80 research outputs found
The Wahlquist metric cannot describe an isolated rotating body
It is proven that the Wahlquist perfect fluid space-time cannot be smoothly
joined to an exterior asymptotically flat vacuum region. The proof uses a power
series expansion in the angular velocity, to a precision of the second order.
In this approximation, the Wahlquist metric is a special case of the rotating
Whittaker space-time. The exterior vacuum domain is treated in a like manner.
We compute the conditions of matching at the possible boundary surface in both
the interior and the vacuum domain. The conditions for matching the induced
metrics and the extrinsic curvatures are mutually contradictory.Comment: 13 pages, 0 figure
Corrections and Comments on the Multipole Moments of Axisymmetric Electrovacuum Spacetimes
Following the method of Hoenselaers and Perj\'{e}s we present a new corrected
and dimensionally consistent set of multipole gravitational and electromagnetic
moments for stationary axisymmetric spacetimes. Furthermore, we use our results
to compute the multipole moments, both gravitational and electromagnetic, of a
Kerr-Newman black hole.Comment: This is a revised and corrected versio
Magnetic Surfaces in Stationary Axisymmetric General Relativity
In this paper a new method is derived for constructing electromagnetic
surface sources for stationary axisymmetric electrovac spacetimes endowed with
non-smooth or even discontinuous
Ernst potentials. This can be viewed as a generalization of some classical
potential theory results, since lack of continuity of the potential is related
to dipole density and lack of smoothness, to monopole density. In particular
this approach is useful for constructing the dipole source for the magnetic
field. This formalism involves solving a linear elliptic differential equation
with boundary conditions at infinity. As an example, two different models of
surface densities for the Kerr-Newman electrovac spacetime are derived.Comment: 15 page
Singular sources in the Demianski-Newman spacetimes
The analysis of singular regions in the NUT solutions carried out in the
recent paper (Manko and Ruiz, 2005 Class. Quantum Grav. 22, p.3555) is now
extended to the Demianski-Newman vacuum and electrovacuum spacetimes. We show
that the effect which produces the NUT parameter in a more general situation
remains essentially the same as in the purely NUT solutions: it introduces the
semi-infinite singularities of infinite angular momenta and positive or
negative masses depending on the interrelations between the parameters; the
presence of the electromagnetic field additionally endows the singularities
with electric and magnetic charges. The exact formulae describing the mass,
charges and angular momentum distributions in the Demianski-Newman solutions
are obtained and concise general expressions P_n=(m+i\nu)(ia)^n,
Q_n=(q+ib)(ia)^n for the entire set of the respective Beig-Simon multipole
moments are derived. These moments correspond to a unique choice of the
integration constant in the expression of the metric function \omega which is
different from the original choice made by Demianski and Newman.Comment: 22 pages, 5 figures; submitted to Classical and Quantum Gravit
On the gravitational field of static and stationary axial symmetric bodies with multi-polar structure
We give a physical interpretation to the multi-polar Erez-Rozen-Quevedo
solution of the Einstein Equations in terms of bars. We find that each
multi-pole correspond to the Newtonian potential of a bar with linear density
proportional to a Legendre Polynomial. We use this fact to find an integral
representation of the function. These integral representations are
used in the context of the inverse scattering method to find solutions
associated to one or more rotating bodies each one with their own multi-polar
structure.Comment: To be published in Classical and Quantum Gravit
New first integral for twisting type-N vacuum gravitational fields with two non-commuting Killing vectors
A new first integral for the equations corresponding to twisting type-N
vacuum gravitational fields with two non-commuting Killing vectors is
introduced. A new reduction of the problem to a complex second-order ordinary
differential equation is given. Alternatively, the mentioned first integral can
be used in order to provide a first integral of the second-order complex
equation introduced in a previous treatment of the problem.Comment: 7 pages, LaTeX, uses ioplppt.sty and iopl12.sty; to be published in
Class. Quantum Gra
Geodesics around Weyl-Bach's Ring Solution
We explore some of the gravitational features of a uniform ring both in the
Newtonian potential theory and in General Relativity. We use a spacetime
associated to a Weyl static solution of the vacuum Einstein's equations with
ring like singularity. The Newtonian motion for a test particle in the
gravitational field of the ring is studied and compared with the corresponding
geodesic motion in the given spacetime. We have found a relativistic peculiar
attraction: free falling particle geodesics are lead to the inner rim but never
hit the ring.Comment: 8 figures, 14 pages. LaTeX w/ subfigure, graphic
Toroidal metrics: gravitational solenoids and static shells
In electromagnetism a current along a wire tightly wound on a torus makes a
solenoid whose magnetic field is confined within the torus. In Einstein's
gravity we give a corresponding solution in which a current of matter moves up
on the inside of a toroidal shell and down on the outside, rolling around the
torus by the short way. The metric is static outside the torus but stationary
inside with the gravomagnetic field confined inside the torus, running around
it by the long way. This exact solution of Einstein's equations is found by
fitting Bonnor's solution for the metric of a light beam, which gives the
required toroidal gravomagnetic field inside the torus, to the general Weyl
static external metric in toroidal coordinates, which we develop. We deduce the
matter tensor on the torus and find when it obeys the energy conditions. We
also give the equipotential shells that generate the simple Bach-Weyl metric
externally and find which shells obey the energy conditions.Comment: To appear in Class. Quantum Gra
Gravitationally induced electromagnetism at the Compton scale
It is shown that Einstein gravity tends to modify the electric and magnetic
fields appreciably at distances of the order of the Compton wavelength. At that
distance the gravitational field becomes spin dominated rather than mass
dominated. The gravitational field couples to the electromagnetic field via the
Einstein-Maxwell equations which in the simplest model causes the electrostatic
field of charged spinning particles to acquire an oblate structure relative to
the spin direction. For electrons and protons, a pure Coulomb field is
therefore likely to be incompatible with general relativity at the Compton
scale. In the simplest model, the magnetic dipole corresponds to the Dirac
g-factor, g=2. Also, it follows from the form of the electric field that the
electric dipole moment vanishes, in agreement with current experimental limits
for the electron. Quantitatively, the classical Einstein-Maxwell theory
predicts the magnetic and electric dipoles of the electron to an accuracy of
about one part in 10^{-3} or better. Going to the next multipole order, one
finds that the first non-vanishing higher multipole is the electric quadrupole
moment which is predicted to be -124 barn for the electron. Any non-zero value
of the electric quadrupole moment for the electron or the proton would be a
clear sign of curvature due to the implied violation of rotation invariance.
There is also a possible spherical modification of the Coulomb force
proportional to r^{-4}. However, the size of this effect is well below current
experimental limits. The corrections to the hydrogen spectrum are expected to
be small but possibly detectable.Comment: 11 pages, 3 figures: revised version published in Class. Quantum
Grav. 23 (2006) 3111-3122; Conclusions unchange
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