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Employing the Noether charge technique and Visser’s Euclidean approach the entropy of the nonlinear black hole described by the perturbative solution of the system of coupled equations of the quadratic gravity and nonlinear electrodynamics is constructed. The solution is parametrized by the exact location of the event horizon and charge. Special emphasis is put on the extremal configuration. Consequences of the second choice of the boundary conditions, in which the solution is parametrized by the charge and the total mass as seen by a distant observer is briefly examined.

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The Mathisson equations under the Frenkel–Mathisson supplementary condition are studied in a Schwarzschild field. The choice of solutions, which describe the motions of the proper center of mass of a spinning test particle, is discussed, and the calculation procedure for highly relativistic motions is proposed. The very motions are important for astrophysics while investigating possible effects of the gravitational spin-orbit interaction on the particle’s world line and trajectory.

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The positivity of the matter-energy density in the Universe, defined from the energy-momentum tensor as \(\rho \equiv T^0_0\) — one of the initial assumptions in the positive-energy conjecture of Arnowitt et al. — is related to the Lorentzian signature of space-time, assumed to be spatially flat, via the Friedmann equation, by applying the Faddeev (Newton–Wigner) propagator \(K\) for the cosmological Schrödinger equation in the semi-classical approximation, the corresponding Euclidean propagator, which allows negative \(\rho \), decaying on the Planck time-scale. A corollary of this result is that the masses of all elementary particles, and hence of all astrophysical bodies and black holes, are positive semi-definite.

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We comment on the recent article of M.W. Evans, Spin Connection Resonance in Gravitational General Relativity, Acta Phys. Pol. B 38, 2211 (2007). We point out that the equations underlying Evans’ theory are highly problematic. Moreover, we demonstrate that the so-called “spin connection resonance”, predicted by Evans, cannot be derived from the equation he used. We provide an exact solution of Evans’ corresponding equation and show that it has definitely no resonance solutions.

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The question of smoothness at the ergosurface of the space-time metric constructed out of solutions \(({\cal E},\varphi )\) of the Ernst electro-vacuum equations is considered. We prove smoothness of those ergosurfaces at which \(\Re {\cal E}\) provides the dominant contribution to \(f=-(\Re {\cal E} + |\varphi |^2)\) at the zero-level-set of \(f\). Some partial results are obtained in the remaining cases: in particular we give examples of leading-order solutions with singular isolated “ergocircles”.

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Conformal rescaling of conformal Yano–Killing tensors and relations between Yano and CYK tensors are discussed. Pullback of these objects to a submanifold is used to construct all solutions of a CYK equation in anti-de Sitter and de Sitter space-times. Properties of asymptotic conformal Yano–Killing tensors are examined for asymptotic anti-de Sitter space-times. Explicit asymptotic forms of them are derived. The results are used to construct asymptotic charges in asymptotic AdS space-time. Well known examples like Schwarzschild–AdS, Kerr–AdS and NUT–AdS are examined carefully in the construction of the concept of energy, angular momentum and dual mass in asymptotic AdS space-time.

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This work covers methodology of solving QCD evolution equation of the parton distribution using Markovian Monte Carlo (MMC) algorithms in a class of models ranging from DGLAP to CCFM. One of the purposes of the above MMCs is to test the other more sophisticated Monte Carlo programs, the so-called Constrained Monte Carlo (CMC) programs, which will be used as a building block in the parton shower MC. This is why the mapping of the evolution variables (eikonal variable and evolution time) into four-momenta is also defined and tested. The evolution time is identified with the rapidity variable of the emitted parton. The presented MMCs are tested independently, with \(\sim 0.1\%\) precision, against the non-MC program APCheb especially devised for this purpose.

