21,127 research outputs found
Quantum Gravity as a Deformed Topological Quantum Field Theory
It is known that the Einstein-Hilbert action with a positive cosmological
constant can be represented as a perturbation of the SO(4,1) BF theory by a
symmetry-breaking term quadratic in the B field. Introducing fermionic matter
generates additional terms in the action which are polynomial in the tetrads
and the spin connection. We describe how to construct the generating functional
in the spin foam formalism for a generic BF theory when the sources for the B
and the gauge field are present. This functional can be used to obtain a path
integral for General Relativity with matter as a perturbative series whose the
lowest order term is a path integral for a topological gravity coupled to
matter.Comment: 7 pages, talk presented at the QG05 conference, 12-16 September 2005,
Cala Gonone, Ital
Poincare invariant gravity with local supersymmetry as a gauge theory for the M-algebra
Here we consider a gravitational action having local Poincare invariance
which is given by the dimensional continuation of the Euler density in ten
dimensions. It is shown that the local supersymmetric extension of this action
requires the algebra to be the maximal extension of the N=1 super-Poincare
algebra. The resulting action is shown to describe a gauge theory for the
M-algebra, and is not the eleven-dimensional supergravity theory of
Cremmer-Julia-Scherk. The theory admits a class of vacuum solutions of the form
S^{10-d} x Y_{d+1}, where Y_{d+1} is a warped product of R with a d-dimensional
spacetime. It is shown that a nontrivial propagator for the graviton exists
only for d=4 and positive cosmological constant. Perturbations of the metric
around this solution reproduce linearized General Relativity around
four-dimensional de Sitter spacetime.Comment: Final version as published in Physics Letters B. Title changed in
journal, some corrections, new references and comments adde
Universally Coupled Massive Gravity
We derive Einstein's equations from a linear theory in flat space-time using
free-field gauge invariance and universal coupling. The gravitational potential
can be either covariant or contravariant and of almost any density weight. We
adapt these results to yield universally coupled massive variants of Einstein's
equations, yielding two one-parameter families of distinct theories with spin 2
and spin 0. The Freund-Maheshwari-Schonberg theory is therefore not the unique
universally coupled massive generalization of Einstein's theory, although it is
privileged in some respects. The theories we derive are a subset of those found
by Ogievetsky and Polubarinov by other means. The question of positive energy,
which continues to be discussed, might be addressed numerically in spherical
symmetry. We briefly comment on the issue of causality with two observable
metrics and the need for gauge freedom and address some criticisms by
Padmanabhan of field derivations of Einstein-like equations along the way.Comment: Introduction notes resemblance between Einstein's discovery process
and later field/spin 2 project; matches journal versio
Cosmological Constant and Local Gravity
We discuss the linearization of Einstein equations in the presence of a
cosmological constant, by expanding the solution for the metric around a flat
Minkowski space-time. We demonstrate that one can find consistent solutions to
the linearized set of equations for the metric perturbations, in the Lorentz
gauge, which are not spherically symmetric, but they rather exhibit a
cylindrical symmetry. We find that the components of the gravitational field
satisfying the appropriate Poisson equations have the property of ensuring that
a scalar potential can be constructed, in which both contributions, from
ordinary matter and , are attractive. In addition, there is a
novel tensor potential, induced by the pressure density, in which the effect of
the cosmological constant is repulsive. We also linearize the Schwarzschild-de
Sitter exact solution of Einstein's equations (due to a generalization of
Birkhoff's theorem) in the domain between the two horizons. We manage to
transform it first to a gauge in which the 3-space metric is conformally flat
and, then, make an additional coordinate transformation leading to the Lorentz
gauge conditions. We compare our non-spherically symmetric solution with the
linearized Schwarzschild-de Sitter metric, when the latter is transformed to
the Lorentz gauge, and we find agreement. The resulting metric, however, does
not acquire a proper Newtonian form in terms of the unique scalar potential
that solves the corresponding Poisson equation. Nevertheless, our solution is
stable, in the sense that the physical energy density is positive.Comment: 7 pages revtex, no figures; discussion on light bending added, no
effect on conclusions, version to appear in Physical Review D
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