Stability of Higher Dimensional Black Holes

2022 Fiscal Year Final Research Report

• Project/Area Number: 15K05092
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Particle/Nuclear/Cosmic ray/Astro physics
• Research Institution: Kindai University
• Principal Investigator: Ishibashi Akihiro 近畿大学, 理工学部, 教授 (10469877)
• Project Period (FY): 2015-04-01 – 2023-03-31
• Keywords: ブラックホール / 一般相対論 / 重力理論 / 超弦理論 / 宇宙論 / 高次元時空

Outline of Final Research Achievements

I studied the stability of higher dimensional black holes based on the following three viewpoints: I. to establish general criteria for black hole instabililty, II. to derive master equations for massive bosonic perturbations of some classes of higher dimensional black holes, III. to obtain general criteria for black hole stability based on the null energy conditions. For item I, we have successfully established a general criterion for the onset of super-radiant instability of asymptotically AdS, rotating black holes. For item II, by taking the so called "Large D expansion" we studied instability of asymptotically AdS black holes. We have also successfully derived master equations for massive vector and tensor perturbations on a class of static, extremal black holes. As for item III, we have proposed a novel notion of energy conditions, that is called "Conformally Averaged Null Energy Condition" which is expected to apply for stability analyses in the AdS/CFT correspondence.

Free Research Field

一般相対論・重力理論

Academic Significance and Societal Importance of the Research Achievements

高次元ブラックホールの安定性基準を確立したことにより、真空のダイナミカルな選択機構や余剰次元のコンパクト化機構など、超弦理論における動的現象に対する示唆を得ることができた。また、多様な高次元ブラックホール時空を、安定性の観点から系統的に分類することが可能となった。この成果は、ゲージ・重力対応を用いた応用を通して物性論や原子核物理など他の分野にも波及効果がある。また、重力現象の何が4次元に特有なのかを深く理解することが可能となり、宇宙物理学にとっても意義がある成果といえよう。我々の住む宇宙が本質的には高次元時空であると明らかになれば、人々の世界観に大きなインパクトを与え得る。