Vladimír Balek

The Shell of Incoherent Charged Matter Falling onto a Charged Rotating Black Hole

The motion of the shell of charged testparticles falling radially from rest at infinity withzero total angular momentum onto a Kerr–Newmanblack hole is studied. The shell, initially spherical,becomes prolate along the axis of symmetry of the holeduring the fall. The shape of the shell from theviewpoint of distant observers is characterized by meansof the photons moving along geodesics of the outgoing principal null congruence. The motion of theshell is examined analytically for large distances andnear the horizon. In the special case, when at largedistances of the hole the attractive Newtongravitational force is compensated by the repulsive Coulombforce, the complete motion is given explicitly in termsof elementary functions.

The effect of a radiation-like solid on CMB anisotropies

We compute the power in the lowest multipoles of CMB anisotropies in the presence of radiation-like solid, a hypothetical new kind of radiation with nonzero shear modulus. If only the ordinary Sachs-Wolfe effect is taken into account, the shear modulus to energy density ratio must be in absolute value of order

Plane waves in a relativistic, homogeneous and isotropic elastic continuum

10^{-5}

Generating heavy particles with energy and momentum conservation

or less for the theory to be consistent with observations within cosmic variance. With the integrated Sachs-Wolfe effect switched on, the constraint is relaxed almost by two orders of magnitude.

On the logical independence of the identities defining the stochastic independence of random events

The propagation of gravitational and acoustic plane waves in a flat universe filled with a general relativistic, homogeneous and isotropic, spatially flat continuum is studied. The continuum is described by analogues of nonrelativistic characteristics, namely energy per particle, pressure and Lame coefficients, and considered in the comoving proper-time gauge. For all modes with the given wave covector, differential equations governing the time dependence of the amplitudes are derived. In particular, longitudinal acoustic waves are described, in analogy with the nonrelativistic theory, by two coupled first-order equations. As an example, plane waves in a stiff ultrarigid continuum are considered.

Effect of radiation-like solid on small-scale CMB anisotropies

Abstract We propose a novel algorithm, called REGGAE, for the generation of momenta of a given sample of particle masses, evenly distributed in Lorentz-invariant phase space and obeying energy and momentum conservation. In comparison to other existing algorithms, REGGAE is designed for the use in multiparticle production in hadronic and nuclear collisions where many hadrons are produced and a large part of the available energy is stored in the form of their masses. The algorithm uses a loop simulating multiple collisions which lead to production of configurations with reasonably large weights. Program summary Program title: REGGAE (REscattering-after-Genbod GenerAtor of Events) Catalogue identifier: AEJR_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEJR_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1523 No. of bytes in distributed program, including test data, etc.: 9608 Distribution format: tar.gz Programming language: C++ Computer: PC Pentium 4, though no particular tuning for this machine was performed. Operating system: Originally designed on Linux PC with g++, but it has been compiled and ran successfully on OS X with g++ and MS Windows with Microsoft Visual C++ 2008 Express Edition, as well. RAM: This depends on the number of particles which are generated. For 10 particles like in the attached example it requires about 120 kB. Classification: 11.2 Nature of problem: The task is to generate momenta of a sample of particles with given masses which obey energy and momentum conservation. Generated samples should be evenly distributed in the available Lorentz-invariant phase space. Solution method: In general, the algorithm works in two steps. First, all momenta are generated with the GENBOD algorithm. There, particle production is modeled as a sequence of two-body decays of heavy resonances. After all momenta are generated this way, they are reshuffled. Each particle undergoes a collision with some other partner such that in the pair center of mass system the new directions of momenta are distributed isotropically. After each particle collides only a few times, the momenta are distributed evenly across the whole available phase space. Starting with GENBOD is not essential for the procedure but it improves the performance. Running time: This depends on the number of particles and number of events one wants to generate. On a LINUX PC with 2 GHz processor, generation of 1000 events with 10 particles each takes about 3 s.

From 'Nothing' to Inflation and Back Again

For an arbitrary subselection of the identities defining the stochastic independence (of several events), there exist random events, with prescribed probabilities, satisfying only the identities from the subselection. A similar statement holds if the events are required to be exchangeable.

Mechanical models in nonparametric regression

We compute the CMB angular power spectrum in the presence of a radiation-like solid - elastic matter with the same pressure to energy density ratio as radiation but with nonzero shear modulus. For the values of shear modulus that are close enough to zero, so that the effect of the solid on large-scale anisotropies remains within cosmic variance, we find that there is an observable effect of the solid on small-scale anisotropies.

The puzzle of very soft photon production in hadronic interactions

A procedure for solving Wheeler-DeWitt equation in Euclidean region, following step by step the construction of tunneling wave function in nonrelativistic quantum mechanics by Banks, Bender and Wu, is proposed. Solutions for a universe satisfying no-boundary condition and a universe created from ‘nothing’ are compared to the corresponding solutions for a particle in a two-dimensional potential well, and effects of indefiniteness of metric and zero energy in Wheeler-DeWitt equation are discussed.

The motion of charged particles in the field of rotating charged black holes and naked singularities

A common motif in the expositions of spline-based methods in statistical smoothing or numerical interpolation is an allusion to mechanical analogies—motivated perhaps by a desire to provide some explanation why the resulting shapes ought to be regarded as “natural”. The univariate case has its Oxford English Dictionary reference to draftsman spline as “a flexible strip of wood or hard rubber used by draftsmen in laying out broad sweeping curves”, which suggests (amiss!) that the eponymous mathematical object shares exactly the same properties. The introduction of “thin-plate spline” in the bivariate domain usually comes with a more distinctive story about the deformation of an elastic flat thin plate—for instance, page 139 of Green and Silverman [14] or page 108 of Small [32]: if the plate is deformed to the shape of the function f , and is small, then the bending energy is (up to the first order) proportional to the smoothing penalty. The importance attached by the scientific community to such trivia varies: while some consider it a signal from Nature, indicating the righteous path in the potentially endless forest of possibilities—see especially Bookstein [3, 4, 5], but also Bookstein and Green [6], Small [32], Dryden and Mardia [10]—for others it is a marginal curiosity, not deserving to stand in the path of the appreciation of computational and theoretical properties. In our case, the desire of the second author to comprehend the connection between thin-plate splines and total variation penalties led him to cross-questioning of the first author, theoretical physicist with principal interests in gravitation and cosmology; the latter reluctantly, but eventually cooperatively descended into the caverns of “engineering”—theory of elastic and plastic behavior of solid bodies. The unveiled connection not only turned out to be interesting, but yielded also a practical return for the second author: the elucidated mechanical models hinted Koenker and Mizera [19] where—that is, in which community—to look for relevant algorithmic solutions for their proposals. Which could be the end of the story were it not for queries that started to come occassionally thereafter, about a text documenting the apocryphal knowledge. So, here finally an attempt to produce one. The available space allows only for an overview of physical facts relevant to nonparametric regression; for somewhat nonstandard physical derivations (albeit perhaps unsurprising for an expert in solid mechanics), we refer to Balek [2].