Extremal conditions in early universe cosmology.

Some aspects of Special Relativity have remained largely unresolved and unexplored even after more than a century since its formulation; this is particularly true in the case of relativistic thermodynamics. Attempts to derive a relativistic temperature transformation have met with limited success, particularly when trying to transform a scalar temperature. Much more credible results have emerged when the inverse temperature (a van-Kampen Israel future-directed timelike 4-vector) was invoked. In this dissertation, the first self-consistent formulations of the relativistic Wien’s Displacement Law and the relativistic Stefan-Boltzmann Law are presented. Also examined is the use of occupation number and the inverse temperature 4-vector to justify temperature inflation of the Cosmic Microwave Background for any relativistic observer. The interaction of the Hawking spectrum of a 1 attometer (10-18 m) primordial black hole with an incoming composite particle reveals that when a primordial black hole reaches the Planck scale, its absorptivity and emissivity cause it to effectively become a white hole for the final instant of its existence.