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.

The orientation of planes of dwarf galaxies in the quasi-linear Universe

ABSTRACT To date at least 10 highly flattened planes of dwarf galaxies are claimed to have been discovered in the Local Universe. The origin of these planes of galaxies remains unknown. One suggestion is that they are related to the large-scale structure of the cosmic web. A recent study found that the normal of a number of these dwarf galaxy planes is very closely aligned with the eigenvector of the shear tensor corresponding to the direction of greatest collapse obtained by reconstructing the full velocity field in the linear regime. Here we extend that work by both considering an additional 5 planes beyond the five examined previously and examining the alignment with respect to the quasi-linear field, a more sophisticated reconstruction, which is a better approximation on smaller (quasi-linear) scales. Our analysis recovers the previous result while not finding a significantly tight alignment with the additional five planes. However, the additional five plane normals also do not appear to be randomly oriented. We conclude that this could be due either to the normals of the new planes being poorly defined and described; the quasi-linear field at those locations being poorly constrained; or different formation mechanisms for the orientation of planes of dwarf galaxies.

Dynamics of evolving self-gravitating models in extended teleparallel gravity

The self-gravitating spherically symmetric fluid models are being studied taking power-law model in extended teleparallel (or [Formula: see text]) gravity. We form a set of governing equations which describes the dynamics of stellar evolution in the presence of torsion scalar (dark energy candidate) by incorporating power-law model in [Formula: see text] gravity along with dynamical terms like shear tensor, anisotropy, expansion scalar, dissipation, Weyl tensor and energy inhomogeneity. We explore some particular models of fluid according to various dynamical scenarios for particular values of model parameter [Formula: see text]. It is found that torsion terms associated with [Formula: see text], govern stellar evolution and provide deviation from theory of general relativity (GR). For the case, [Formula: see text], tetrad field is almost negligible and the evolving models are consistent with GR model having cosmological constant. We obtain practicable rate of change of expansion and deformation of fluid models at [Formula: see text].

The Weyl curvature tensor, Cotton–York tensor and gravitational waves: A covariant consideration

[Formula: see text] covariant approach to cosmological perturbation theory often employs the electric part ([Formula: see text]), the magnetic part ([Formula: see text]) of the Weyl tensor or the shear tensor ([Formula: see text]) in a phenomenological description of gravitational waves. The Cotton–York tensor is rarely mentioned in connection with gravitational waves in this approach. This tensor acts as a source for the magnetic part of the Weyl tensor which should not be neglected in studies of gravitational waves in the [Formula: see text] formalism. The tensor is only mentioned in connection with studies of “silent model” but even there the connection with gravitational waves is not exhaustively explored. In this study, we demonstrate that the Cotton–York tensor encodes contributions from both electric and magnetic parts of the Weyl tensor and in directly from the shear tensor. In our opinion, this makes the Cotton–York tensor arguably the natural choice for linear gravitational waves in the [Formula: see text] covariant formalism. The tensor is cumbersome to work with but that should negate its usefulness. It is conceivable that the tensor would equally be useful in the metric approach, although we have not demonstrated this in this study. We contend that the use of only one of the Weyl tensor or the shear tensor, although phenomenologically correct, leads to loss of information. Such information is vital particularly when examining the contribution of gravitational waves to the anisotropy of an almost-Friedmann–Lamitre–Robertson–Walker (FLRW) universe. The recourse to this loss is the use Cotton–York tensor.

Bianchi type VI cosmological model with electromagnetic field in Lyra geometry

Bianchi type VI cosmological model in the presence of electromagnetic field with variable magnetic permeability in the framework of Lyra geometry is presented. An exact solution is introduced by considering that the eigenvalue [Formula: see text] of the shear tensor [Formula: see text] is proportional to the scalar expansion Θ of the model, that is, C = (AB)L, where A, B, and C are the coefficients of the metric and L is a constant. Bianchi type V, III, and I cosmological models are given as special cases of Bianchi type VI. Physical and geometrical properties of the models are discussed.

The Peak/Dip Picture of the Cosmic Web

The initial shear field plays a central role in the formation of large-scale structures, and in shaping the geometry, morphology, and topology of the cosmic web. We discuss a recent theoretical framework for the shear tensor, termed the ‘peak/dip picture’, which accounts for the fact that halos/voids may form from local extrema of the density field – rather than from random spatial positions; the standard Doroshkevich's formalism is generalized, to include correlations between the density Hessian and shear field at special points in space around which halos/voids may form. We then present the ‘peak/dip excursion-set-based’ algorithm, along with its most recent applications – merging peaks theory with the standard excursion set approach.

The beaming of subhalo accretion

We examine the infall pattern of subhaloes onto hosts in the context of the large-scale structure. We find that the infall pattern is essentially driven by the shear tensor of the ambient velocity field. Dark matter subhaloes are preferentially accreted along the principal axis of the shear tensor which corresponds to the direction of weakest collapse. We examine the dependence of this preferential infall on subhalo mass, host halo mass and redshift. Although strongest for the most massive hosts and the most massive subhaloes at high redshift, the preferential infall of subhaloes is effectively universal in the sense that its always aligned with the axis of weakest collapse of the velocity shear tensor. It is the same shear tensor that dictates the structure of the cosmic web and hence the shear field emerges as the key factor that governs the local anisotropic pattern of structure formation. Since the small (sub-Mpc) scale is strongly correlated with the mid-range (∼ 10 Mpc) scale - a scale accessible by current surveys of peculiar velocities - it follows that findings presented here open a new window into the relation between the observed large scale structure unveiled by current surveys of peculiar velocities and the preferential infall direction of the Local Group. This may shed light on the unexpected alignments of dwarf galaxies seen in the Local Group.

STRUCTURE SCALARS IN CHARGED PLANE SYMMETRY

We consider non-adiabatic flow of the fluid possessing dissipation in the form of shearing viscosity in electromagnetic field. The scalar functions (structure scalars) for charged plane symmetry are formulated and are related with the physical variables of the fluid. We also develop a relationship between the Weyl tensor and other physical variables by using Taub mass formalism. The role of electric charge as well as its physical significance for the evolution of the shear tensor and expansion scalar are also explored. Finally, we discuss a special case for dust with cosmological constant.