Mathematical Theory of Black Holes in Higher Dimensions
Nedkova, Petya, Yazadjiev, Stoytcho
- 出版商: Springer
- 出版日期: 2024-08-17
- 售價: $3,500
- 貴賓價: 9.5 折 $3,325
- 語言: 英文
- 頁數: 241
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031614917
- ISBN-13: 9783031614910
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商品描述
This book portraits the mathematical theory which lies behind black hole solutions in spacetimes with an extra dimension. Step by step the authors build a comprehensive picture of the main concepts and tools necessary to understand these geometries. In this way the book addresses questions like: How do we describe black holes in higher dimensions? How can we construct such geometries explicitly as exact solutions to the field equations? How many independent solutions can exist and how are they classified?
The book concentrates on five-dimensional stationary and axisymmetric spacetimes in electro-vacuum and systematically introduces the most important black geometries which can arise in these settings. The authors follow the natural progress of the research area by initially describing the first results that were obtained intuitively and sparkled interest in the community. Then the elaborate mathematical techniques are introduced which allow to systematically construct exact black hole solutions. Topics like the integrability of the theory, the hidden symmetries of the field equations, the available Bäcklund transformations and solution generation techniques based on the inverse scattering method are covered. The last part of the book is devoted to uniqueness theorems showing how to classify the black hole spacetimes and distinguish the non-equivalent ones.
The book is not just a mere collection of facts but a methodological description of the most important mathematical techniques and constructions in an active research area. The discussion is pedagogical and all the methods are demonstrated on a variety of examples. Most of the book is adapted to the level of a graduate student possessing a basic knowledge of general relativity and differential equations, and can serve as a practical guide for quickly acquiring the specific concepts and calculation techniques. Both authors have contributed to the research area by their original results, and share their own experience and perspective.
商品描述(中文翻譯)
本書描繪了存在於額外維度的時空中黑洞解的數學理論。作者逐步建立了理解這些幾何所需的主要概念和工具的全面圖景。這樣，本書探討了以下問題：我們如何在更高維度中描述黑洞？我們如何能夠將這些幾何明確地構造為場方程的精確解？可以存在多少獨立解，並且它們是如何被分類的？
本書集中於五維靜態和軸對稱的電真空時空，並系統性地介紹了在這些環境中可能出現的最重要的黑幾何。作者遵循研究領域的自然進展，最初描述了直觀獲得的第一批結果，並引發了社群的興趣。接著，介紹了精緻的數學技術，這些技術允許系統性地構造精確的黑洞解。書中涵蓋了理論的可積性、場方程的隱藏對稱性、可用的Bäcklund變換以及基於反散射方法的解生成技術等主題。本書的最後一部分專門討論唯一性定理，展示如何對黑洞時空進行分類並區分非等價的時空。
本書不僅僅是事實的簡單集合，而是對一個活躍研究領域中最重要的數學技術和構造的系統性描述。討論具有教學性，所有方法都在各種例子中進行演示。本書的大部分內容適合擁有一般相對論和微分方程基本知識的研究生，並可作為快速掌握特定概念和計算技術的實用指南。兩位作者都以其原創成果對研究領域做出了貢獻，並分享了他們自己的經驗和觀點。
作者簡介
Petya Nedkova is an associate professor at Sofia University, Bulgaria. In 2012 she obtained her PhD in mathematical physics from Sofia University and worked as a postdoctoral researcher at Oldenburg University, Germany, funded by a DAAD research grant. In 2013 she became an assistant professor at Sofia University and was promoted to an associate professor after defending her habilitation. From 2013 to 2020 she worked partially as a guest researcher at Oldenburg University. In higher dimensional gravity she contributed to constructing exact black hole solutions and studying their thermodynamics. Her research interests range from mathematical physics to relativistic astrophysics, including topics on gravitational lensing, black hole imaging, accretion disks and exotic compact objects.
Stoytcho Yazadjiev is a professor in theoretical and mathematical physics at Sofia University, Bulgaria, where he obtained his PhD in 2000. He has specialized at Göttingen University, Germany, and Tübingen University, Germany, as a Humboldt fellow. His research interests are focused on theoretical, mathematical and computational physics and especially on general relativity and modified theories of gravity. Within the framework of higher dimensional gravity, his contributions range from construction of exact solutions to black hole uniqueness theorems.
作者簡介(中文翻譯)
Petya Nedkova 是保加利亞索非亞大學的副教授。她於2012年在索非亞大學獲得數學物理學博士學位，並在德國奧爾登堡大學擔任博士後研究員，該職位由DAAD研究獎學金資助。2013年，她成為索非亞大學的助理教授，並在完成其資格論文後晉升為副教授。從2013年到2020年，她部分時間擔任奧爾登堡大學的客座研究員。在高維重力方面，她對構建精確的黑洞解和研究其熱力學做出了貢獻。她的研究興趣涵蓋數學物理到相對論天體物理學，包括引力透鏡、黑洞成像、吸積盤和奇異緊湊物體等主題。
Stoytcho Yazadjiev 是保加利亞索非亞大學的理論與數學物理學教授，他於2000年獲得博士學位。他曾在德國哥廷根大學和德國圖賓根大學作為洪堡學者進行專業研究。他的研究興趣集中在理論、數學和計算物理，特別是廣義相對論和修正重力理論。在高維重力的框架內，他的貢獻涵蓋從構建精確解到黑洞唯一性定理的研究。
