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

Search for Supergalactic Anisotropies in the 3B Catalog

The angular distribution of GRBs is isotropic, while the brightness distribution of bursts shows a reduced number of faint events. These observations favor a cosmological burst origin. If GRBs are indeed at cosmological distances and if they trace luminous matter, we must eventually find an anisotropic distribution of bright bursts. If a significant number of bursts originate at redshifts less than z~1, the concentration of nearby galaxies towards the supergalactic plane is pronounced enough that we could discover the corresponding clustering of burst locations. We used the 3B catalog to search for a pattern visible in supergalactic coordinates. No compelling evidence for anisotropies was found. The absence of anisotropies in SG coordinates implies a minimum sampling distance of 200h^-1 Mpc.Comment: 5 pages, uuencoded postscript, to appear in the Proceedings of the Huntsville Conference on Gamma Ray Burst

Comprehensive Solution to the Cosmological Constant, Zero-Point Energy, and Quantum Gravity Problems

We present a solution to the cosmological constant, the zero-point energy, and the quantum gravity problems within a single comprehensive framework. We show that in quantum theories of gravity in which the zero-point energy density of the gravitational field is well-defined, the cosmological constant and zero-point energy problems solve each other by mutual cancellation between the cosmological constant and the matter and gravitational field zero-point energy densities. Because of this cancellation, regulation of the matter field zero-point energy density is not needed, and thus does not cause any trace anomaly to arise. We exhibit our results in two theories of gravity that are well-defined quantum-mechanically. Both of these theories are locally conformal invariant, quantum Einstein gravity in two dimensions and Weyl-tensor-based quantum conformal gravity in four dimensions (a fourth-order derivative quantum theory of the type that Bender and Mannheim have recently shown to be ghost-free and unitary). Central to our approach is the requirement that any and all departures of the geometry from Minkowski are to be brought about by quantum mechanics alone. Consequently, there have to be no fundamental classical fields, and all mass scales have to be generated by dynamical condensates. In such a situation the trace of the matter field energy-momentum tensor is zero, a constraint that obliges its cosmological constant and zero-point contributions to cancel each other identically, no matter how large they might be. Quantization of the gravitational field is caused by its coupling to quantized matter fields, with the gravitational field not needing any independent quantization of its own. With there being no a priori classical curvature, one does not have to make it compatible with quantization.Comment: Final version, to appear in General Relativity and Gravitation (the final publication is available at http://www.springerlink.com). 58 pages, revtex4, some additions to text and some added reference

Open Questions in Classical Gravity

We discuss some outstanding open questions regarding the validity and uniqueness of the standard second order Newton-Einstein classical gravitational theory. On the observational side we discuss the degree to which the realm of validity of Newton's Law of Gravity can actually be extended to distances much larger than the solar system distance scales on which the law was originally established. On the theoretical side we identify some commonly accepted but actually still open to question assumptions which go into the formulating of the standard second order Einstein theory in the first place. In particular, we show that while the familiar second order Poisson gravitational equation (and accordingly its second order covariant Einstein generalization) may be sufficient to yield Newton's Law of Gravity they are not in fact necessary. The standard theory thus still awaits the identification of some principle which would then make it necessary too. We show that current observational information does not exclusively mandate the standard theory, and that the conformal invariant fourth order theory of gravity considered recently by Mannheim and Kazanas is also able to meet the constraints of data, and in fact to do so without the need for any so far unobserved non-luminous or dark matter.Comment: UCONN-93-1, plain TeX format, 22 pages (plus 7 figures - send requests to [email protected]). To appear in a special issue of Foundations of Physics honoring Professor Fritz Rohrlich on the occasion of his retirement, L. P. Horwitz and A. van der Merwe Editors, Plenum Publishing Company, N.Y., Fall 199

Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart

In a recent paper Bender and Mannheim showed that the unequal-frequency fourth-order derivative Pais-Uhlenbeck oscillator model has a realization in which the energy eigenvalues are real and bounded below, the Hilbert-space inner product is positive definite, and time evolution is unitary. Central to that analysis was the recognition that the Hamiltonian $H_{\rm PU}$ of the model is PT symmetric. This Hamiltonian was mapped to a conventional Dirac-Hermitian Hamiltonian via a similarity transformation whose form was found exactly. The present paper explores the equal-frequency limit of the same model. It is shown that in this limit the similarity transform that was used for the unequal-frequency case becomes singular and that $H_{\rm PU}$ becomes a Jordan-block operator, which is nondiagonalizable and has fewer energy eigenstates than eigenvalues. Such a Hamiltonian has no Hermitian counterpart. Thus, the equal-frequency PT theory emerges as a distinct realization of quantum mechanics. The quantum mechanics associated with this Jordan-block Hamiltonian can be treated exactly. It is shown that the Hilbert space is complete with a set of nonstationary solutions to the Schr\"odinger equation replacing the missing stationary ones. These nonstationary states are needed to establish that the Jordan-block Hamiltonian of the equal-frequency Pais-Uhlenbeck model generates unitary time evolution.Comment: 39 pages, 0 figure