43 research outputs found
Stationary generalized Kerr-Schild spacetimes
In this paper we have applied the generalized Kerr-Schild transformation
finding a new family of stationary perfect-fluid solutions of the Einstein
field equations. The procedure used combines some well-known techniques of null
and timelike vector fields, from which some properties of the solutions are
studied in a coordinate-free way. These spacetimes are algebraically special
being their Petrov types II and D. This family includes all the classical
vacuum Kerr-Schild spacetimes, excepting the plane-fronted gravitational waves,
and some other interesting solutions as, for instance, the Kerr metric in the
background of the Einstein Universe. However, the family is much more general
and depends on an arbitrary function of one variable.Comment: 21 pages, LaTeX 2.09. To be published in Journal of Mathematical
Physic
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
Expanding, axisymmetric pure-radiation gravitational fields with a simple twist
New expanding, axisymmetric pure-radiation solutions are found, exploiting
the analogy with the Euler-Darboux equation for aligned colliding plane waves.Comment: revtex, 5 page
Pure-radiation gravitational fields with a simple twist and a Killing vector
Pure-radiation solutions are found, exploiting the analogy with the Euler-
Darboux equation for aligned colliding plane waves and the Euler-Tricomi
equation in hydrodynamics of two-dimensional flow. They do not depend on one of
the spacelike coordinates and comprise the Hauser solution as a special
subcase.Comment: revtex, 9 page
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
Rotating perfect fluid sources of the NUT metric
Locally rotationally symmetric perfect fluid solutions of Einstein's
gravitational equations are matched along the hypersurface of vanishing
pressure with the NUT metric. These rigidly rotating fluids are interpreted as
sources for the vacuum exterior which consists only of a stationary region of
the Taub-NUT space-time. The solution of the matching conditions leaves
generally three parameters in the global solution. Examples of perfect fluid
sources are discussed.Comment: 8 pages, late
Yang's gravitational theory
Yang's pure space equations (C.N. Yang, Phys. Rev. Lett. v.33, p.445 (1974))
generalize Einstein's gravitational equations, while coming from gauge theory.
We study these equations from a number of vantage points: summarizing the work
done previously, comparing them with the Einstein equations and investigating
their properties. In particular, the initial value problem is discussed and a
number of results are presented for these equations with common energy-momentum
tensors.Comment: 28 pages, to appear in Gen. Rel. Gra
Null dust in canonical gravity
We present the Lagrangian and Hamiltonian framework which incorporates null
dust as a source into canonical gravity. Null dust is a generalized Lagrangian
system which is described by six Clebsch potentials of its four-velocity Pfaff
form. The Dirac--ADM decomposition splits these into three canonical
coordinates (the comoving coordinates of the dust) and their conjugate momenta
(appropriate projections of four-velocity). Unlike ordinary dust of massive
particles, null dust therefore has three rather than four degrees of freedom
per space point. These are evolved by a Hamiltonian which is a linear
combination of energy and momentum densities of the dust. The energy density is
the norm of the momentum density with respect to the spatial metric. The
coupling to geometry is achieved by adding these densities to the gravitational
super-Hamiltonian and supermomentum. This leads to appropriate Hamiltonian and
momentum constraints in the phase space of the system. The constraints can be
rewritten in two alternative forms in which they generate a true Lie algebra.
The Dirac constraint quantization of the system is formally accomplished by
imposing the new constraints as quantum operator restrictions on state
functionals. We compare the canonical schemes for null and ordinary dust and
emhasize their differences.Comment: 25 pages, REVTEX, no figure
Lower-order ODEs to determine new twisting type N Einstein spaces via CR geometry
In the search for vacuum solutions, with or without a cosmological constant,
of the Einstein field equations of Petrov type N with twisting principal null
directions, the CR structures to describe the parameter space for a congruence
of such null vectors provide a very useful tool. A work of Hill, Lewandowski
and Nurowski has given a good foundation for this, reducing the field equations
to a set of differential equations for two functions, one real, one complex, of
three variables. Under the assumption of the existence of one Killing vector,
the (infinite-dimensional) classical symmetries of those equations are
determined and group-invariant solutions are considered. This results in a
single ODE of the third order which may easily be reduced to one of the second
order. A one-parameter class of power series solutions, g(w), of this
second-order equation is realized, holomorphic in a neighborhood of the origin
and behaving asymptotically as a simple quadratic function plus lower-order
terms for large values of w, which constitutes new solutions of the twisting
type N problem. The solution found by Leroy, and also by Nurowski, is shown to
be a special case in this class. Cartan's method for determining equivalence of
CR manifolds is used to show that this class is indeed much more general.
In addition, for a special choice of a parameter, this ODE may be integrated
once, to provide a first-order Abel equation. It can also determine new
solutions to the field equations although no general solution has yet been
found for it.Comment: 28 page