41 research outputs found
Radiation in Yang-Mills formulation of gravity and a generalized pp-wave metric
The variational methods implemented on a quadratic Yang-Mills type Lagrangian
yield two sets of equations interpreted as the field equations and the
energy-momentum tensor for the gravitational field. A covariant condition is
imposed on the energy-momentum tensor to represent the radiation field. A
generalized pp-wave metric is found to simultaneously satisfy both the field
equations and the radiation condition. The result is compared with that of
Lichn\'{e}rowicz.Comment: 5 pages; e mail: [email protected]
Killing-Yano symmetry for a class of spacetimes admitting parallel null 1-planes
A possible generalization of plane fronted waves with parallel rays
(gpp-wave) fall into a more general class of metrics admitting parallel null
1-planes. For gpp-wave metric, the zero-curvature condition is given, the
Killing-Yano tensors of order two and three are found and the corresponding
Killing tensors are constructed. Henceforth, the compatibility between
geometric duality and non-generic symmetries is presented.Comment: 11 pages, LaTeX, to be published in Il Nuovo Cimento
Dual Metrics and Non-Generic Supersymmetries for a Class of Siklos Spacetimes
The presence of Killing-Yano tensors implies the existence of non-generic
supercharges in spinning point particle theories on curved backgrounds. Dual
metrics are defined through their associated non-degenerate Killing tensors of
valence two. Siklos spacetimes, which are the only non-trivial Einstein spaces
conformal to non-flat pp-waves are investigated in regards to the existence of
their corresponding Killing and Killing-Yano tensors. It is found that under
some restrictions, pp-wave metrics and Siklos spacetimes admit dual metrics and
non-generic supercharges. Possible significance of those dual spacetimes are
discussed.Comment: LaTeX, 8 page
Kaluza-Klein Reduction of a Quadratic Curvature Model
Palatini variational principle is implemented on a five dimensional quadratic
curvature gravity model, rendering two sets of equations which can be
interpreted as the field equations and the stress-energy tensor. Unification of
gravity with electromagnetism and the scalar dilaton field is achieved through
the Kaluza-Klein dimensional reduction mechanism. The reduced curvature
invariant, field equations and the stress-energy tensor in four dimensional
spacetime are obtained. The structure of the interactions among the constituent
fields is exhibited in detail. It is shown that the Lorentz force naturally
emerges from the reduced field equations and the equations of the standard
Kaluza-Klein theory is demonstrated to be intrinsically contained in this
model.Comment: 10 page
Lens optics as an optical computer for group contractions
It is shown that the one-lens system in para-axial optics can serve as an
optical computer for contraction of Wigner's little groups and an analogue
computer which transforms analytically computations on a spherical surface to
those on a hyperbolic surface. It is shown possible to construct a set of
Lorentz transformations which leads to a two-by-two matrix whose expression is
the same as those in the para-axial lens optics. It is shown that the lens
focal condition corresponds to the contraction of the O(3)-like little group
for a massive particle to the E(2)-like little group for a massless particle,
and also to the contraction of the O(2,1)-like little group for a space-like
particle to the same E(2)-like little group. The lens-focusing transformations
presented in this paper allow us to continue analytically the spherical O(3)
world to the hyperbolic O(2,1) world, and vice versa.Comment: 14 pages, RevTeX, no figure