New Forms Of Five-dimensional Neutral Rotating Squashed Black Holes And Their Thermodynamic Properties

Black holes are the most fundamental and important objects predicted by Einstein's General Relativity.The construction of exact solutions of black holes and studying their properties can help us deepen our understanding of the nature of gravity and the basic properties of space-times.Due to various kinds of exotic properties of higher dimensional black holes different from their four-dimensional counterparts,they attract a great deal of interest.The five-dimensional squashed black holes have become a hot topic of current researches about gravity in recent ten years.Since Ishihara and Matsuno first used the squashing transformation to obtain the static charged squashed black hole in five dimensions,many squashed black hole solutions have been obtained by this method in various gravity theories.Although it is much simpler to adopt the squashing transformation to obtain a new corresponding solution from the known one,while for the rotating(charged)cases,the metric expressions after making the suitable coordinate transformations become very involved and are not helpful to analyze their thermodynamic properties,and the related expressions for thermodynamical quantities appear to be complicated too.The topics of this thesis are to revisit the five-dimensional uncharged rotating squashed black hole by adopting a new strategy,focusing on two aspects: to construct two simpler forms for the solution and to study its thermodynamic properties.We shall adopt two different metric ansatz and solve directly the vacuum Einstein's field equations to obtain two new and simple forms for the five-dimensional neutral rotating squashed black holes.Then its thermodynamic properties are investigated by means of the counter-term method.Compared with the previous results given by Wang,both our new metric forms and their associated thermodynamic expressions are very concise and elegant.The thesis is composed of five chapters,of which the chapters from the second to the fourth are the most important parts and constitute some innovational researches.In the first chapter,after a brief introduction to black hole thermodynamics,the species of black hole solutions in five dimensions and squashed black holes,we present the background acknowledge underlying this thesis and the significance of the subjects.In the second chapter,under the assumption of the metric of dimensional reduction along the fifth spatial dimension,a new simple form for the five-dimensional neutral rotating squashed black hole solution is obtained and its conserved charges are calculated by using the counter-term method,followed by a thorough analysis of its thermodynamic properties.In the third chapter,we change to use a different metric ansatz of time-like dimensional reduction,and get another new but rather simple form for the rotating uncharged squashed black hole solution.We then find its relation to the solution presented in the last chapter and investigate its thermodynamics in detail.The fourth chapter is devoted to establishing the relation of our two new forms for the neutral rotating squashed black hole solution presented above to the Wang's solution and Dobiasch-Maison's solution.The fifth chapter briefly summarizes the main results obtained in this thesis and outlines our future research plan.