Metric nonsymmetric theory of gravitation: the analogue of the theorem of Birkhoff

Abstract

We prove that a spherically symmetric solution of the field equations of the metric nonsymmetric theory of gravitation developed previously is necessarily static.This is the analogue of the well known Birkhoff theorem in general relativity.

Analogue of the theorem of Birkhoff in a metric nonsymmetric theory of the gravitational-electromagnetic field

“…The metric is the same one considered in [1], with the components g 00 , g 11 and g [01] depending on r and t, g 00 = γ(r,t) = e ν(r,t) , g 11 = −α(r,t) = −e µ(r,t) ,…”

“…Recently [1] we have shown that the solution of the field equations of a metric nonsymmetric theory of gravitation [2-I,II] outside a spherically symmetric time-dependent matter distribution is necessarily static. This is the analogue of the theorem of Birkhoff of general relativity (GR).…”

Pulsar binary systems in a nonsymmetric theory of gravitation II. Dipole radiation

“…Next in [3] the conservation laws associated to the theory were studied. In [4] we have proved the analogue of the GR static theorem, that is, that the field outside of a time-dependent spherically symmetric source is necessarily static. More recently [5] a post-Newtonian approximation of the theory was developed with the purpose of application to pulsar binary star systems.…”

Teoría relativista de gravitación para la dinámica Newtoniana modificada

“…A viable explanation for the questions that have been raised about dark matter is to assume that gravity is not well understood. If we adopt the modied Newtonian dynamics (MOND) theory [16], this theory corrects Newton's laws for small accelerations [7] [8].…”