Hans C. Ohanian

On the focusing of gravitational radiation

We investigate the gain in intensity that can be achieved by using a massive object as a ‘lens’ to focus gravitational radiation incident on the object from a point-like source. An object of massM produces a gain in intensity of the order ofαGM/λc2 whereα is a numerical factor which depends on the mass distribution andλ is the wavelength of the radiation. For large mass, the gain is large, but occurs only in a beam of small angular width.

Gravitation and the new improved energy‐momentum tensor

We give precise definitions of the weak and strong principles of equivalence and show that the new gravitational theory based on the improved energy‐momentum tensor of Callan, Coleman, and Jackiw [Ann. Phys. (N.Y.) 59, 42 (1970)] satisfies both of these principles. As a consequence of the equality between the 4‐momentum given by the canonical energy‐momentum tensor and the ``momentum given by the pseudotensor that is the source of gravitation, the weak principle is also shown to hold in more general Einstein theories. Investigation of the interactions of a scalar field in the new gravitational theory shows that, besides the familiar long range interaction, there exists a new short range gravitational interaction between any scalar field and other matter.

Inertial and gravitational mass in the brans-dicke theory

Abstract We investigate the equality of inertial and gravitational mass in the Brans-Dicke theory of gravitation in both the classical and quantum case. We derive a general expression for the ratio of inertial to gravitational mass for any classical static or quasistatic system. Although the ratio differs from one, in violation of the principle of equivalence, the difference is small (of the order of magnitude of (gravitational potential energy)/(rest mass)). In the quantum case, we find that the gravitational self-energy of a particle contributes to the gravitational mass in such a way that the principle of equivalence is not necessarily satisfied. Thus, in contrast to Einsteins theory, the Brans-Dicke theory does not contain the principle of equivalence for quantum particles.

Cosmological changes in atomic and nuclear constants

We use geochronological and cosmological data to obtain upper limits on the rates of change of the following “constants”: proton mass, neutron mass, fine structure constant, weak interaction constant, strong interaction constant, and “range” of nuclear forces. If the rates of change of all these constants are correlated, then the available data permit changes much in excess of the limits that have been obtained by Dyson and others from the assumption that only one or two constants change. As an application of our results, we note that the disagreement between atomic time and ephemeris time reported by Van Flandern can be explained by a change in an atomic constant (magnetic moment of proton or, equivalently, pion mass) rather than a change in the gravitational constant.

SCALAR-TENSOR THEORIES AND THE PRINCIPLE OF EQUIVALENCE.

We investigate the restrictions on scalar-tensor theories of gravitation implied by the assumptions: (i) the field equations are derivable from an action principle, (ii) units of mass length and time are defined by atomic standards, and (iii) the principle of equivalence holds whenever gravitational self-energy can be neglected. We show that in all these theories the presence of gravitational energy in a system leads to violations of the principle of equivalence.

Black holes and gravitational collapse

Lasciate ogni speranza voi chentrate. Dante Alighieri, The Inferno The dimensionless quantity GM / rc 2 may be regarded as a measure of the strength of the gravitational field. This quantity enters into the formulas for light deflection, time delay, gravitational redshift, perihelion precession, and so on. The small magnitude of the relativistic gravitational effects in the Solar System is related to the small magnitude of this quantity; even at the solar surface, GM / rc 2 is only 2 × 10 −6 . Large relativistic effects are found in the gravitational field in the neighborhood of an extremely compact mass, where GM / rc 2 can attain values of the order of magnitude of 1. For example, near such a compact mass, at a radius r = 3 GM / c 2 , the deflection of light in the Schwarzschild field becomes so large that a light signal will move in a closed circular orbit around the central mass. The relativistic effects become spectacular when r = 2 GM / c 2 . The gravitational fields at this radius are so strong that nothing can escape from their grip. Light signals, particles, and even spacecraft with the most powerful engines are inexorably pulled inward.