Using a maximal solvable subalgebra of the Lie algebras \(\frak {g}_{n}=\frak {sl}(2,\mathbb {R})\) \(\overrightarrow {\oplus }_{D_{n}}(n+1)L_{1}\) we reduce the problem of obtaining the Casimir operators to the integration of only one linear partial differential equation. This reduction allows to prove various results on the admissible degrees of invariants of \(\frak {g}_{n}\), and to construct the quadratic Casimir invariant explicitly for even \(n\). It is moreover shown, that only for 4 values \(\frak {g}_{n}\) arises as a non-trivial contraction of Lie algebras. We also point out that the order of a Casimir operator in a fundamental basis of invariants can exceed the dimension of the Lie algebra.

The recently found shock wave solution in the scalar field model with the field potential \(V(\phi )=|\phi \,|\) is generalised to the case \(V(\phi )=|\phi \,|-\frac {1}{2}\lambda \phi ^2\). We find two kinds of the shock waves, which are analogous of compression and expansion waves. The dependence of the waves on the parameter \(\lambda \) is investigated in detail.

Two general-relativistic hydrodynamical models are considered: a model of self-gravitating static configurations of perfect fluid and a model of steady accretion of fluid onto a black hole. We generalise analytic results obtained for the original polytropic versions of these models onto a wider class of barotropic equations of state. The knowledge about the polytropic solutions is used to establish bounds on certain characteristic quantities appearing in both cases.

Homogeneous isotropic gravitating models are discussed in the framework of gauge approach to gravitation. Generalized cosmological Friedmann equations without specific solutions are deduced for models filled with scalar fields and usual gravitating matter. Extreme conditions leading to gravitational repulsion effect are analyzed.

This study is purposed to elaborate the problem of energy and momentum distribution of the Bell–Szekeres space time in general theory of relativity. In this connection, we use the energy-momentum definition of Møller and obtain that the energy momentum distributions (due to matter plus field) are vanishing everywhere. This results are exactly the same as viewpoint of Aygün et al. and agree with a previous work of Rosen, Saltı et al. and Johri et al. who investigated the problem of the energy in Friedmann–Robertson–Walker universe. The result that the total energy-momentum of the universe in these models are zero support the viewpoint of Tryon.

We adopt Leaver’s [E. Leaver, Proc. R. Soc. Lond.A402, 285 (1985)] method to determine quasi normal frequencies of the Schwarzschild black hole in higher (\(D \geq 10\)) dimensions. In \(D\)-dimensional Schwarzschild metric, when \(D\) increases, more and more singularities, spaced uniformly on the unit circle \(|r|=1\), approach the horizon at \(r=r_{\rm h}=1\). Thus, a solution satisfying the outgoing wave boundary condition at the horizon must be continued to some mid point and only then the continued fraction condition can be applied. This prescription is general and applies to all cases for which, due to regular singularities on the way from the point of interest to the irregular singularity, Leaver’s method in its original setting breaks down. We illustrate the method calculating gravitational vector and tensor quasinormal frequencies of the Schwarzschild black hole in \(D=11\) and \(D=10\) dimensions. We also give the details for the \(D=9\) case, considered in the work of P. Bizoń, T. Chmaj, A. Rostworowski, B.G. Schmidt and Z. Tabor, Phys. Rev.D72, 121502(R) (2005).

We make the case for the existence of a, hitherto unknown and unobserved, hierarchy of ever more compact cosmic objects in the universe. This hypothesis is based on (i) the assumption of “elementary” particle sub-constituents on several levels below the presently known, inspired by Glashow’s “blooming desert” [S. Glashow, The Future of Elementary Particle Physics, in Proceedings of the Cargese Summer Institute, Cargese, France, July 9–29, 1979, Plenum Press 1980], (ii) the existence of nearly scale-invariant density fluctuations in the early universe, e.g. as predicted by inflationary models [A. Guth, Phys. Rev.D23, 347 (1981), J.M. Bardeen, P.J. Steinhardt, M.S. Turner, Phys. Rev.D28, 679 (1983)], (iii) our own previous theoretical work showing that a class of objects considerably more compact than previously thought possible in astrophysics can exist [J. Hansson, F. Sandin, Phys. Lett.B616, 1 (2005)]. We also give several independent arguments strongly pointing towards the non-existence of black holes. Some brief suggestions on observational signals due to the hierarchy, both in collected astronomical data and in possible future observations, concludes the paper.

Mechanical Maxwell’s demons, such as Smoluchowski’s trapdoor and Feynman’s ratchet and pawl need external energy source to operate. If you cease to feed a demon the Second Law of thermodynamics will quickly stop its operation. Nevertheless, if the parity is an unbroken symmetry of nature, it may happen that a small modification leads to demons which do not need feeding. Such demons can act like perpetuum mobiles of the second kind: extract heat energy from only one reservoir, use it to do work and be isolated from the rest of ordinary world. Yet the Second Law is not violated because the demons pay their entropy cost in the hidden (mirror) sector of the world by emitting mirror photons.

