On Gravitational Collapse in the Nonsymmetric Gravitational Theory

The analytical structure of the difference between the static vacuum solution in the nonsymmetric gravitational theory (NGT) and the Schwarzschild solution of Einstein’s gravitational theory (EGT) is studied. It is proved that a smooth matching of the solutions does not exist in the range 0 < r ≤ 2M , for any non-zero values of the parameters M and s of the NGT solution. This means that one cannot consider the difference between the two solutions using perturbation theory in this range of r. Assuming that the exterior solution in gravitational collapse is a small, time dependent perturbation of the static solution for a non-zero, generic NGT source (s 6= 0) and mass density, it is shown that the matching of the interior and exterior solutions will not lead to black hole event horizons. Typeset using REVTEX 1 In Einstein’s gravitational theory (EGT), the collapse of a star leads inevitably to the formation of a black hole event horizon and a singularity at the center of collapse [1]. The event horizon is an infinite red shift surface in any coordinate frame of reference, which separates the spacetime manifold into two causally disconnected pieces. It has been conjectured that in the gravitational collapse of a star in the nonsymmetric gravitational theory (NGT), a black hole event horizon will not form and the appearance of a singularity at the center of collapse is not inevitable [2,3]. A detailed analysis of the gravitational collapse problem has been carried out [4], using a new version of NGT which has a physically consistent linear approximation without ghost poles, tachyons and possesses good asymptotic behavior [6–8]. An analysis of the spherically symmetric NGT system [6,9], showed that a Birkhoff theorem does not exist in NGT, i.e., the spherically symmetric vacuum solution is time dependent. Recently, Burko and Ori [10] have claimed that black holes can be anticipated in gravitational collapse in NGT. They used the linear approximation for g[μν], expanded about the background Schwarzschild solution of EGT. In the following, we shall study the analytic properties of the static NGT solution and consider its consequences for the collapse of a star. This solution holds in the long-range approximation in which μ ≈ 0, where μ = 1/r0 is a “mass” parameter and the longrange approximation holds for large r0. Since we do not have a rigorous dynamical vacuum solution for NGT, we shall make the reasonable physical assumption that a quasi-static solution for the exterior of a star exists such that the limit of this solution to the static solution is smooth, i.e., the time dependent part of the solution is small and the dominant static piece determines the qualitative behavior of the solution [4]. The NGT solution is a two-parameter static spherically symmetric solution, in which the parameter M is the mass and s is a dimensionless real parameter associated with the strength of the coupling of g[μν] to matter. We can model s by the expression [4]: