1,057 research outputs found
The Exact Geometry of a Kerr-Taub-NUT Solution of String Theory
In this paper we study a solution of heterotic string theory corresponding to
a rotating Kerr-Taub-NUT spacetime. It has an exact CFT description as a
heterotic coset model, and a Lagrangian formulation as a gauged WZNW model. It
is a generalisation of a recently discussed stringy Taub-NUT solution, and is
interesting as another laboratory for studying the fate of closed timelike
curves and cosmological singularities in string theory. We extend the
computation of the exact metric and dilaton to this rotating case, and then
discuss some properties of the metric, with particular emphasis on the
curvature singularities.Comment: 14 pages, 3 figure
Minisuperspace Examples of Quantization Using Canonical Variables of the Ashtekar Type: Structure and Solutions
The Ashtekar variables have been use to find a number of exact solutions in
quantum gravity and quantum cosmology. We investigate the origin of these
solutions in the context of a number of canonical transformations (both complex
and real) of the basic Hamiltonian variables of general relativity. We are able
to present several new solutions in the minisuperspace (quantum cosmology)
sector. The meaning of these solutions is then discussed.Comment: 23 pages, latex, 3 figures (uuencoded, separate file
Hidden symmetries and Killing tensors on curved spaces
Higher order symmetries corresponding to Killing tensors are investigated.
The intimate relation between Killing-Yano tensors and non-standard
supersymmetries is pointed out. In the Dirac theory on curved spaces,
Killing-Yano tensors generate Dirac type operators involved in interesting
algebraic structures as dynamical algebras or even infinite dimensional
algebras or superalgebras. The general results are applied to space-times which
appear in modern studies. One presents the infinite dimensional superalgebra of
Dirac type operators on the 4-dimensional Euclidean Taub-NUT space that can be
seen as a twisted loop algebra. The existence of the conformal Killing-Yano
tensors is investigated for some spaces with mixed Sasakian structures.Comment: 12 pages; talk presented at Group 27 Colloquium, Yerevan, Armenia,
August 200
Exact Solutions of Five Dimensional Anisotropic Cosmologies
We solve the five dimensional vacuum Einstein equations for several kinds of
anisotropic geometries. We consider metrics in which the spatial slices are
characterized as Bianchi types-II and V, and the scale factors are dependent
both on time and a non-compact fifth coordinate. We examine the behavior of the
solutions we find, noting for which parameters they exhibit contraction over
time of the fifth scale factor, leading naturally to dimensional reduction. We
explore these within the context of the induced matter model: a Kaluza-Klein
approach that associates the extra geometric terms due to the fifth coordinate
with contributions to the four dimensional stress-energy tensor.Comment: 11 page
General Gauss-Bonnet brane cosmology
We consider 5-dimensional spacetimes of constant 3-dimensional spatial
curvature in the presence of a bulk cosmological constant. We find the general
solution of such a configuration in the presence of a Gauss-Bonnet term. Two
classes of non-trivial bulk solutions are found. The first class is valid only
under a fine tuning relation between the Gauss-Bonnet coupling constant and the
cosmological constant of the bulk spacetime. The second class of solutions are
static and are the extensions of the AdS-Schwarzchild black holes. Hence in the
absence of a cosmological constant or if the fine tuning relation is not true,
the generalised Birkhoff's staticity theorem holds even in the presence of
Gauss-Bonnet curvature terms. We examine the consequences in brane world
cosmology obtaining the generalised Friedmann equations for a perfect fluid
3-brane and discuss how this modifies the usual scenario.Comment: 20 pages, no figures, typos corrected, refs added, section IV changed
yielding novel result
Surface Layers in General Relativity and Their Relation to Surface Tensions
For a thin shell, the intrinsic 3-pressure will be shown to be analogous to
-A, where A is the classical surface tension: First, interior and exterior
Schwarzschild solutions will be matched together such that the surface layer
generated at the common boundary has no gravitational mass; then its intrinsic
3-pressure represents a surface tension fulfilling Kelvin's relation between
mean curvature and pressure difference in the Newtonian limit. Second, after a
