121 research outputs found
Spinor formulation of topologically massive gravity
In the framework of real 2-component spinors in three dimensional space-time
we present a description of topologically massive gravity (TMG) in terms of
differential forms with triad scalar coefficients. This is essentially a real
version of the Newman-Penrose formalism in general relativity. A triad
formulation of TMG was considered earlier by Hall, Morgan and Perjes, however,
due to an unfortunate choice of signature some of the spinors underlying the
Hall-Morgan-Perjes formalism are real, while others are pure imaginary. We
obtain the basic geometrical identities as well as the TMG field equations
including a cosmological constant for the appropriate signature. As an
application of this formalism we discuss the Bianchi Type exact
solutions of TMG and point out that they are parallelizable manifolds. We also
consider various re-identifications of these homogeneous spaces that result in
black hole solutions of TMG.Comment: An expanded version of paper published in Classical and Quantum
Gravity 12 (1995) 291
Topologically massive magnetic monopoles
We show that in the Maxwell-Chern-Simons theory of topologically massive
electrodynamics the Dirac string of a monopole becomes a cone in anti-de Sitter
space with the opening angle of the cone determined by the topological mass
which in turn is related to the square root of the cosmological constant. This
proves to be an example of a physical system, {\it a priory} completely
unrelated to gravity, which nevertheless requires curved spacetime for its very
existence. We extend this result to topologically massive gravity coupled to
topologically massive electrodynamics in the framework of the theory of Deser,
Jackiw and Templeton. These are homogeneous spaces with conical deficit. Pure
Einstein gravity coupled to Maxwell-Chern-Simons field does not admit such a
monopole solution
Poisson Structures for Aristotelian Model of Three Body Motion
We present explicitly Poisson structures, for both time-dependent and
time-independent Hamiltonians, of a dynamical system with three degrees of
freedom introduced and studied by Calogero et al [2005]. For the
time-independent case, new constant of motion includes all parameters of the
system. This extends the result of Calogero et al [2009] for semi-symmetrical
motion. We also discuss the case of three bodies two of which are not
interacting with each other but are coupled with the interaction of third one
Applications of Temperley-Lieb algebras to Lorentz lattice gases
Motived by the study of motion in a random environment we introduce and
investigate a variant of the Temperley-Lieb algebra. This algebra is very rich,
providing us three classes of solutions of the Yang-Baxter equation. This
allows us to establish a theoretical framework to study the diffusive behaviour
of a Lorentz Lattice gas. Exact results for the geometrical scaling behaviour
of closed paths are also presented.Comment: 10 pages, latex file, one figure(by request
Multi-Hamiltonian structure of Plebanski's second heavenly equation
We show that Plebanski's second heavenly equation, when written as a
first-order nonlinear evolutionary system, admits multi-Hamiltonian structure.
Therefore by Magri's theorem it is a completely integrable system. Thus it is
an example of a completely integrable system in four dimensions
Impulsive spherical gravitational waves
Penrose's identification with warp provides the general framework for
constructing the continuous form of impulsive gravitational wave metrics. We
present the 2-component spinor formalism for the derivation of the full family
of impulsive spherical gravitational wave metrics which brings out the power in
identification with warp and leads to the simplest derivation of exact
solutions. These solutions of the Einstein vacuum field equations are obtained
by cutting Minkowski space into two pieces along a null cone and re-identifying
them with warp which is given by an arbitrary non-linear holomorphic
transformation. Using 2-component spinor techniques we construct a new metric
describing an impulsive spherical gravitational wave where the vertex of the
null cone lies on a world-line with constant acceleration
Partner symmetries of the complex Monge-Ampere equation yield hyper-Kahler metrics without continuous symmetries
We extend the Mason-Newman Lax pair for the elliptic complex Monge-Amp\`ere
equation so that this equation itself emerges as an algebraic consequence. We
regard the function in the extended Lax equations as a complex potential. We
identify the real and imaginary parts of the potential, which we call partner
symmetries, with the translational and dilatational symmetry characteristics
respectively. Then we choose the dilatational symmetry characteristic as the
new unknown replacing the K\"ahler potential which directly leads to a Legendre
transformation and to a set of linear equations satisfied by a single real
potential. This enables us to construct non-invariant solutions of the Legendre
transform of the complex Monge-Amp\`ere equation and obtain hyper-K\"ahler
metrics with anti-self-dual Riemann curvature 2-form that admit no Killing
vectors.Comment: submitted to J. Phys.
The black holes of topologically massive gravity
We show that an analytical continuation of the Vuorio solution to
three-dimensional topologically massive gravity leads to a two-parameter family
of black hole solutions, which are geodesically complete and causally regular
within a certain parameter range. No observers can remain static in these
spacetimes. We discuss their global structure, and evaluate their mass, angular
momentum, and entropy, which satisfy a slightly modified form of the first law
of thermodynamics.Comment: 10 pages; Eq. (15) corrected, references added, version to appear in
Classical and Quantum Gravit
Topologically massive gravito-electrodynamics: exact solutions
We construct two classes of exact solutions to the field equations of
topologically massive electrodynamics coupled to topologically massive gravity
in 2 + 1 dimensions. The self-dual stationary solutions of the first class are
horizonless, asymptotic to the extreme BTZ black-hole metric, and regular for a
suitable parameter domain. The diagonal solutions of the second class, which
exist if the two Chern-Simons coupling constants exactly balance, include
anisotropic cosmologies and static solutions with a pointlike horizon.Comment: 15 pages, LaTeX, no figure
Anti-self-dual Riemannian metrics without Killing vectors, can they be realized on K3?
Explicit Riemannian metrics with Euclidean signature and anti-self dual
curvature that do not admit any Killing vectors are presented. The metric and
the Riemann curvature scalars are homogenous functions of degree zero in a
single real potential and its derivatives. The solution for the potential is a
sum of exponential functions which suggests that for the choice of a suitable
domain of coordinates and parameters it can be the metric on a compact
manifold. Then, by the theorem of Hitchin, it could be a class of metrics on
, or on surfaces whose universal covering is .Comment: Misprints in eqs.(9-11) corrected. Submitted to Classical and Quantum
Gravit
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