69 research outputs found
Exact General Relativistic Thick Disks
A method to construct exact general relativistic thick disks that is a simple
generalization of the ``displace, cut and reflect'' method commonly used in
Newtonian, as well as, in Einstein theory of gravitation is presented. This
generalization consists in the addition of a new step in the above mentioned
method. The new method can be pictured as a ``displace, cut, {\it fill} and
reflect'' method. In the Newtonian case, the method is illustrated in some
detail with the Kuzmin-Toomre disk. We obtain a thick disk with acceptable
physical properties. In the relativistic case two solutions of the Weyl
equations, the Weyl gamma metric (also known as Zipoy-Voorhees metric) and the
Chazy-Curzon metric are used to construct thick disks. Also the Schwarzschild
metric in isotropic coordinates is employed to construct another family of
thick disks. In all the considered cases we have non trivial ranges of the
involved parameter that yield thick disks in which all the energy conditions
are satisfied.Comment: 11 pages, RevTex, 9 eps figs. Accepted for publication in PR
Maximal Acceleration Is Nonrotating
In a stationary axisymmetric spacetime, the angular velocity of a stationary
observer that Fermi-Walker transports its acceleration vector is also the
angular velocity that locally extremizes the magnitude of the acceleration of
such an observer, and conversely if the spacetime is also symmetric under
reversing both t and phi together. Thus a congruence of Nonrotating
Acceleration Worldlines (NAW) is equivalent to a Stationary Congruence
Accelerating Locally Extremely (SCALE). These congruences are defined
completely locally, unlike the case of Zero Angular Momentum Observers (ZAMOs),
which requires knowledge around a symmetry axis. The SCALE subcase of a
Stationary Congruence Accelerating Maximally (SCAM) is made up of stationary
worldlines that may be considered to be locally most nearly at rest in a
stationary axisymmetric gravitational field. Formulas for the angular velocity
and other properties of the SCALEs are given explicitly on a generalization of
an equatorial plane, infinitesimally near a symmetry axis, and in a slowly
rotating gravitational field, including the weak-field limit, where the SCAM is
shown to be counter-rotating relative to infinity. These formulas are evaluated
in particular detail for the Kerr-Newman metric. Various other congruences are
also defined, such as a Stationary Congruence Rotating at Minimum (SCRAM), and
Stationary Worldlines Accelerating Radially Maximally (SWARM), both of which
coincide with a SCAM on an equatorial plane of reflection symmetry.
Applications are also made to the gravitational fields of maximally rotating
stars, the Sun, and the Solar System.Comment: 64 pages, no figures, LaTeX, Sections 10 and 11 added with
applications to maximally rotating stellar models of Cook, Shapiro, and
Teukolsky and to the Sun and Solar System with recent data from Pijpers that
the Sun has angular momentum 1.80 x 10^{75} = 0.216 M^2 = 47 hectares = 116
acres (with 0.8% uncertainty) and quadrupole moment (2.18 x 10^{-7})MR^2 =
1.60 x 10^{14} m^3 = 3.7 x 10^{117} (with 3% uncertaity), accepted Feb. 27
for Classical and Quantum Gravit
Periastron shift in Weyl class spacetimes
The periastron position advance for geodesic motion in axially symmetric
solutions of the Einstein field equations belonging to the Weyl class of vacuum
solutions is investigated. Explicit examples corresponding to either static
solutions (single Chazy-Curzon, Schwarzschild and a pair of them), or
stationary solution (single rotating Chazy-Curzon and Kerr black hole) are
discussed. The results are then applied to the case of S2-SgrA binary
system of which the periastron position advance will be soon measured with a
great accuracy.Comment: To appear on General Relativity and Gravitation, vol. 37, 200
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