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

工作性质： 该计划的目的是更好地理解引力，黑洞，宇宙的起源和演化。根据爱因斯坦的广义相对论（GR）（我们今天拥有的最好的引力理论），黑洞是时空中物质密度如此之大的区域，以至于它在时空中形成了洞。我将更仔细地研究黑洞的演化，使用理论家最喜欢的工具之一，称为时空共形映射，用于研究时空。该工具包括改变事件的长度和持续时间，而不改变该事件的坐标。由于黑洞的热力学和力学是紧密交织在一起的，通过使用这一宝贵的理论工具研究后者，我将为前者带来更多的光明。 另一方面，最近对宇宙微波背景（CMB）（一种充满天空的热辐射）的观测精度的提高，为检验任何偏离GR的引力模型提供了一个宝贵的工具。我将继续研究我最近修改的引力模型（（变幂）定律模型），并将其与来自天空的最新数据进行比较。最后，最近引力物理学中一个非常活跃的研究是利用热力学来获得宇宙的动力学。我将扩展我以前在这个主题上的研究，以获得宇宙学和修正的引力理论之间的联系，以提供所有可能的理论约束。 研究的重要性： 这项工作将有助于我们对黑洞的理解，也有助于我们对宇宙及其演化的理解。 预期成果： 时空热力学：这项工作将使我能够提取有价值的结果之间的差异GR和它的修改在这样的极端条件下，在一个黑洞的存在。它还将揭示更多关于黑洞热力学的信息，人们普遍认为它将为我们提供微观水平上对引力的理解。 宇宙的演化：我将从一般的修正引力模型中，特别是从我最近的模型中，提取出面对天空观测所必需的理论参数。这项工作将告诉我们更多关于如何（或不）修改GR。然后我将比较这些结果与使用基于几何学的宇宙学发现的结果，以便更好地理解后者。 主要优点： 通过有助于更好地理解黑洞和宇宙的起源，这项工作将有助于阐明宇宙的起源及其演变，并提供有关黑洞基本物理学的具体签名，这些黑洞可能被最近的事件视界望远镜观察到，滑铁卢大学和圆周理论物理研究所正在参与，计划于2017年首次拍摄银河系中心巨大黑洞的图像。

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.