8,559 research outputs found
Determining parameters of the Neugebauer family of vacuum spacetimes in terms of data specified on the symmetry axis
We express the complex potential E and the metrical fields omega and gamma of
all stationary axisymmetric vacuum spacetimes that result from the application
of two successive quadruple-Neugebauer (or two double-Harrison) transformations
to Minkowski space in terms of data specified on the symmetry axis, which are
in turn easily expressed in terms of multipole moments. Moreover, we suggest
how, in future papers, we shall apply our approach to do the same thing for
those vacuum solutions that arise from the application of more than two
successive transformations, and for those electrovac solutions that have axis
data similar to that of the vacuum solutions of the Neugebauer family.
(References revised following response from referee.)Comment: 18 pages (REVTEX
Generating anisotropic fluids from vacuum Ernst equations
Starting with any stationary axisymmetric vacuum metric, we build anisotropic
fluids. With the help of the Ernst method, the basic equations are derived
together with the expression for the energy-momentum tensor and with the
equation of state compatible with the field equations. The method is presented
by using different coordinate systems: the cylindrical coordinates
and the oblate spheroidal ones. A class of interior solutions matching with
stationary axisymmetric asymptotically flat vacuum solutions is found in oblate
spheroidal coordinates. The solutions presented satisfy the three energy
conditions.Comment: Version published on IJMPD, title changed by the revie
A new form of the rotating C-metric
In a previous paper, we showed that the traditional form of the charged
C-metric can be transformed, by a change of coordinates, into one with an
explicitly factorizable structure function. This new form of the C-metric has
the advantage that its properties become much simpler to analyze. In this
paper, we propose an analogous new form for the rotating charged C-metric, with
structure function G(\xi)=(1-\xi^2)(1+r_{+}A\xi)(1+r_{-}A\xi), where r_\pm are
the usual locations of the horizons in the Kerr-Newman black hole. Unlike the
non-rotating case, this new form is not related to the traditional one by a
coordinate transformation. We show that the physical distinction between these
two forms of the rotating C-metric lies in the nature of the conical
singularities causing the black holes to accelerate apart: the new form is free
of torsion singularities and therefore does not contain any closed timelike
curves. We claim that this new form should be considered the natural
generalization of the C-metric with rotation.Comment: 13 pages, LaTe
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
Fully Electrified Neugebauer Spacetimes
Generalizing a method presented in an earlier paper, we express the complex
potentials E and Phi of all stationary axisymmetric electrovac spacetimes that
correspond to axis data of the form E(z,0) = (U-W)/(U+W) , Phi(z,0) = V/(U+W) ,
where U = z^{2} + U_{1} z + U_{2} , V = V_{1} z + V_{2} , W = W_{1} z + W_{2} ,
in terms of the complex parameters U_{1}, V_{1}, W_{1}, U_{2}, V_{2} and W_{2},
that are directly associated with the various multipole moments. (Revised to
clarify certain subtle points.)Comment: 25 pages, REVTE
On interrelations between Sibgatullin's and Alekseev's approaches to the construction of exact solutions of the Einstein-Maxwell equations
The integral equations involved in Alekseev's "monodromy transform" technique
are shown to be simple combinations of Sibgatullin's integral equations and
normalizing conditions. An additional complex conjugation introduced by
Alekseev in the integrands makes his scheme mathematically inconsistent;
besides, in the electrovac case all Alekseev's principal value integrals
contain an intrinsic error which has never been identified before. We also
explain how operates a non-trivial double-step algorithm devised by Alekseev
for rewriting, by purely algebraic manipulations and in a different (more
complicated) parameter set, any particular specialization of the known
analytically extended N-soliton electrovac solution obtained in 1995 with the
aid of Sibgatullin's method.Comment: 7 pages, no figures, section II extende
Approaches to the Monopole-Dynamic Dipole Vacuum Solution Concerning the Structure of its Ernst's Potential on the Symmetry Axis
The FHP algorithm allows to obtain the relativistic multipole moments of a
vacuum stationary axisymmetric solution in terms of coefficients which appear
in the expansion of its Ernst's potential on the symmetry axis. First of all,
we will use this result in order to determine, at a certain approximation
degree, the Ernst's potential on the symmetry axis of the metric whose only
multipole moments are mass and angular momentum.
By using Sibgatullin's method we analyse a series of exacts solutions with
the afore mentioned multipole characteristic. Besides, we present an
approximate solution whose Ernst's potential is introduced as a power series of
a dimensionless parameter. The calculation of its multipole moments allows us
to understand the existing differences between both approximations to the
proposed pure multipole solution.Comment: 24 pages, plain TeX. To be published in General Relativity and
Gravitatio
Nonlinear viscosity and velocity distribution function in a simple longitudinal flow
A compressible flow characterized by a velocity field is
analyzed by means of the Boltzmann equation and the Bhatnagar-Gross-Krook
kinetic model. The sign of the control parameter (the longitudinal deformation
rate ) distinguishes between an expansion () and a condensation ()
phenomenon. The temperature is a decreasing function of time in the former
case, while it is an increasing function in the latter. The non-Newtonian
behavior of the gas is described by a dimensionless nonlinear viscosity
, that depends on the dimensionless longitudinal rate . The
Chapman-Enskog expansion of in powers of is seen to be only
asymptotic (except in the case of Maxwell molecules). The velocity distribution
function is also studied. At any value of , it exhibits an algebraic
high-velocity tail that is responsible for the divergence of velocity moments.
For sufficiently negative , moments of degree four and higher may diverge,
while for positive the divergence occurs in moments of degree equal to or
larger than eight.Comment: 18 pages (Revtex), including 5 figures (eps). Analysis of the heat
flux plus other minor changes added. Revised version accepted for publication
in PR
Generating branes via sigma-models
Starting with the D-dimensional Einstein-dilaton-antisymmetric form equations
and assuming a block-diagonal form of a metric we derive a -dimensional
-model with the target space or its non-compact form. Various solution-generating techniques are
developed and applied to construct some known and some new -brane solutions.
It is shown that the Harrison transformation belonging to the
subgroup generates black -branes from the seed Schwarzschild solution. A
fluxbrane generalizing the Bonnor-Melvin-Gibbons-Maeda solution is constructed
as well as a non-linear superposition of the fluxbrane and a spherical black
hole. A new simple way to endow branes with additional internal structure such
as plane waves is suggested. Applying the harmonic maps technique we generate
new solutions with a non-trivial shell structure in the transverse space
(`matrioshka' -branes). It is shown that the -brane intersection rules
have a simple geometric interpretation as conditions ensuring the symmetric
space property of the target space. Finally, a Bonnor-type symmetry is used to
construct a new magnetic 6-brane with a dipole moment in the ten-dimensional
IIA theory.Comment: 21 pages Late
Black Hole Pair Creation and the Entropy Factor
It is shown that in the instanton approximation the rate of creation of black
holes is always enhanced by a factor of the exponential of the black hole
entropy relative to the rate of creation of compact matter distributions
(stars). This result holds for any generally covariant theory of gravitational
and matter fields that can be expressed in Hamiltonian form. It generalizes the
result obtained previously for the pair creation of magnetically charged black
holes by a magnetic field in Einstein--Maxwell theory. The particular example
of pair creation of electrically charged black holes by an electric field in
Einstein--Maxwell theory is discussed in detail.Comment: (12 pages, ReVTeX) Revised version of "Pair Creation of Electrically
Charged Black Holes". New section shows that the BH pair creation rate is
enhanced by a factor for any Hamiltonian gravity + matter
theor
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