Topics in Spherically Symmetric Spacetimes

Throughout this thesis, we explore mathematical and physical ideas pertaining to much wider theoretical understandings through the context of convenient stellar models described by spherically symmetric perfect fluid stars. These relativistic models allow for an ease of computation and analysis in more physically interesting situations.

Of direct investigation in this thesis is the construction and physical viability of multi-layered stellar models, that is stellar objects with controlled discontinuities in their equation of state. Here, the conditions for junction-free thin-shell intermediary boundary layers are calculated in general through Israel–Lanczos–Sen formalism, then applied to ideal metrics to produce and discuss tractable examples.

Additionally, we investigate and produce counter-examples to modern theories involving maximal quantities, namely maximum power, using intuitive definitions. These analyses include evaluations of physical reasonability, such as through the enforcement of energy conditions across a given spacetime. Here, we aim to voice arguments for definitional caution, regarding the scope of maximal theories. The philosophical nature of such theories remains outside of the scope and consideration of this thesis.

Overall, in this thesis is presented a series of mathematical and physical analyses through the well-understood medium of isotropic perfect fluids, within the framework of general relativity. Our approach is designed to create extension agnostic results, that can be developed and extrapolated to higher complexities as one desires.