abstract

The \(\tau \)-decay library TAUOLA has gained popularity over the last decade. However, with the continuously increasing precision of the data, some of its functionality has become insufficient. One of the requirements is the implementation of decays into five mesons plus a neutrino with a realistic decay amplitude. This note describes a step into this direction. For the \(2\pi ^-\pi ^+2\pi ^0\) mode the three decay chains \(\tau ^- \to a_1^- \nu \to \rho ^-(\to \pi ^-\pi ^0) \omega (\to \pi ^-\pi ^+\pi ^0) \nu \), \(\tau ^-\!\to \!a_1^- \nu \!\to \! a_1^-(\to \! 2\pi ^-\pi ^+) f_0 (\to \! 2\pi ^0) \nu \), and \(\tau ^- \!\to \! a_1^- \nu \to a_1^-(\to \!\pi ^-2\pi ^0) f_0 (\to \! \pi ^+\pi -) \nu \) are introduced with simple assumptions about the couplings and propagators of the various resonances. Similar amplitudes (without the \(\rho \omega \) contributions) are adopted for the \(\pi ^-4\pi ^0\) and \(3\pi ^-2\pi ^+\) modes. The five-pion amplitude is thus based on a simple model, which, however, can be considered as a first realistic example. Phase-space generation includes the possibility of presampling the \(\omega \) and \(a_1\) resonances, in one channel only, however. This is probably sufficient for the time being, both for physics applications and for tests. The technical test of the new part of the generator is performed by comparing Monte Carlo and analytical results. To this end a non-realistic, but easy to calculate, purely scalar amplitude for the decay into five massless pions was used.

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The elastic scattering of \(p\)-\(^{16}\)O data at different proton incident energies have been analyzed using single-folding model. In the present calculations analytical expressions for the real part of the optical potential are derived by folding different sets of nucleon–nucleon (NN) interactions to different forms of densities of the target nucleus. The theoretical calculations of the differential cross sections as well as analyzing power gave a reasonable fit to that of the experimental data.

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Bose–Einstein correlations between identical pions close in phase-space is thought to be responsible for the observed distortion in mass spectra of non-identical pions. For example in the decays \(\rho ^0 \rightarrow \pi ^+ \pi ^-\) and \(\rho ^\pm \rightarrow \pi ^\pm \pi ^0\), such distortions are a residual effect where the pions from the \(\rho \) decay interact with other identical pions that are close in phase-space. Such interactions can be significant in, for example, hadronic decays of \(Z\) bosons where pion multiplicities are high, and resonances such as \(\rho \) mesons decay with a very short lifetime thereby creating pions that are close to prompt pions created directly. We present the Söding model and show that it has been used successfully to model distortions in \(\pi ^\pm \pi ^0\) mass spectra in hadronic \(Z\) decays recorded by ALEPH.

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The effects of interpreting classical phase-space distributions as Wigner functions, which is common in models of multiparticle production, are discussed. The temperature for the classical description is always higher than that for its Wigner function interpretation. A rough estimate shows that the corresponding correction is proportional to \(R^{-2}\), where \(R\) is the radius of the interaction region, and that it is negligible for heavy ion scattering, but at the few percent level for \(e^+e^-\) annihilations.

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The possibility to simulate an effective medium with a permittivity close to zero in some frequency band with as consequence that such a medium suitably excited behaves for the outside world as an ultrarefractive antenna with a narrow radiation pattern was recently proved. We prove here that slabs and cylinders made of a Tellegen chiral metamaterial with zero permittivity excited with a time harmonic filamentous current respecting the symmetry of these structures constitute ultrarefractive antennas. We also analyze the equations satisfied by the electromagnetic field inside and outside a metaTellegen paraboloid of revolution excited with an electric current running along its axis.

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A clusterization process in two-dimensional system of granular hard disks is investigated by two novel numerical methods: the nearest neighbourhood density and the anti-percolation function. The tendency of the band like structures in the clustered state is recognized to be driven by two factors: the stretching forces at the junction of two clusters (or two parts of one cluster) with different kinetic energies and the density fluctuations, which act as a seed for the empty ponds (voids free of particles). Moreover, the examples (and animations) of the collision of two clusters and the breakup of the granular band are presented.

abstract

The effects of the inhomogeneity of the mass distribution in the early universe and of the cosmological constant on the variation of the fine structure constant have been investigated. It has been suggested that the variation of the fine structure constant may be attributed to the intrinsic scale dependence of the fundamental constants of nature. The effect of the vacuum polarisation on the variation of fine structure constant has also been investigated and some interesting observations are made.