197 research outputs found
Exterior and interior metrics with quadrupole moment
We present the Ernst potential and the line element of an exact solution of
Einstein's vacuum field equations that contains as arbitrary parameters the
total mass, the angular momentum, and the quadrupole moment of a rotating mass
distribution. We show that in the limiting case of slowly rotating and slightly
deformed configuration, there exists a coordinate transformation that relates
the exact solution with the approximate Hartle solution. It is shown that this
approximate solution can be smoothly matched with an interior perfect fluid
solution with physically reasonable properties. This opens the possibility of
considering the quadrupole moment as an additional physical degree of freedom
that could be used to search for a realistic exact solution, representing both
the interior and exterior gravitational field generated by a self-gravitating
axisymmetric distribution of mass of perfect fluid in stationary rotation.Comment: Latex, 15 pages, 3 figures, final versio
New Black Hole Solutions in Brans-Dicke Theory of Gravity
Existence check of non-trivial, stationary axisymmetric black hole solutions
in Brans-Dicke theory of gravity in different direction from those of Penrose,
Thorne and Dykla, and Hawking is performed. Namely, working directly with the
known explicit spacetime solutions in Brans-Dicke theory, it is found that
non-trivial Kerr-Newman-type black hole solutions different from general
relativistic solutions could occur for the generic Brans-Dicke parameter values
-5/2\leq \omega <-3/2. Finally, issues like whether these new black holes carry
scalar hair and can really arise in nature and if they can, what the associated
physical implications would be are discussed carefully.Comment: 20 pages, no figure, Revtex, version to appear in Phys. Rev.
The evolution of cosmic string loops in Kerr-de Sitter spacetimes
The equation of cosmic string loops in Kerr-de Sitter spacetimes is derived.
Having solved the equation numerically, we find that the loops can expand and
exist except for too small ones.Comment: 8 page
Lense-Thirring Precession in Pleba\'nski-Demia\'nski spacetimes
An exact expression of Lense-Thirring precession rate is derived for
non-extremal and extremal Pleba\'nski-Demia\'nski spacetimes. This formula is
used to find the exact Lense-Thirring precession rate in various axisymmetric
spacetimes, like: Kerr, Kerr-Newman, Kerr-de Sitter etc. We also show, if the
Kerr parameter vanishes in Pleba\'nski-Demia\'nski(PD) spacetime, the
Lense-Thirring precession does not vanish due to the existence of NUT charge.
To derive the LT precession rate in extremal Pleba\'nski-Demia\'nski we first
derive the general extremal condition for PD spacetimes. This general result
could be applied to get the extremal limit in any stationary and axisymmetric
spacetimes.Comment: 9 pages, Some special modifications are mad
Initial data for a head on collision of two Kerr-like black holes with close limit
We prove the existence of a family of initial data for the Einstein vacuum
equation which can be interpreted as the data for two Kerr-like black holes in
arbitrary location and with spin in arbitrary direction. This family of initial
data has the following properties: (i) When the mass parameter of one of them
is zero or when the distance between them goes to infinity, it reduces exactly
to the Kerr initial data. (ii) When the distance between them is zero, we
obtain exactly a Kerr initial data with mass and angular momentum equal to the
sum of the mass and angular momentum parameters of each of them. The initial
data depends smoothly on the distance, the mass and the angular momentum
parameters.Comment: 15 pages, no figures, Latex2
Boundary value problems for the stationary axisymmetric Einstein equations: a disk rotating around a black hole
We solve a class of boundary value problems for the stationary axisymmetric
Einstein equations corresponding to a disk of dust rotating uniformly around a
central black hole. The solutions are given explicitly in terms of theta
functions on a family of hyperelliptic Riemann surfaces of genus 4. In the
absence of a disk, they reduce to the Kerr black hole. In the absence of a
black hole, they reduce to the Neugebauer-Meinel disk.Comment: 46 page
Approximate gravitational field of a rotating deformed mass
A new approximate solution of vacuum and stationary Einstein field equations
is obtained. This solution is constructed by means of a power series expansion
of the Ernst potential in terms of two independent and dimensionless parameters
representing the quadrupole and the angular momentum respectively. The main
feature of the solution is a suitable description of small deviations from
spherical symmetry through perturbations of the static configuration and the
massive multipole structure by using those parameters. This quality of the
solution might eventually provide relevant differences with respect to the
description provided by the Kerr solution.Comment: 16 pages. Latex. To appear in General Relativity and Gravitatio
A rotating three component perfect fluid source and its junction with empty space-time
The Kerr solution for empty space-time is presented in an ellipsoidally
symmetric coordinate system and it is used to produce generalised ellipsoidal
metrics appropriate for the generation of rotating interior solutions of
Einstein's equations. It is shown that these solutions are the familiar static
perfect fluid cases commonly derived in curvature coordinates but now endowed
with rotation. The resulting solutions are also discussed in the context of
T-solutions of Einstein's equations and the vacuum T-solution outside a
rotating source is presented. The interior source for these solutions is shown
not to be a perfect fluid but rather an anisotropic three component perfect
fluid for which the energy momentum tensor is derived. The Schwarzschild
interior solution is given as an example of the approach.Comment: 14 page
Complex Kerr Geometry and Nonstationary Kerr Solutions
In the frame of the Kerr-Schild approach, we consider the complex structure
of Kerr geometry which is determined by a complex world line of a complex
source. The real Kerr geometry is represented as a real slice of this complex
structure. The Kerr geometry is generalized to the nonstationary case when the
current geometry is determined by a retarded time and is defined by a
retarded-time construction via a given complex world line of source. A general
exact solution corresponding to arbitrary motion of a spinning source is
obtained. The acceleration of the source is accompanied by a lightlike
radiation along the principal null congruence. It generalizes to the rotating
case the known Kinnersley class of "photon rocket" solutions.Comment: v.3, revtex, 16 pages, one eps-figure, final version (to appear in
PRD), added the relation to twistors and algorithm of numerical computations,
English is correcte
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