2,488 research outputs found
Non-existence of stationary two-black-hole configurations: The degenerate case
In a preceding paper we examined the question whether the spin-spin repulsion
and the gravitational attraction of two aligned sub-extremal black holes can
balance each other. Based on the solution of a boundary value problem for two
separate (Killing-) horizons and a novel black hole criterion we were able to
prove the non-existence of the equilibrium configuration in question. In this
paper we extend the non-existence proof to extremal black holes.Comment: 18 pages, 2 figure
Differentially rotating disks of dust: Arbitrary rotation law
In this paper, solutions to the Ernst equation are investigated that depend
on two real analytic functions defined on the interval [0,1]. These solutions
are introduced by a suitable limiting process of Backlund transformations
applied to seed solutions of the Weyl class. It turns out that this class of
solutions contains the general relativistic gravitational field of an arbitrary
differentially rotating disk of dust, for which a continuous transition to some
Newtonian disk exists. It will be shown how for given boundary conditions (i.
e. proper surface mass density or angular velocity of the disk) the
gravitational field can be approximated in terms of the above solutions.
Furthermore, particular examples will be discussed, including disks with a
realistic profile for the angular velocity and more exotic disks possessing two
spatially separated ergoregions.Comment: 23 pages, 3 figures, submitted to 'General Relativity and
Gravitation
Dirichlet Boundary Value Problems of the Ernst Equation
We demonstrate how the solution to an exterior Dirichlet boundary value
problem of the axisymmetric, stationary Einstein equations can be found in
terms of generalized solutions of the Backlund type. The proof that this
generalization procedure is valid is given, which also proves conjectures about
earlier representations of the gravitational field corresponding to rotating
disks of dust in terms of Backlund type solutions.Comment: 22 pages, to appear in Phys. Rev. D, Correction of a misprint in
equation (4
Non-existence of stationary two-black-hole configurations
We resume former discussions of the question, whether the spin-spin repulsion
and the gravitational attraction of two aligned black holes can balance each
other. To answer the question we formulate a boundary value problem for two
separate (Killing-) horizons and apply the inverse (scattering) method to solve
it. Making use of results of Manko, Ruiz and Sanabria-G\'omez and a novel black
hole criterion, we prove the non-existence of the equilibrium situation in
question.Comment: 15 pages, 3 figures; Contribution to Juergen Ehlers Memorial Issue
(GeRG journal
Proof of a generalized Geroch conjecture for the hyperbolic Ernst equation
We enunciate and prove here a generalization of Geroch's famous conjecture
concerning analytic solutions of the elliptic Ernst equation. Our
generalization is stated for solutions of the hyperbolic Ernst equation that
are not necessarily analytic, although it can be formulated also for solutions
of the elliptic Ernst equation that are nowhere axis-accessible.Comment: 75 pages (plus optional table of contents). Sign errors in elliptic
case equations (1A.13), (1A.15) and (1A.25) are corrected. Not relevant to
proof contained in pape
Ellipsoidal shapes in general relativity: general definitions and an application
A generalization of the notion of ellipsoids to curved Riemannian spaces is
given and the possibility to use it in describing the shapes of rotating bodies
in general relativity is examined. As an illustrative example, stationary,
axisymmetric perfect-fluid spacetimes with a so-called confocal inside
ellipsoidal symmetry are investigated in detail under the assumption that the
4-velocity of the fluid is parallel to a time-like Killing vector field. A
class of perfect-fluid metrics representing interior NUT-spacetimes is obtained
along with a vacuum solution with a non-zero cosmological constant.Comment: Latex, 22 pages, Revised version accepted in Class. Quantum. Grav.,
references adde
Phase field modelling of grain boundary premelting using obstacle potentials
We investigate the multi-order parameter phase field model of Steinbach and
Pezzolla [I. Steinbach, F. Pezzolla, A generalized field method for multiphase
transformations using interface fields, Physica D 134 (1999) 385-393]
concerning its ability to describe grain boundary premelting. For a single
order parameter situation solid-melt interfaces are always attractive, which
allows to have (unstable) equilibrium solid-melt-solid coexistence above the
bulk melting point. The temperature dependent melt layer thickness and the
disjoining potential, which describe the interface interaction, are affected by
the choice of the thermal coupling function and the measure to define the
amount of the liquid phase. Due to the strictly finite interface thickness also
the interaction range is finite. For a multi-order parameter model we find
either purely attractive or purely repulsive finite-ranged interactions. The
premelting transition is then directly linked to the ratio of the grain
boundary and solid-melt interfacial energy.Comment: 12 page
Infrared observations of Phobos and Deimos from Viking
The surface thermal properties of Phobos and Deimos have been determined from observations made with the Viking Orbiter Infrared Thermal Mapper (IRTM), at wavelengths ranging from 6 to 20 μm. The data, composed of both global and high-resolution infrared photometry of the satellite surfaces as well as eclipse observations, indicate surface material of low thermal conductivity comparable to that of the earth's moon. Values of the thermal inertia I consistent with the data for Phobos are 0.9 ≲ I ≲ 1.6 × 10^(−3) cal cm^(−2) s^(−1/2) K^(−1), and 0.6 ≲ I ≲ 2.0 × 10^(−3) cal cm^(−2) s^(−1/2) K^(−1) for Deimos. It is concluded that both satellites are covered with a vertically uniform layer of finely divided material at least several centimeters thick. Observed differences between brightness temperatures at different wavelengths on Phobos are due mainly to topographic slopes and to the presence of ∼5% by area high inertia or blocky material
Integrable Systems in Stringy Gravity
Static axisymmetric Einstein-Maxwell-Dilaton and stationary axisymmetric
Einstein-Maxwell-Dilaton-Axion (EMDA) theories in four space-time dimensions
are shown to be integrable by means of the inverse scattering transform method.
The proof is based on the coset-space representation of the 4-dim theory in a
space-time admitting a Killing vector field. Hidden symmetry group of the
four-dimensional EMDA theory, unifying T and S string dualities, is shown to be
Sp(2, R) acting transitively on the coset Sp(2, R)/U(2). In the case of
two-parameter Abelian space-time isometry group, the hidden symmetry is the
corresponding infinite-dimensional group of the Geroch-Kinnersley-Chitre type.Comment: 8 pages, LATEX, MSU-DTP-94/21, October 9
Universal properties of distorted Kerr-Newman black holes
We discuss universal properties of axisymmetric and stationary configurations
consisting of a central black hole and surrounding matter in Einstein-Maxwell
theory. In particular, we find that certain physical equations and inequalities
(involving angular momentum, electric charge and horizon area) are not
restricted to the Kerr-Newman solution but can be generalized to the situation
where the black hole is distorted by an arbitrary axisymmetric and stationary
surrounding matter distribution.Comment: 7 page
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