Black hole thermodynamics, spacetime conformal mappings, cosmological perturbations, and modified gravity.

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Nature of the work:***The aim of this program is to achieve a better understanding of gravity, black holes, and the beginning as well as the evolution of the Universe. Black holes are regions of spacetime where matter is so dense that it literally forms holes in spacetime according to Einstein's General Relativity (GR) (the best theory of gravity we have today). I will examine more closely the evolution of black holes using one of theorists' favorite tools, called spacetime conformal mapping, for studying spacetime. This tool consists in changing the lengths and the duration of an event without changing the coordinates of that event. Since the thermodynamics and the mechanics of black holes are deeply intertwined, by studying the latter using this precious theoretical tool I will bring more light to the former.***On the other hand, the increased precision of recent observations of the Cosmic Microwave Background (CMB) (a thermal radiation filling the sky) gives a precious tool to put to test any model of gravity that departs from GR. I will pursue my investigation on my recent model of modified gravity ((varying power)-law model) and confront it with the latest data from the sky. Finally, a very active research in gravitational physics recently is the use of thermodynamics to obtain the dynamics of the Universe. I will extend my previous research on this topic to obtain a link between cosmology and modified gravity theories in view of providing all the possible theoretical constraints on both.******Importance of the research:***This work will contribute to our understanding of black holes, and to our understanding of the Universe and its evolution. ******Expected results:***Spacetime thermodynamics: This work will allow me to extract valuable results concerning the difference between GR and its modifications in such extreme conditions as in the presence of a black hole. It will also shed more light on black hole thermodynamics which is widely believed that it will provide us with an understanding of gravity at the microscopic level.***Evolution of the Universe: I will extract from modified gravity models in general, and from my recent model in particular, the theoretical parameters necessary to be confronted with observations of the sky. This work will tell us more about how to (or not to) modify GR. I will then compare those results with what is found using thermodynamics-based cosmology for a better understanding of the latter.******Main benefits:***By contributing to a better understanding of black holes and the beginning of the Universe, this work will help shed light on the origins of the Universe and its evolution, as well as provide specific signatures about the fundamental physics of black holes that might be observed by the recent Event Horizon Telescope, in which the University of Waterloo and the Perimeter Institute for Theoretical Physics are taking part, scheduled to give its first images of the giant black hole at the center of our galaxy in 2017.