<p><strong>The future of theoretical physics is unclear. Two large areas that fall under the umbrella of theoretical physics are cosmology and quantum gravity. Modern cosmology is relatively a much younger field than quantum gravity, and both of these fields require further developments of general relativity. In this thesis we do not hope to resolve the problems facing modern cosmology or theories of quantum gravity. Rather, we will conduct original research into aspects of general relativity that may be used in the future to aid the development and testing of theories of cosmology and quantum gravity.</strong></p><p>It is our view that the largest problem facing astrophysics and cosmology stem from the existence of the dark sector of the Universe. The implication here being that more than ninety percent of the energy density of the Universe is “missing in action” and seemingly consists of dark energy and dark matter. Furthermore, it is apparent that there exist conceptual flaws in our understanding of observational concepts such as expansion versus motion and observer biases. To this end, we investigate the standard spacetime metric used in cosmology, the Friedmann–Lemaˆıtre-Roberston–Walker (FLRW) metric in a peculiar coordinate system — the Painlev´e–Gullstrand coordinates. In this coordinate system (slicing), space is no longer expanding, rather, the galaxies are receding from each other. We hope this will aid in the understanding of expansion, motion, curvature, and observer bias with future work. We further investigate the possibility of black holes in cosmology being directly coupled to the accelerated expansion of the Universe — in other words, black holes as a source for dark energy. However, we show that this is highly implausible.</p><p>Relatively recently it has been postulated that the near black hole horizon limit may be a regime where quantum gravity effects become relevant i.e., quantum gravity may not be restricted to near the Planck scale. We investigate a curious model of black and white holes that shows how one may transition into the other over a finite period of time. This is research conducted in the near horizon limit of the Schwarzschild black hole. We introduce a time dependent function into the usual Schwarzschild black hole spacetime (leaving this new spacetime not a simple coordinate transformed version of the original). This function allows the black hole to transition into a white hole. Importantly, the action for this transition can be shown to be zero, meaning it can be added to the Feynman path integral at no cost.</p><p>Finally, we move to investigating the black hole memory effect. During the last decade, there has been an interesting connection made between the Bondi– Metzner–Sachs (BMS) group — an infinite dimensional group of symmetries found at null infinity — and the gravitational memory effect. In particular, it was shown that the passage of a gravitational wave that alters a Schwarzschild black hole is seen as a supertranslation of the spacetime at null infinity. We extend these calculations to the Kerr and Kerr–Newman black holes. Hence, showing that there may be a way to verify the abstract mathematical ideas predicated on the BMS group by detection of the memory effect in future observations.</p><p>It is our hope that when future gravitational wave detectors such as the laser-interferometer-space-antenna (LISA) are launched, research conducted in this thesis may shed light on how the memory may relate to black holes in their asymptotic & near horizon limits to aid our understanding of the nature of quantum gravity.</p>
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