suitable definition of mean curvature, the general relativistic analogue to
Kelvin's relation will be proven to be contained in the equation of motion of
the surface layer.Comment: 12 pages, LaTeX, no figur
Spinning test particles and clock effect in Schwarzschild spacetime
We study the behaviour of spinning test particles in the Schwarzschild
spacetime. Using Mathisson-Papapetrou equations of motion we confine our
attention to spatially circular orbits and search for observable effects which
could eventually discriminate among the standard supplementary conditions
namely the Corinaldesi-Papapetrou, Pirani and Tulczyjew. We find that if the
world line chosen for the multipole reduction and whose unit tangent we denote
as is a circular orbit then also the generalized momentum of the
spinning test particle is tangent to a circular orbit even though and
are not parallel four-vectors. These orbits are shown to exist because the spin
induced tidal forces provide the required acceleration no matter what
supplementary condition we select. Of course, in the limit of a small spin the
particle's orbit is close of being a circular geodesic and the (small)
deviation of the angular velocities from the geodesic values can be of an
arbitrary sign, corresponding to the possible spin-up and spin-down alignment
to the z-axis. When two spinning particles orbit around a gravitating source in
opposite directions, they make one loop with respect to a given static observer
with different arrival times. This difference is termed clock effect. We find
that a nonzero gravitomagnetic clock effect appears for oppositely orbiting
both spin-up or spin-down particles even in the Schwarzschild spacetime. This
allows us to establish a formal analogy with the case of (spin-less) geodesics
on the equatorial plane of the Kerr spacetime. This result can be verified
experimentally.Comment: IOP macros, eps figures n. 2, to appear on Classical and Quantum
gravity, 200
Geodesic motions versus hydrodynamic flows in a gravitating perfect fluid: Dynamical equivalence and consequences
Stimulated by the methods applied for the observational determination of
masses in the central regions of the AGNs, we examine the conditions under
which, in the interior of a gravitating perfect fluid source, the geodesic
motions and the general relativistic hydrodynamic flows are dynamically
equivalent to each other. Dynamical equivalence rests on the functional
similarity between the corresponding (covariantly expressed) differential
equations of motion and is obtained by conformal transformations. In this case,
the spaces of the solutions of these two kinds of motion are isomorphic. In
other words, given a solution to the problem "hydrodynamic flow in a perfect
fluid", one can always construct a solution formally equivalent to the problem
"geodesic motion of a fluid element" and vice versa. Accordingly, we show that,
the observationally determined nuclear mass of the AGNs is being overestimated
with respect to the real, physical one. We evaluate the corresponding
mass-excess and show that it is not always negligible with respect to the mass
ofthe central dark object, while, under circumstances, can be even larger than
the rest-mass of the circumnuclear gas involved.Comment: LaTeX file, 22 page
Collapsing shells of radiation in anti-de Sitter spacetimes and the hoop and cosmic censorship conjectures
Gravitational collapse of radiation in an anti-de Sitter background is
studied. For the spherical case, the collapse proceeds in much the same way as
in the Minkowski background, i.e., massless naked singularities may form for a
highly inhomogeneous collapse, violating the cosmic censorship, but not the
hoop conjecture. The toroidal, cylindrical and planar collapses can be treated
together. In these cases no naked singularity ever forms, in accordance with
the cosmic censorship. However, since the collapse proceeds to form toroidal,
cylindrical or planar black holes, the hoop conjecture in an anti-de Sitter
spacetime is violated.Comment: 4 pages, Revtex Journal: to appear in Physical Review
Evolution of high-frequency gravitational waves in some cosmological models
We investigate Isaacson's high-frequency gravitational waves which propagate
in some relevant cosmological models, in particular the FRW spacetimes. Their
time evolution in Fourier space is explicitly obtained for various metric forms
of (anti--)de Sitter universe. Behaviour of high-frequency waves in the
anisotropic Kasner spacetime is also described.Comment: 14 pages, 8 figures, to appear in Czech. J. Phy
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