923 research outputs found
Spacetime: Arena or Reality?
For small values of the mass (in relation to the angular momentum and
electric charge), the Kerr-Newman (KN) solution of Einstein equation reduces to
a naked singularity of circular shape. By considering the Hawking and Ellis
extended interpretation of the KN spacetime, as well as Wheeler's idea of
"charge without charge", the non-trivial topological structure of the extended
KN spatial section is found to represent gravitational states with
half-integral angular momentum. As a consequence, it can be consistently
interpreted as a model for the electron-positron system, in which the concepts
of mass, charge and spin emerge from the spacetime geometry. According to this
model, therefore, instead of a simple arena, spacetime must have a concrete
existence, being responsible -- through its highly non-trivial topological
structures -- for the building blocks of (at least some of) the existing matter
in the universe.Comment: Chapter in the book "Relativity and the Dimensionality of the World",
Springer series "Fundamental Theories of Physics", Vol. 153 (2007). Volume
Editor: Vesselin Petko
Kerr-Newman solution as a Dirac particle
For m^2 < a^2 + q^2, with m, a, and q respectively the source mass, angular
momentum per unit mass, and electric charge, the Kerr--Newman (KN) solution of
Einstein's equation reduces to a naked singularity of circular shape, enclosing
a disk across which the metric components fail to be smooth. By considering the
Hawking and Ellis extended interpretation of the KN spacetime, it is shown
first that, similarly to the electron-positron system, this solution presents
four inequivalent classical states. Next, it is shown that due to the
topological structure of the extended KN spacetime it does admit states with
half-integral angular momentum. This last property is corroborated by the fact
that, under a rotation of the space coordinates, those inequivalent states
transform into themselves only after a 4pi rotation. As a consequence, it
becomes possible to naturally represent them in a Lorentz spinor basis. The
state vector representing the whole KN solution is then constructed, and its
evolution is shown to be governed by the Dirac equation. The KN solution can
thus be consistently interpreted as a model for the electron-positron system,
in which the concepts of mass, charge and spin become connected with the
spacetime geometry. Some phenomenological consequences of the model are
explored.Comment: 19 pages, 6 figures. References added, section 2 enhanced, an
appendix and one figure adde
Vibrating soap films: An analog for quantum chaos on billiards
We present an experimental setup based on the normal modes of vibrating soap
films which shows quantum features of integrable and chaotic billiards. In
particular, we obtain the so-called scars -narrow linear regions with high
probability along classical periodic orbits- for the classically chaotic
billiards. We show that these scars are also visible at low frequencies.
Finally, we suggest some applications of our experimental setup in other
related two-dimensional wave phenomena.Comment: 5 pages, 7 figures. Better Postscript figures available on reques
Torsion and Gravitation: A new view
According to the teleparallel equivalent of general relativity, curvature and
torsion are two equivalent ways of describing the same gravitational field.
Despite equivalent, however, they act differently: whereas curvature yields a
geometric description, in which the concept of gravitational force is absent,
torsion acts as a true gravitational force, quite similar to the Lorentz force
of electrodynamics. As a consequence, the right-hand side of a
spinless-particle equation of motion (which would represent a gravitational
force) is always zero in the geometric description, but not in the teleparallel
case. This means essentially that the gravitational coupling prescription can
be minimal only in the geometric case. Relying on this property, a new
gravitational coupling prescription in the presence of curvature and torsion is
proposed. It is constructed in such a way to preserve the equivalence between
curvature and torsion, and its basic property is to be equivalent with the
usual coupling prescription of general relativity. According to this view, no
new physics is connected with torsion, which appears as a mere alternative to
curvature in the description of gravitation. An application of this formulation
to the equations of motion of both a spinless and a spinning particle is madeComment: To appear on IJMP
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