched membrane to the black hole horizon. Nevertheless, direct computations of the new terms for exact (Schwarzschild and Kerr) black hole solutions prompt the standard form of the RDNS equations, due to the non-expanding horizon property of these solutions. Therefore, the reduction of the extended RDNS equations to their classical form may be viewed as an additional consistency condition in the exact black hole solutions hydrodynamics, and may serve as a non-trivial test for various viable approximations of spacetime metrics. We compare in detail the Parikh-Wilczek Membrane Approach with the Gourgoulhon-Jaramillo method of a null-hypersurface description, as well as give the link of the obtained results to our previous work on the Kerr black holes.

We construct series of solutions for the Kerr-type rotating black hole with non-trivial matter in flat and (A)dS backgrounds. Symmetry arguments and singularity analysis in the proposed black hole models fix the free parameters of the solutions, and the study of popular energy conditions makes it possible to impose constraints on configuration and field content of external matter. The resulted geometry of spacetimes is featured by a special type singularity in the north and south pole directions, inducing the bipolar outflow of particles from black holes. As a step toward the construction of a non-stationary rotating black hole solution in the presence of matter, we explore the zero angular momentum limit of the constructed metrics. The use of the Eddington-Finkelstein coordinates allows us to find a generalization of the proposed construction to the Vaidya-type black hole. Finally, employing the Newman-Janis algorithm, we find the corresponding generalization of the Kerr-Vaidya black hole solution.

We fill some of the existing gaps in the correspondence between supersymmetric quantum mechanics and the inverse scattering transform by extending the consideration to the case of paired stationary and nonstationary Hamiltonians. We formulate the Goursat problem corresponding to the case and explicitly construct the kernel of the nonlocal inverse scattering transform, which solves it. As a result, we find a way of constructing non-Hermitian Hamiltonians from the initially Hermitian ones that leads, in the case of real-valued spectra of both potentials, to pairing of ${\cal CPT/PT}$-invariant Hamiltonians. The relevance of our proposal to quantum optics and optical waveguide technology, as well as to nonlinear dynamics and black hole physics, is briefly discussed.

We consider subtleties of the horizon (null-hypersurface) limit in the Parikh-Wilczek Membrane Approach to Black Holes. Specifically, we refine the correspondence between the (projected) Einstein equations of gravity with matter and the Raychaudhuri-Damour-Navier-Stokes (RDNS) equations of relativistic hydrodynamics. For a general configuration of gravity with matter we obtain additional terms in the hydrodynamic equations, which include logarithmic derivarives of a parameter (the regularization function) determining the proximity of a stretched membrane to the BH horizon. Direct computation of the new terms for exact (Schwarzschild and Kerr) solutions to the Einstein equations results in vanishing the additions to the RDNS equations in the horizon limit. For spacetimes, which are not exact solutions to the Einstein equations, as, for instance, for space-time configurations mimicking black holes, taking into account new terms in the RDNS equations is the mandatory operation. We also comment the correspondence between the horizon limit of the Parikh-Wilczek Membrane Approach and the Gourgoulhon-Jaramillo method of a null-hypersurface description, as well as the link of the obtained results to our previous work on the Kerr black holes.

We consider the membrane viewpoint a l\`a Parikh-Wilczek on the Kerr solution for a rotating black hole. Computing the stress-energy tensor of a close-to-the-horizon stretched membrane and comparing it to the stress-tensor of a viscous fluid, we recover transport coefficients in terms of the Kerr geometry. Viscosities of the dual fluid remain constant, while the rest of the transport coefficients become complex functions of radial and angle coordinates. We study the qualitative behavior of the pressure, expansion, and energy/momentum densities for two specific black holes: the slowly rotating black hole, with the angular momentum of one percent of the black hole mass squared, and the extremal Kerr black hole. For the Kerr solution in the Boyer-Lindquist coordinates, these transport coefficients generally have poles at different values of the radial coordinate in the range between the horizon and the Schwarzschild radius of the black hole, in dependence on the fixed angle direction. We briefly discuss our findings in the context of a relation between the Membrane Paradigm and the AdS/CFT correspondence, the KSS bound violation, the coordinate choice, and a non-stationary extension of the Kerr solution.

We study features of tunneling dynamics in an exactly-solvable model of N=4 supersymmetric quantum mechanics with a multi-well potential and with broken reflective symmetry. Quantum systems with a phenomenological potential of this type demonstrate the phenomenon of partial localization of under-barrier states, possibly resulting in the appearance of the so-called "resonant" tunneling, or the phenomenon of coherent tunneling destruction, referring to the complete localization. Taking the partial localization and the coherent tunneling destruction as basic examples, we indicate main advantages of using isospectral exactly-solvable Hamiltonians in studies quantum mechanical systems with two- and three-well potentials. They, in particular, are: having enough freedom of changing the potential shape in a wide range, that allows one to choose an exactly-solvable model close to characteristics of the phenomenological one; ability of changing the number of local minima and symmetry characteristics of the potential (symmetric or deformed) without changing the main part of the spectrum; engaging a smart basis of states, that dramatically decreases the dimensionality of matrices used in the diagonalization procedure of the corresponding spectral problem.

We recently studied the energy behavior of a quantum‐corrected time‐dependent black hole. The system analyzed was a quantum‐corrected Kerr solution that settles down to a stationary configuration as the time dependence fades out. A trans‐Planckian energy scaling in the vicinity of the event horizon resulted, and we proposed the trans‐Planckian radiation to be the missing link in the glowing mechanism of active galactic nuclei. The main goal of the present work is to examine the scaling and structure of the radiation by analyzing the quantum momentum density. We again observe a trans‐Planckian behavior. Furthermore, the momentum density displays structures that are indicative of a disk‐like configuration near the equator and a collimated outflow of matter from the poles. The bipolar outflow (disk‐like structure) should be an essential part of the underlying mechanism for jets (accretion disks) of active galactic nuclei.