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

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

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

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.

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 $R \times S^3$. The $SO(4,2)$ 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 $T^{00}$ should not be imposed on the physical states {\it a priori} either, but only the weaker condition $\langle \dot T^{00} \rangle = 0$. We present an explicit example of the quantization and diffeomorphism constraints on $R \times S^3$ for a free conformal scalar field.Comment: PlainTeX File, 37 page

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.

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

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

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

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