Bi-metric theory and singularities in relativity

Astronomy and Astrophysics – Astronomy

Scientific paper

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Metric Space, Relativity, Riemann Manifold, Singularity (Mathematics), Space-Time Functions, Astronomical Models, Black Holes (Astronomy), Covariance, Equivalence, Field Theory (Physics), Gravitational Collapse, Gravitational Fields, Stellar Structure, Tensor Analysis

Scientific paper

A bi-metric formulation of the general theory of relativity is presented. In this formulation, a second metric tensor is assigned to each point of space-time (a four-dimensional, Riemannian curved space with its own associated metric tensor) by mapping the Riemannian space on a flat space with which the second tensor is associated. The presence of the flat-space metric tensor is shown to improve the formalism of general relativity. Physically, it enables one to distinguish between the true gravitational field and the inertial field. An attempt is made to set up a bi-metric theory of gravitation which satisfies the covariance and equivalence principles, but is different from general relativity. In particular, the black-hole singularity is eliminated. A comparison is made between models of stellar structure and gravitational collapse obtained using general relativity and the bi-metric gravitation theory.

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