Scale-covariant theory of gravitation and astrophysical applications

Journal Article · Thu Sep 15 00:00:00 EDT 1977 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.16.1643· OSTI ID:5349910

Canuto, V; Adams, P J; Hsieh, S; Tsiang, E

By associating the mathematical operation of scale transformation with the physics of using different dynamical systems to measure space-time distances, we formulate a scale-covariant theory of gravitation. Corresponding to each dynamical system of units is a gauge condition which determines the otherwise arbitrary gauge function. For gravitational units, the gauge condition is chosen so that the standard Einstein equations are recovered. Assuming the atomic units, derivable from atomic dynamics, to be distinct from the gravitational units, a different gauge condition must be imposed. It is suggested that Dirac's large-number hypothesis be used for the determination of this condition so that gravitational phenomena can be described in atomic units. The result allows a natural interpretation of the possible variation of the gravitational constant without compromising the validity of general relativity. A geometrical interpretation of the scale-covariant theory is possible if the covariant tensors in Riemannian space are replaced by cocovariant cotensors in an integrable Weyl space. A scale-invariant action principle is constructed from the metrical potentials of the integrable Weyl space. Application of the dynamical equations in atomic units to cosmology yields a family of homogeneous solutions characterized by R approx. t for large cosmological times. Equations of motion in atomic units are solved for spherically symmetric gravitational fields. Expressions for perihelion shift and light deflection are derived. They do not differ from the predictions of general relativity except for secular variations, having the age of the universe as a time scale. Similar variations of periods and radii for planetary orbits are also derived.

• Research Organization: NASA, Institute for Space Studies, Goddard Space Flight Center, New York, New York 10025
• OSTI ID: 5349910
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 16:6; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
657003 -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ASTROPHYSICS
COSMOLOGY
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EINSTEIN FIELD EQUATIONS
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
GRAVITATION
GRAVITATIONAL FIELDS
HYDRODYNAMIC MODEL
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MATHEMATICAL SPACE
PARTICLE MODELS
RIEMANN SPACE
SPACE
SPACE-TIME
STATISTICAL MODELS
THERMODYNAMIC MODEL
WAVE EQUATIONS
WEYL UNIFIED THEORY