Infrared effects in the late stages of black hole evaporation

As a black hole evaporates, each outgoing Hawking quantum carries away some of the black holes asymptotic charges associated with the extended Bondi-Metzner-Sachs group. These include the Poincaré charges of energy, linear momentum, intrinsic angular momentum, and orbital angular momentum or center-of-mass charge, as well as extensions of these quantities associated with supertranslations and super-Lorentz transformations, namely supermomentum, superspin and super center-of-mass charges (also known as soft hair). Since each emitted quantum has fluctuations that are of order unity, fluctuations in the black hole’s charges grow over the course of the evaporation. We estimate the scale of these fluctuations using a simple model. The results are, in Planck units: (i) The black hole position has a uncertainty of $$ \sim {M}_i^2 $$ ∼ M i 2 at late times, where Mi is the initial mass (previously found by Page). (ii) The black hole mass M has an uncertainty of order the mass M itself at the epoch when M ∼ $$ {M}_i^{2/3} $$ M i 2 / 3 , well before the Planck scale is reached. Correspondingly, the time at which the evaporation ends has an uncertainty of order $$ \sim {M}_i^2 $$ ∼ M i 2 . (iii) The supermomentum and superspin charges are not independent but are determined from the Poincaré charges and the super center-of-mass charges. (iv) The supertranslation that characterizes the super center-of-mass charges has fluctuations at multipole orders l of order unity that are of order unity in Planck units. At large l, there is a power law spectrum of fluctuations that extends up to l ∼ $$ {M}_i^2/M $$ M i 2 / M , beyond which the fluctuations fall off exponentially, with corresponding total rms shear tensor fluctuations ∼ MiM−3/2.

Geometrical interpretation of the pilot wave theory and manifestation of spinor fields

Using the hydrodynamical formalism of quantum mechanics for a Schrödinger spinning particle developed by Takabayashi, Vigier, and followers, which involves vortical flows, we propose a new geometrical interpretation of the pilot wave theory. The spinor wave in this interpretation represents an objectively real field, and the evolution of a material particle controlled by the wave is a manifestation of the geometry of space. We assume this field to have a geometrical nature, basing on the idea that the intrinsic angular momentum, the spin, modifies the geometry of the space, which becomes a manifold, represented as a vector bundle with a base formed by the translational coordinates and time, and the fiber of the bundle, specified at each point by the field of a tetrad $e^a_{\mu}$, forms from bilinear combinations of the spinor wave function. It has been shown that the spin vector rotates following the geodesic of the space with torsion, and the particle moves according to the geometrized guidance equation. This fact explains the self-action of the spinning particle. We show that the curvature and torsion of the spin vector line is determined by the space torsion of the absolute parallelism geometry.

Solutions to Schrödinger’s equation

Eigenstates of the square well potential are calculated and displayed. Barrier penetration and the connection to total internal reflection are explained. α‎–decay by barrier penetration is calculated and used to explain Geiger–Nuttall plots. Gauss–Hermite solutions to the harmonic oscillator potential are deduced and displayed. Zero point fluctuations are introduced. Hydrogen atom eigenstate wavefunctions for the Coulomb potential are calculated and displayed. Principal, orbital angular momentum and intrinsic angular momentum quantum numbers and their allowed combinations are discussed and interpreted: n, l, ml, s and ms. The Stern–Gerlach experiment and Pauli’s perception that electron spin is half-integral are presented; as are Beth’s experiment and photon spin. Dominance of electric dipole transitions and resulting selection rules discussed. Fine spectral structure and spin-orbit coupling are described. Nuclear spin and resulting hyperfine spectral structure are introduced. Landé factors introduced.

ALMA survey of Class II protoplanetary disks in Corona Australis: a young region with low disk masses

Context. In recent years, the disk populations in a number of young star-forming regions have been surveyed with the Atacama Large Millimeter/submillimeter Array (ALMA). Understanding the disk properties and their correlation with the properties of the central star is critical to understanding planet formation. In particular, a decrease of the average measured disk dust mass with the age of the region has been observed, consistent with grain growth and disk dissipation. Aims. We aim to compare the general properties of disks and their host stars in the nearby (d = 160 pc) Corona Australis (CrA) star forming region to those of the disks and stars in other regions. Methods. We conducted high-sensitivity continuum ALMA observations of 43 Class II young stellar objects in CrA at 1.3 mm (230 GHz). The typical spatial resolution is ~0.3′′. The continuum fluxes are used to estimate the dust masses of the disks, and a survival analysis is performed to estimate the average dust mass. We also obtained new VLT/X-shooter spectra for 12 of the objects in our sample for which spectral type (SpT) information was missing. Results. Twenty-four disks were detected, and stringent limits have been put on the average dust mass of the nondetections. Taking into account the upper limits, the average disk mass in CrA is 6 ± 3 M⊕. This value is significantly lower than that of disks in other young (1–3 Myr) star forming regions (Lupus, Taurus, Chamaeleon I, and Ophiuchus) and appears to be consistent with the average disk mass of the 5–10 Myr-old Upper Sco. The position of the stars in our sample on the Herzsprung-Russel diagram however seems to confirm that CrA has an age similar to Lupus. Neither external photoevaporation nor a lower-than-usual stellar mass distribution can explain the low disk masses. On the other hand, a low-mass disk population could be explained if the disks were small, which could happen if the parent cloud had a low temperature or intrinsic angular momentum, or if the angular momentum of the cloud were removed by some physical mechanism such as magnetic braking. Even in detected disks, none show clear substructures or cavities. Conclusions. Our results suggest that in order to fully explain and understand the dust mass distribution of protoplanetary disks and their evolution, it may also be necessary to take into consideration the initial conditions of star- and disk-formation process. These conditions at the very beginning may potentially vary from region to region, and could play a crucial role in planet formation and evolution.

