Dinner with Jesus and Other Left-Handed Story-Sermons

Reviewed Book: Chatfield, Donald F. Dinner with Jesus and Other Left-Handed Story-Sermons. Grand Rapids: Zondervan, 1988

Causal Structure of Vacuum Solutions to Conformal(Weyl) Gravity

Using Penrose diagrams the causal structure of the static spherically symmetric vacuum solution to conformal (Weyl) gravity is investigated. A striking aspect of the solution is an unexpected physical singularity at $r=0$ caused by a linear term in the metric. We explain how to calculate the deflection of light in coordinates where the metric is manifestly conformal to flat i.e. in coordinates where light moves in straight lines.Comment: 18 pages, 2 figures, title and abstract changed, contents essentially unaltered accepted for publication in General Relativity and Gravitatio

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

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.

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

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.

Energy in Generic Higher Curvature Gravity Theories

We define and compute the energy of higher curvature gravity theories in arbitrary dimensions. Generically, these theories admit constant curvature vacua (even in the absence of an explicit cosmological constant), and asymptotically constant curvature solutions with non-trivial energy properties. For concreteness, we study quadratic curvature models in detail. Among them, the one whose action is the square of the traceless Ricci tensor always has zero energy, unlike conformal (Weyl) gravity. We also study the string-inspired Einstein-Gauss-Bonnet model and show that both its flat and Anti-de-Sitter vacua are stable.Comment: 18 pages, typos corrected, one footnote added, to appear 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

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

Renormalization Group and Decoupling in Curved Space: II. The Standard Model and Beyond

We continue the study of the renormalization group and decoupling of massive fields in curved space, started in the previous article and analyse the higher derivative sector of the vacuum metric-dependent action of the Standard Model. The QCD sector at low-energies is described in terms of the composite effective fields. For fermions and scalars the massless limit shows perfect correspondence with the conformal anomaly, but similar limit in a massive vector case requires an extra compensating scalar. In all three cases the decoupling goes smoothly and monotonic. A particularly interesting case is the renormalization group flow in the theory with broken supersymmetry, where the sign of one of the beta-functions changes on the way from the UV to IR.Comment: 27 pages, 8 figure