Evolution of winding strings in spacetimes with cycles whose proper lengths depend on time is examined. It was established earlier that extended objects wrapping the shrinking dimension in compactified Milne spacetime enjoy classically nonsingular evolution. Extensions of this observation to other spacetimes are discussed.

Ionization potential is customarily associated with the work required to remove electrons from atoms, but in a series of recent papers by A. Widom and L. Larsen, electron captures are shown to occur at ionization potential. Theirs is a wet method, but this paper will show how a dry method using quasi-superconductors should achieve the same objective. The method will be applied to the transmutation of nuclear waste.

Meson–meson scattering amplitudes within the ’t Hooft model are considered. The results show that within this model the meson–meson scattering at low energies proceeds by the exchange of an isoscalar \(\sigma \)-like resonance, as well as of an isovector \(\rho \)-like resonance. Masses and widths for those resonances are calculated, and their dependence on the quark masses and the quark–gluon coupling strength is studied.

Small momentum transfer elastic proton–proton cross-section at high energies is calculated assuming the nucleon composed of two constituents — a quark and a diquark. A comparison to data (described very well up to \(-t \approx 2\) GeV\(^{2}\)/\(c\)) allows to determine some properties of the constituents. While quark turns out fairly small, the diquark appears to be rather large, comparable to the size of the proton.

Role of the isospin asymmetry in nuclei and neutron stars, with an emphasis on the density dependence of the nuclear symmetry energy, is discussed. The symmetry energy is obtained using the isoscalar as well as isovector components of the density dependent M3Y effective interaction. The constants of density dependence of the effective interaction are obtained by reproducing the saturation energy per nucleon and the saturation density of spin and isospin symmetric cold infinite nuclear matter. Implications for the density dependence of the symmetry energy in case of a neutron star are discussed, and also possible constraints on the density dependence obtained from finite nuclei are compared.

The absolute differential scattering cross sections have been measured from the \((t,t)\) experiments on the \(^{93}\)Nb at \(E_t = 12\) MeV using a tandem accelerator and a multichannel magnetic spectrograph. Optical model parameters have been obtained from an analysis of the data with an optical-model search programme.

A number of multi-variate PDE (probability density estimators) methods are compared for the discrimination of signal from background in the selection of neutral pion candidates reconstructed at the ALEPH experiment at CERN. In this case-study, the question “Which method is the best choice?” reveals that the answer depends strongly on the size of the data set used to train and optimise the method, and the required simplicity of the algorithm.

The motion of a nanoparticle in a narrow, bend channel is used to illustrate features of scattering in systems with semi-open geometries. Under certain general constraints on the geometry, results on the scattering process are established.

The age of the Universe in the \({\mit \Lambda }\)CDM cosmology with \({\mit \Omega }_{{\rm matter}}=0.26\) and \({\mit \Omega }_{{\mit \Lambda }}=0.74\) is the same as in the Milne cosmology which corresponds to an almost empty universe. In both cases it is a reciprocal Hubble constant, 1/\(H_0\), that for now preferred value \(H_0=71\) km/s/Mpc is \(13.7\) billion years. The most curious coincidence is that at the present time, in the \({\mit \Lambda }\)CDM model the decelerated expansion is exactly compensated by the accelerated expansion, as if the Universe coast for \(13.7\) billion years.

Using the MAIN galaxy data from the SDSS Data Release 4 (SDSS4), we further study the Sloan Great Wall by three-dimensional cluster analysis. Because the basic properties of Main galaxies change with redshift, we select 50942 Main galaxies having the same redshift region (\(0.07\leq z\leq 0.09\)) as the Sloan Great Wall from the Main galaxy sample, and construct our SubMain sample. From the SubMain sample, 2013 isolated galaxies are identified at dimensionless radius \(r=1.4\). We perform the comparative studies of galaxy properties among the Sloan Great Wall, isolated galaxies and the SubMain sample in different redshift bins. It turns out that the statistical properties of luminosities and sizes of galaxies for the Sloan Great Wall, isolated galaxies and the SubMain sample are almost the same, the proportion of early-type isolated galaxies is relatively low. We also find that mean color of member galaxies of the Sloan Great Wall is redder than that of isolated galaxies. These results indicate that some properties of galaxies may be closely correlated with the environment or clustering.

The Hubble diagram has a purely kinematical monotonicity constraint. We study its stability under small scalar perturbations in the Robertson–Walker metric and to small peculiar velocities of emitter and receiver. Our analysis is independent of any dynamical hypothesis.

Anthropic principles were grown from the problem of fine tuning. Although anthropic principles have been discussed in cosmology for years there is no exact definition for fine tuning. Starting from the supposed similarity in the topologies of chaotic and fine tuned regions of the proper phase spaces, we introduce an alternative Lyapunov indicator for the measure of fine tuning. This fine-tuning indicator expresses the decrease of life-bearing potentiality of a universe with the increase of the difference from the physical constants of the Universe with maximum life-bearing potentiality.