4,329 research outputs found
Equilibrium configurations of two charged masses in General Relativity
An asymptotically flat static solution of Einstein-Maxwell equations which
describes the field of two non-extreme Reissner - Nordstr\"om sources in
equilibrium is presented. It is expressed in terms of physical parameters of
the sources (their masses, charges and separating distance). Very simple
analytical forms were found for the solution as well as for the equilibrium
condition which guarantees the absence of any struts on the symmetry axis. This
condition shows that the equilibrium is not possible for two black holes or for
two naked singularities. However, in the case when one of the sources is a
black hole and another one is a naked singularity, the equilibrium is possible
at some distance separating the sources. It is interesting that for
appropriately chosen parameters even a Schwarzschild black hole together with a
naked singularity can be "suspended" freely in the superposition of their
fields.Comment: 4 pages; accepted for publication in Phys. Rev.
Integrability of generalized (matrix) Ernst equations in string theory
The integrability structures of the matrix generalizations of the Ernst
equation for Hermitian or complex symmetric -matrix Ernst potentials
are elucidated. These equations arise in the string theory as the equations of
motion for a truncated bosonic parts of the low-energy effective action
respectively for a dilaton and - matrix of moduli fields or for a
string gravity model with a scalar (dilaton) field, U(1) gauge vector field and
an antisymmetric 3-form field, all depending on two space-time coordinates
only. We construct the corresponding spectral problems based on the
overdetermined -linear systems with a spectral parameter and the
universal (i.e. solution independent) structures of the canonical Jordan forms
of their matrix coefficients. The additionally imposed conditions of existence
for each of these systems of two matrix integrals with appropriate symmetries
provide a specific (coset) structures of the related matrix variables. An
equivalence of these spectral problems to the original field equations is
proved and some approach for construction of multiparametric families of their
solutions is envisaged.Comment: 15 pages, no figures, LaTeX; based on the talk given at the Workshop
``Nonlinear Physics: Theory and Experiment. III'', 24 June - 3 July 2004,
Gallipoli (Lecce), Italy. Minor typos, language and references corrections.
To be published in the proceedings in Theor. Math. Phy
D-branes in the WZW model
It is stated in the literature that D-branes in the WZW-model associated with
the gluing condition J = - \bar{J} along the boundary correspond to branes
filling out the whole group volume. We show instead that the end-points of open
strings are rather bound to stay on `integer' conjugacy classes. In the case of
SU(2) level k WZW model we obtain k-1 two dimensional Euclidean D-branes and
two D particles sitting at the points e and -e.Comment: 2 pages, LaTe
Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations
For the fields depending on two of the four space-time coordinates only, the
spaces of local solutions of various integrable reductions of Einstein's field
equations are shown to be the subspaces of the spaces of local solutions of the
``null-curvature'' equations constricted by a requirement of a universal (i.e.
solution independent) structures of the canonical Jordan forms of the unknown
matrix variables. These spaces of solutions of the ``null-curvature'' equations
can be parametrized by a finite sets of free functional parameters -- arbitrary
holomorphic (in some local domains) functions of the spectral parameter which
can be interpreted as the monodromy data on the spectral plane of the
fundamental solutions of associated linear systems. Direct and inverse problems
of such mapping (``monodromy transform''), i.e. the problem of finding of the
monodromy data for any local solution of the ``null-curvature'' equations with
given canonical forms, as well as the existence and uniqueness of such solution
for arbitrarily chosen monodromy data are shown to be solvable unambiguously.
The linear singular integral equations solving the inverse problems and the
explicit forms of the monodromy data corresponding to the spaces of solutions
of the symmetry reduced Einstein's field equations are derived.Comment: LaTeX, 33 pages, 1 figure. Typos, language and reference correction
New Test of Supernova Electron Neutrino Emission using Sudbury Neutrino Observatory Sensitivity to the Diffuse Supernova Neutrino Background
Supernovae are rare nearby, but they are not rare in the Universe, and all
past core-collapse supernovae contributed to the Diffuse Supernova Neutrino
Background (DSNB), for which the near-term detection prospects are very good.
