The proposer will continue his investigations in two areas: i) shock-waves in Einstein's Theory of General Relativity with applications to cosmology and ii) the coupling of Einstein's equations for the gravitational field to other (fundamental) force fields; for example to electromagnetism and nuclear forces. In part i) he will investigate his alternative model to the standard "Big-Bang" cosmology. In this theory, the observable universe began with a shock wave explosion into a stationary (time-independent) space. This explosion created the expanding universe that astronomers observe today. The leading edge of this expansion is modeled by an outward propagating shock-wave. Since shock-waves are irreversible solutions of the equations, information about the past is lost as the shock-wave advances. In this model one should therefore not expect a unique time reversal of the solution all the way back to an initial Big-Bang, whereby the entire universe was compressed into a tiny region. In part ii) the proposer will study how solutions of the equations of Quantum Mechanics change when gravity is taken into account. Up to now, gravity has been ignored in elementary particle theory, because gravity is much weaker than nuclear forces and electromagnetism. Preliminary calculations of the proposer show that in spite of the weakness of the gravitational force, the addition of gravity into the equations has a "smoothing"effect on solutions, and greatly modifies some aspects of elementary particle theory.
The proposer will do research in two areas. First, he will investigate an alternative scenario to the standard "Big-Bang" cosmology. In his model the observable universe began with a shock-wave explosion rather than from an incredibly dense small region the size of a grapefruit. Consistent with some recent astronomical observations of huge energy bursts in the very outer regions of the cosmos, this theory implies that there may be other distant universes which also arise from shock-wave explosions. Secondly, the proposer will study the effect that gravity has on other forces (electromagnetism and nuclear forces). Since the gravitational force is extremely weak in comparison to these other forces, physicists have ignored gravity in studying elementary particles. However, the proposer has found that the inclusion of gravity does actually play a role in elementary particle theory. Furthermore, he will investigate the possibility that quantum-theoretic effects play a role in the study of black holes.
