Closed System of Equations on a Brane

We obtain a generic closed system of equations on a brane that describes its inner evolution and give a method for extending solutions on the brane to the bulk. We also discuss the cosmological implications of the closed system of equations obtained. We consider bulk spaces with both spacelike and timelike extra dimension, with and without the $Z_2$ symmetry of reflection relative to the brane.Comment: 11 pages, revtex. Substantially revised version to be published in PL

Towards a unique formula for neutrino oscillations in vacuum

We show that all correct results obtained by applying quantum field theory to neutrino oscillations can be understood in terms of a single oscillation formula. In particular, the model proposed by Grimus and Stockinger is shown to be a subcase of the model proposed by Giunti, Kim and Lee, while the new oscillation formulas proposed by Ioannisian and Pilaftsis and by Shtanov are disproved. We derive an oscillation formula without making any relativistic assumption and taking into account the dispersion, so that the result is valid for both neutrinos and mesons. This unification gives a stronger phenomenological basis to the neutrino oscillation formula. We also prove that the coherence length can be increased without bound by more accurate energy measurements. Finally, we insist on the wave packet interpretation of the quantum field treatments of oscillations.Comment: 30 pages, 1 figure; the proof that plane wave oscillations do no exist is extended to stationary models; the influence of dispersion is explained in more detail

On a general class of brane-world black holes

We use the general solution to the trace of the 4-dimensional Einstein equations for static, spherically symmetric configurations as a basis for finding a general class of black hole (BH) metrics, containing one arbitrary function $g_{tt} = A(r)$ which vanishes at some $r = r_h > 0$, the horizon radius. Under certain reasonable restrictions, BH metrics are found with or without matter and, depending on the boundary conditions, can be asymptotically flat or have any other prescribed large $r$ behaviour. It is shown that this procedure generically leads to families of solutions unifying non-extremal globally regular BHs with a Kerr-like global structure, extremal BHs and symmetric wormholes. Horizons in space-times with zero scalar curvature are shown to be either simple or double. The same is generically true for horizons inside a matter distribution, but in special cases there can be horizons of any order. A few simple examples are discussed. A natural application of the above results is the brane world concept, in which the trace of the 4D gravity equations is the only unambiguous equation for the 4D metric, and its solutions can be continued into the 5D bulk according to the embedding theorems.Comment: 9 pages, revtex

To the memory of Petr Ivanovich Fomin

Petr Ivanovich Fomin, Doctor of Sciences, Professor in theoretical physics, Corresponding Member of the National Academy of Sciences of Ukraine, Head of the Theoretical Physics Department at the Institute of Applied Physics of the National Academy of Sciences of Ukraine (Sumy), and leading researcher of the Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine (Kyiv) had passed away on the 5th of October, 2011

Quantum cosmology

We discuss quantum-cosmological approach to the problem of initial singularity and origin of our universe, starting with the pioneer idea of quantum creation of the universe put forward by P.I. Fomin.Обговорюється квантово-космологiчний пiдхiд до проблеми початкової сингулярностi i походження нашого Всесвiту, започаткований пiонерською iдеєю квантового народження Всесвiту, запропонованою П.I. Фомiним.Обсуждается квантово-космологический подход к проблеме начальной сингулярности и происхождения нашей Вселенной, начатый пионерской идеей квантового рождения Вселенной, предложенной П.И. Фоминым