The Super-Kamiokande limit on the DSNB electron {\it antineutrino} flux,
cm s, is just above the
range of recent theoretical predictions based on the measured star formation
rate history. We show that the Sudbury Neutrino Observatory should be able to
test the corresponding DSNB electron {\it neutrino} flux with a sensitivity as
low as cm s,
improving the existing Mont Blanc limit by about three orders of magnitude.
While conventional supernova models predict comparable electron neutrino and
antineutrino fluxes, it is often considered that the first (and
forward-directed) SN 1987A event in the Kamiokande-II detector should be
attributed to electron-neutrino scattering with an electron, which would
require a substantially enhanced electron neutrino flux. We show that with the
required enhancements in either the burst or thermal phase fluxes, the
DSNB electron neutrino flux would generally be detectable in the Sudbury
Neutrino Observatory. A direct experimental test could then resolve one of the
enduring mysteries of SN 1987A: whether the first Kamiokande-II event reveals a
serious misunderstanding of supernova physics, or was simply an unlikely
statistical fluctuation. Thus the electron neutrino sensitivity of the Sudbury
Neutrino Observatory is an important complement to the electron antineutrino
sensitivity of Super-Kamiokande in the quest to understand the DSNB.Comment: 10 pages, 3 figure
Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups
In this paper, we construct a Lagrangian submanifold of the moduli space
associated to the fundamental group of a punctured Riemann surface (the space
of representations of this fundamental group into a compact connected Lie
group). This Lagrangian submanifold is obtained as the fixed-point set of an
anti-symplectic involution defined on the moduli space. The notion of
decomposable representation provides a geometric interpretation of this
Lagrangian submanifold
Various versions of analytic QCD and skeleton-motivated evaluation of observables
We present skeleton-motivated evaluation of QCD observables. The approach can
be applied in analytic versions of QCD in certain classes of renormalization
schemes. We present two versions of analytic QCD which can be regarded as
low-energy modifications of the ``minimal'' analytic QCD and which reproduce
the measured value of the semihadronic tau decay ratio r{tau}. Further, we
describe an approach of calculating the higher order analytic couplings Ak
(k=2,3,...) on the basis of logarithmic derivatives of the analytic coupling
A1(Q^2). This approach can be easily applied in any version of analytic QCD. We
adjust the free parameters of the afore-mentioned two analytic models in such a
way that the skeleton-motivated evaluation reproduces the correct known values
of r{tau} and of the Bjorken polarized sum rule (BjPSR) db(Q^2) at a given
point (e.g., at Q^2=2 GeV^2). We then evaluate the low-energy behavior of the
Adler function dv(Q^2) and the BjPSR db(Q^2) in the afore-mentioned evaluation
approach, in the three analytic versions of QCD. We compare with the results
obtained in the ``minimal'' analytic QCD and with the evaluation approach of
Milton et al. and Shirkov.Comment: 30 pages, 14 eps-figures; v3: parameters of the analytic QCD models
M1 and M2 were refined, the numerical results modified accordingly, new
paragraph at the end of Sec.II and at the end of Sec.III, discussion of
Figs.4 extended, references added; version to appear in PR
Physical Principles of the Amplification of Electromagnetic Radiation Due to Negative Electron Masses in a Semiconductor Superlattice
In a superlattice placed in crossed electric and magnetic fields, under
certain conditions, the inversion of electron population can appear at which
the average energy of electrons is above the middle of the miniband and the
effective mass of the electron is negative. This is the implementation of the
negative effective mass amplifier and generator (NEMAG) in the superlattice. It
can result in the amplification and generation of terahertz radiation even in
the absence of negative differential conductivity.Comment: 5 pages, 3 figure
A note on a canonical dynamical r-matrix
It is well known that a classical dynamical -matrix can be associated with
every finite-dimensional self-dual Lie algebra \G by the definition
, where \omega\in \G and is the
holomorphic function given by for
z\in \C\setminus 2\pi i \Z^*. We present a new, direct proof of the statement
that this canonical -matrix satisfies the modified classical dynamical
Yang-Baxter equation on \G.Comment: 17 pages, LaTeX2
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