32,417 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
Gravity and the Quantum: Are they Reconcilable?
General relativity and quantum mechanics are conflicting theories. The seeds
of discord are the fundamental principles on which these theories are grounded.
General relativity, on one hand, is based on the equivalence principle, whose
strong version establishes the local equivalence between gravitation and
inertia. Quantum mechanics, on the other hand, is fundamentally based on the
uncertainty principle, which is essentially nonlocal in the sense that a
particle does not follow one trajectory, but infinitely many trajectories, each
one with a different probability. This difference precludes the existence of a
quantum version of the strong equivalence principle, and consequently of a
quantum version of general relativity. Furthermore, there are compelling
experimental evidences that a quantum object in the presence of a gravitational
field violates the weak equivalence principle. Now it so happens that, in
addition to general relativity, gravitation has an alternative, though
equivalent description, given by teleparallel gravity, a gauge theory for the
translation group. In this theory torsion, instead of curvature, is assumed to
represent the gravitational field. These two descriptions lead to the same
classical results, but are conceptually different. In general relativity,
curvature geometrizes the interaction, while torsion in teleparallel gravity
acts as a force, similar to the Lorentz force of electrodynamics. Because of
this peculiar property, teleparallel gravity describes the gravitational
interaction without requiring any of the equivalence principles. The
replacement of general relativity by teleparallel gravity may, in consequence,
lead to a conceptual reconciliation of gravitation with quantum mechanics.Comment: 15 pages, 2 figures. Talk presented at the conference "Quantum
Theory: Reconsideration of Foundations-3", June 6-11, 2005, Vaxjo University,
Vaxjo, Swede
Gravitation without the equivalence principle
In the general relativistic description of gravitation, geometry replaces the
concept of force. This is possible because of the universal character of free
fall, and would break down in its absence. On the other hand, the teleparallel
version of general relativity is a gauge theory for the translation group and,
as such, describes the gravitational interaction by a force similar to the
Lorentz force of electromagnetism, a non-universal interaction. Relying on this
analogy it is shown that, although the geometric description of general
relativity necessarily requires the existence of the equivalence principle, the
teleparallel gauge approach remains a consistent theory for gravitation in its
absence.Comment: Latex, 11 pages, no figures. Minor presentation changes. Version to
appear in Gen. Rel. Grav. (2004
Doing without the Equivalence Principle
In Einstein's general relativity, geometry replaces the concept of force in
the description of the gravitation interaction. Such an approach rests on the
universality of free-fall--the weak equivalence principle--and would break down
without it. On the other hand, the teleparallel version of general relativity,
a gauge theory for the translation group, describes the gravitational
interaction by a force similar to the Lorentz force of electromagnetism, a
non-universal interaction. It is shown that, similarly to the Maxwell's
description of electromagnetism, the teleparallel gauge approach provides a
consistent theory for gravitation even in the absence of the weak equivalence
principle.Comment: 7 pages, no figures. Talk presented at the "Tenth Marcel Grossmann
Meeting", July 20 to 26, 2003, Rio de Janeiro, Brazil; to be published in the
Proceedings (World Scientific, Singapore, 2005
Quantized fields and gravitational particle creation in f(R) expanding universes
The problem of cosmological particle creation for a spatially flat,
homogeneous and isotropic Universes is discussed in the context of f(R)
theories of gravity. Different from cosmological models based on general
relativity theory, it is found that a conformal invariant metric does not
forbid the creation of massless particles during the early stages (radiation
era) of the Universe.Comment: 14 pages, 2 figure
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