Helicity and Spin of Linearly Polarized Hermite-Gaussian Modes

The angular momentum content and propagation of linearly polarized Hermite-Gaussian modes are analyzed. The helicity gauge invariant continuity equation reveals that the helicity and flow in the direction of propagation are zero. However, the helicity flow exhibits nonvanishing transverse components. These components have been recently described as photonic wheels. These intrinsic angular momentum terms, depending on the criterion, can be associated with spin or orbital momentum. The electric and magnetic contributions to the optical helicity will be shown to cancel out for Hermite-Gaussian modes. The helicity ϱAC here derived is consistent with the interpretation that it represents the projection of the angular momentum onto the direction of motion.

Research on spinalorithronics at the Department of Low Temperature Physics of Kharkov National University in 2017-2019

In this paper is presented a short review of results about spincaloritronics obtained on the low temperature physics chair of the Kharkiv National University from 2017 till 2019 years. In introduction several new directions in magnetoelectronics are discussed- spintronics, spincaloritronics and magnonics- which emerged with the aim to reduce the energy dissipation in devices of usual semiconductor microelectronics. Spintronic devices hold the promise of faster switching speeds, less total energy consumption, and higher density of circuit elements, lowering the heat production per switching element. This could be achieved by employing the spin of the electrons instead of (or in addition to) the charge. The spin corresponds to the additional quantum mechanical property of an electron that can be described as an intrinsic angular momentum. Realization of the existence of the tunneling magnetoresistance effect observed at room temperature is paving the way for the evolution of solid state memory devices, new type of the memory, and fast programmable logic circuits. In spincaloritronics, which is included as an additional complementary branch to the established field of spintronics and thermoelectricity, the transport of charge, magnetization (spin), or heat, occurs when the corresponding particles (electrons, magnons, or phonons) are driven out of thermodynamic equilibrium. Magnonics is the part of spintronics, or in a more general sense is electronics, studying physical properties of magnetic micro- and nanostructures, properties of propagating spin waves and also the possibilities of their application for construction of the elemental base of devices at nanolevel for processing, transmission and memory of the information on the basis of new physical principles. In next section the main results of the four papers, published in Physical Revew B are discussed: 1) nonlinear relaxation between magnons and phonons in insulating ferromagnets 2) role of magnons and the size effect in heat transport through an insulating ferromagnet-insulator interface 3) spin Seebeck effect and phonon energy transfer in heterostructures containing layers of normal metal and ferroinsulator 4) temperature dependence of the magnon-phonon energy relaxation time in a ferromagnet insulator.

Static vacuum solutions on curved space–times with torsion

The Einstein–Cartan–Kibble–Sciama ( ECKS ) theory of gravity naturally extends Einstein’s general relativity ( GR ) to include intrinsic angular momentum (spin) of matter. The main feature of this theory consists of an algebraic relation between space–time torsion and spin of matter, which indeed deprives the torsion of its dynamical content. The Lagrangian of ECKS gravity is proportional to the Ricci curvature scalar constructed out of a general affine connection so that owing to the influence of matter energy–momentum and spin, curvature and torsion are produced and interact only through the space–time metric. In the absence of spin, the space–time torsion vanishes and the theory reduces to GR . It is however possible to have torsion propagation in vacuum by resorting to a model endowed with a nonminimal coupling between curvature and torsion. In the present work we try to investigate possible effects of the higher order terms that can be constructed from space–time curvature and torsion, as the two basic constituents of Riemann–Cartan geometry. We consider Lagrangians that include fourth-order scalar invariants from curvature and torsion and then investigate the resulting field equations. The solutions that we find show that there could exist, even in vacuum, nontrivial static space–times that admit both black holes and naked singularities.

Central charge for the Schwarzschild black hole

Proceeding in exactly the same way as in the derivation of the temperature of a dual CFT for the extremal black hole in the Kerr/CFT correspondence, it is found that the temperature of a chiral, dual CFT for the Schwarzschild black hole is [Formula: see text]. Comparing Cardy’s formula with the Bekenstein–Hawking entropy and using [Formula: see text], it is found that the central charge for the Schwarzschild black hole is of the form [Formula: see text], where [Formula: see text] is the intrinsic angular momentum of the black hole, [Formula: see text]. It is shown that the central charge for any four-dimensional (4D) extremal black hole is of the same form. The possible universality of this form is briefly discussed.