Theory of gravitation with an alternative to black holes

Abstract

A gauge theory of gravitation is proposed in which the Lagrangian is constructed from vierbein-based invariants rather than local affine connections. The vierbein invariants are more basic than the connection-based invariants: involving coefficients of lower-order differential forms, providing a reasonable field energy-momentum tensor, and not requiring arbitrary introduction of quantities into the gauge-theory formalism in the special case of scalar wave functions. Covariance of the equations notwithstanding, the speed of light measured with atomic clocks and rigid rulers is hypothesized to be independent of direction in a gravitational field. This hypothesis constrains the Lagrangian for variations which give the field equations in the operationally significant class of coordinate systems whose time and spatial intervals are directly measurable with these same clocks and rulers. Out of the general family of quadratic Lagrangians permitted by this constraint, only two possible Lagrangians are selected by the standard weak-field observational tests (perihelion precession, light deflection, etc.) of the general theory of relativity. Although both of these Lagrangians give solutions which agree with the standard weak-field observational tests of the general theory of relativity, they do give different predictions in other situations: (1) For a static spherically symmetric field, one Lagrangian gives the standard isotropic Schwarzschild metric of the Einstein general theory of relativity, while the second yields a metric of the exponential form proposed by Yilmaz. Thus, the second predicts that a very massive body does not create the black hole predicted by the first Lagrangian, but rather a "dark red hole" from which radiation can escape red-shifted to longer wavelengths. (2) The source terms for gravitational radiation differ for the two Lagrangians. (3) A cosmology is predicted in which the expanding universe has zero curvature and involves the continuous creation of matter following a big bang.