179 research outputs found
Shortcuts to high symmetry solutions in gravitational theories
We apply the Weyl method, as sanctioned by Palais' symmetric criticality
theorems, to obtain those -highly symmetric -geometries amenable to explicit
solution, in generic gravitational models and dimension. The technique consists
of judiciously violating the rules of variational principles by inserting
highly symmetric, and seemingly gauge fixed, metrics into the action, then
varying it directly to arrive at a small number of transparent, indexless,
field equations. Illustrations include spherically and axially symmetric
solutions in a wide range of models beyond D=4 Einstein theory; already at D=4,
novel results emerge such as exclusion of Schwarzschild solutions in cubic
curvature models and restrictions on ``independent'' integration parameters in
quadratic ones. Another application of Weyl's method is an easy derivation of
Birkhoff's theorem in systems with only tensor modes. Other uses are also
suggested.Comment: 10 page
Effective actions with fixed points, (error in derivation of coefficient corrected)
The specific form of the constant term in the asymptotic expansion of the
heat-kernel on an axially-symmetric space with a codimension two fixed-point
set of conical singularities is used to determine the associated conformal
change of the effective action in four dimensions. Another derivation of the
relevant coefficient is presented.Comment: 10p,uses JyTeX,MUTP/94/1
The tetralogy of Birkhoff theorems
We classify the existent Birkhoff-type theorems into four classes: First, in
field theory, the theorem states the absence of helicity 0- and spin 0-parts of
the gravitational field. Second, in relativistic astrophysics, it is the
statement that the gravitational far-field of a spherically symmetric star
carries, apart from its mass, no information about the star; therefore, a
radially oscillating star has a static gravitational far-field. Third, in
mathematical physics, Birkhoff's theorem reads: up to singular exceptions of
measure zero, the spherically symmetric solutions of Einstein's vacuum field
equation with Lambda = 0 can be expressed by the Schwarzschild metric; for
Lambda unequal 0, it is the Schwarzschild-de Sitter metric instead. Fourth, in
differential geometry, any statement of the type: every member of a family of
pseudo-Riemannian space-times has more isometries than expected from the
original metric ansatz, carries the name Birkhoff-type theorem. Within the
fourth of these classes we present some new results with further values of
dimension and signature of the related spaces; including them are some
counterexamples: families of space-times where no Birkhoff-type theorem is
valid. These counterexamples further confirm the conjecture, that the
Birkhoff-type theorems have their origin in the property, that the two
eigenvalues of the Ricci tensor of two-dimensional pseudo-Riemannian spaces
always coincide, a property not having an analogy in higher dimensions. Hence,
Birkhoff-type theorems exist only for those physical situations which are
reducible to two dimensions.Comment: 26 pages, updated references, minor text changes, accepted by Gen.
Relat. Gra
A new duality transformation for fourth-order gravity
We prove that for non-linear L = L(R), the Lagrangians L and \hat L give
conformally equivalent fourth-order field equations being dual to each other.
The proof represents a new application of the fact that the operator
is conformally invariant.Comment: 11 pages, LaTeX, no figures. Gen. Relat. Grav. in prin
Newtonian Limit of Conformal Gravity
We study the weak-field limit of the static spherically symmetric solution of
the locally conformally invariant theory advocated in the recent past by
Mannheim and Kazanas as an alternative to Einstein's General Relativity. In
contrast with the previous works, we consider the physically relevant case
where the scalar field that breaks conformal symmetry and generates fermion
masses is nonzero. In the physical gauge, in which this scalar field is
constant in space-time, the solution reproduces the weak-field limit of the
Schwarzschild--(anti)DeSitter solution modified by an additional term that,
depending on the sign of the Weyl term in the action, is either oscillatory or
exponential as a function of the radial distance. Such behavior reflects the
presence of, correspondingly, either a tachion or a massive ghost in the
spectrum, which is a serious drawback of the theory under discussion.Comment: 9 pages, comments and references added; the version to be published
in Phys. Rev.
Higher Dimensional Schwinger-like Anomalous Effective Action
We construct explicit form of the anomalous effective action, in arbitrary
even dimension, for Abelian vector and axial gauge fields coupled to Dirac
fermions. It turns out to be a surprisingly simple extension of 2D Schwinger
model effective action.Comment: 7 pages, no figures, ReVTeX, to appear in Phys.Rev.
Implications of Cosmic Repulsion for Gravitational Theory
In this paper we present a general, model independent analysis of a recently
detected apparent cosmic repulsion, and discuss its potential implications for
gravitational theory. In particular, we show that a negatively spatially curved
universe acts like a diverging refractive medium, to thus naturally cause
galaxies to accelerate away from each other. Additionally, we show that it is
possible for a cosmic acceleration to only be temporary, with some accelerating
universes actually being able to subsequently recontract.Comment: RevTeX, 13 page
Quantum Diffeomorphisms and Conformal Symmetry
We analyze the constraints of general coordinate invariance for quantum
theories possessing conformal symmetry in four dimensions. The character of
these constraints simplifies enormously on the Einstein universe . The global conformal symmetry algebra of this space determines
uniquely a finite shift in the Hamiltonian constraint from its classical value.
In other words, the global Wheeler-De Witt equation is {\it modified} at the
quantum level in a well-defined way in this case. We argue that the higher
moments of should not be imposed on the physical states {\it a priori}
either, but only the weaker condition . We
present an explicit example of the quantization and diffeomorphism constraints
on for a free conformal scalar field.Comment: PlainTeX File, 37 page
Local and global gravity
Our long experience with Newtonian potentials has inured us to the view that
gravity only produces local effects. In this paper we challenge this quite
deeply ingrained notion and explicitly identify some intrinsically global
gravitational effects. In particular we show that the global cosmological
Hubble flow can actually modify the motions of stars and gas within individual
galaxies, and even do so in a way which can apparently eliminate the need for
galactic dark matter. Also we show that a classical light wave acquires an
observable, global, path dependent phase in traversing a gravitational field.
Both of these effects serve to underscore the intrinsic difference between
non-relativistic and relativistic gravity.Comment: LaTeX, 20 pages plus three figures in two postscript files. To appear
in a special issue of Foundations of Physics honoring Professor Lawrence
Horwitz on the occasion of his 65th birthday; A. van der Merwe and S. Raby,
Editors, Plenum Publishing Company, N.Y., 199
Thermodynamics of Quantum Fields in Black Hole Backgrounds
We discuss the relation between the micro-canonical and the canonical
ensemble for black holes, and highlight some problems associated with extreme
black holes already at the classical level. Then we discuss the contribution of
quantum fields and demonstrate that the partition functions for scalar and
Dirac (Majorana) fields in static space-time backgrounds, can be expressed as
functional integrals in the corresponding optical space, and point out that the
difference between this and the functional integrals in the original metric is
a Liouville-type action. The optical method gives both the correction to the
black hole entropy and the bulk contribution to the entropy due to the
radiation, while (if the Liouville term is ignored) the conical singularity
method just gives the divergent contribution to the black hole entropy. A
simple derivation of a general formula for the free energy in the
high-temperature approximation is given and applied to various cases. We
conclude with a discussion of the second law.Comment: 26 pages, latex, no figures. References added, minor error correcte
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