38 research outputs found
Aichelburg-Sexl boost of an isolated source in general relativity
A study of the Aichelburg--Sexl boost of the Schwarzschild field is described
in which the emphasis is placed on the field (curvature tensor) with the metric
playing a secondary role. This is motivated by a description of the Coulomb
field of a charged particle viewed by an observer whose speed relative to the
charge approaches the speed of light. Our approach is exemplified by carrying
out an Aichelburg-- Sexl type boost on the Weyl vacuum gravitational field due
to an isolated axially symmetric source. Detailed calculations of the boosts
transverse and parallel to the symmetry axis are given and the results, which
differ significantly, are discussed.Comment: 25 pages, LateX2
Potential Conservation Laws
We prove that potential conservation laws have characteristics depending only
on local variables if and only if they are induced by local conservation laws.
Therefore, characteristics of pure potential conservation laws have to
essentially depend on potential variables. This statement provides a
significant generalization of results of the recent paper by Bluman, Cheviakov
and Ivanova [J. Math. Phys., 2006, V.47, 113505]. Moreover, we present
extensions to gauged potential systems, Abelian and general coverings and
general foliated systems of differential equations. An example illustrating
possible applications of proved statements is considered. A special version of
the Hadamard lemma for fiber bundles and the notions of weighted jet spaces are
proposed as new tools for the investigation of potential conservation laws.Comment: 36 pages, extended versio
Geodesic deviation in pp-wave spacetimes of quadratic curvature gravity
We write the equation of geodesic deviations in the spacetime of -waves
in terms of the Newman-Penrose scalars and apply it to study gravitational
waves in quadratic curvature gravity. We show that quadratic curvature gravity
-waves can have a transverse helicity-0 polarization mode and two
transverse helicity-2 general relativity-like wave polarizations. A concrete
example is given in which we analyze the wave polarizations of an exact
impulsive gravitational wave solution to quadratic curvature gravity.Comment: 16 pages, no figures, accepted in Physical Review
PP-waves, Israel's Matching conditions, Brane-world scenarios and BPS states in gravity
The matching between two 4-dimensional PP-waves is discussed by using
Israel's matching conditions. Physical consequences on the dynamics of (cosmic)
strings are analyzed. The extension to space-time of arbitrary dimension is
discussed and some interesting features related to the brane world scenario,
BPS states in gravity and Dirac-like quantization conditions are briefly
described.Comment: 16 pages, no figures. Accepted for pubblication on Classical and
Quantum Gravit
On the Geroch-Traschen class of metrics
We compare two approaches to semi-Riemannian metrics of low regularity. The maximally 'reasonable' distributional setting of Geroch and Traschen is shown to be consistently contained in the more general setting of nonlinear distributional geometry in the sense of Colombea
Symmetries and geodesics in (anti-)de Sitter spacetimes with nonexpanding impulsive waves
We consider a class of exact solutions which represent nonexpanding impulsive
waves in backgrounds with nonzero cosmological constant. Using a convenient
5-dimensional formalism it is shown that these spacetimes admit at least three
global Killing vector fields. The same geometrical approach enables us to find
all geodesics in a simple explicit form and describe the effect of impulsive
waves on test particles. Timelike geodesics in the axially-symmetric
Hotta-Tanaka spacetime are studied in detail. It is also demonstrated that for
vanishing cosmological constant, the symmetries and geodesics reduce to those
for well-known impulsive pp-waves.Comment: 16 pages, 3 figures, LaTeX 2e. To appear in Class. Quantum Gra
Nonisospectral integrable nonlinear equations with external potentials and their GBDT solutions
Auxiliary systems for matrix nonisospectral equations, including coupled NLS
with external potential and KdV with variable coefficients, were introduced.
Explicit solutions of nonisospectral equations were constructed using the GBDT
version of the B\"acklund-Darboux transformation
Motions and world-line deviations in Einstein-Maxwell theory
We examine the motion of charged particles in gravitational and
electro-magnetic background fields. We study in particular the deviation of
world lines, describing the relative acceleration between particles on
different space-time trajectories. Two special cases of background fields are
considered in detail: (a) pp-waves, a combination of gravitational and
electro-magnetic polarized plane waves travelling in the same direction; (b)
the Reissner-Nordstr{\o}m solution. We perform a non-trivial check by computing
the precession of the periastron for a charged particle in the
Reissner-Nordstr{\o}m geometry both directly by solving the geodesic equation,
and using the world-line deviation equation. The results agree to the order of
approximation considered.Comment: 23 pages, no figure
Local conservation laws of second-order evolution equations
Generalizing results by Bryant and Griffiths [Duke Math. J., 1995, V.78,
531-676], we completely describe local conservation laws of second-order
(1+1)-dimensional evolution equations up to contact equivalence. The possible
dimensions of spaces of conservation laws prove to be 0, 1, 2 and infinity. The
canonical forms of equations with respect to contact equivalence are found for
all nonzero dimensions of spaces of conservation laws.Comment: 11 pages, minor correction