Spacetime stability and construction of model for dark energy/modified gravity

• Project/Area Number: 16K05344
• 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: Nagoya University
• Principal Investigator: Shiromizu Tetsuya 名古屋大学, 多元数理科学研究科, 教授 (10282716)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000); Fiscal Year 2019: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000); Fiscal Year 2018: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000); Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2016: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
• Keywords: 時空の安定性 / 正エネルギー定理 / ブラックホール / 強重力場 / 正質量定理 / ダークエネルギー / 唯一性定理 / 逆曲率流 / 共形スカラー場 / 時空の唯一性 / 正江ネルギー定理 / ペンローズ不等式 / 一般相対性理論 / 修正重力 / 微分幾何学

Outline of Final Research Achievements

In our study, we explored the extension of PET. Since direct attack needs a long time and we knew the relation between the proof of PET and black hole, we decided to investigate the uniqueness theorem for black holes and mathematical structure of strong gravity region.More concretely, we could show that (i)systematic derivation of the key identity appeared in the proof of the black hole uniqueness, (ii)the uniqueness of photon sphere in general relativity with conformal scalar, (iii)formulation and area inequality of strong gravity region, and so on. At the same time, we look at the detail of the proof of PET with an aid of mathematicians. Now we are preparing a paper on PET which is applicable to cosmology.

Academic Significance and Societal Importance of the Research Achievements

正エネルギー定理は時空の安定性を保証するものである。我々の宇宙が突然消えてなくならないのはなぜか。正エネルギー定理が成り立っているからである。ダークエネルギーなどが存在する場合、時空の安定性の保証はない。本来であるならば、まずはこの安定性をクリアした理論のみが考察の対象となるべきである。本研究で得られた成果は、関連するブラックホールに関するものであったが、それを通じて正エネルギー定理の証明の理解が大いに進んだ。その結果、より宇宙論に応用しやすい証明を思いつくに至った。宇宙がなぜ安定なのか、という基本的な人類の問いに答えることが本研究の先に見えてくるだろう。

Research Products

• [Journal Article] Transversely trapping surfaces: Dynamical version (2020)
  • Author(s): Yoshino Hirotaka、Izumi Keisuke、Shiromizu Tetsuya、Tomikawa Yoshimune
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 2020 Issue: 2
  • DOI: 10.1093/ptep/ptz161
  • Peer Reviewed / Open Access
• [Journal Article] Divergence equations and uniqueness theorem of static black holes (2018)
  • Author(s): M. Nozawa, T. Shiromizu, K. Izumi, S. Yamada
  • Journal Title: Class. Quant. Grav. Volume: 35 Issue: 17 Pages: 175009-175009
  • DOI: 10.1088/1361-6382/aad206
  • Peer Reviewed / Open Access
• [Journal Article] On uniqueness of static spacetimes with non-trivial conformal scalar field (2017)
  • Author(s): Y.Tomikawa, T.Shiromizu and K.Izumi
  • Journal Title: Class. Quant.Grav Volume: 34 Issue: 15 Pages: 155004-155004
  • DOI: 10.1088/1361-6382/aa7906
  • Peer Reviewed
• [Journal Article] Extension of photon surfaces and their area: Static and stationary spacetimes (2017)
  • Author(s): H.Yoshino, K.Izumi, T.Shiromizu and Y.Tomikawa
  • Journal Title: PTEP Volume: 2017 Issue: 6
  • DOI: 10.1093/ptep/ptx072
  • Peer Reviewed / Open Access
• [Journal Article] On uniqueness of static black hole with conformal scalar hair (2017)
  • Author(s): Y. Tomikawa, T. Shiromizu, K. Izumi
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 2017 Issue: 3
  • DOI: 10.1093/ptep/ptx033
  • Peer Reviewed
• [Journal Article] Area bound for a surface in a strong gravity region (2017)
  • Author(s): Tetsuya Shiromizu, Yoshimune Tomikawa, Keisuke Izumi, Hirotaka Yoshino
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 2017 Issue: 3
  • DOI: 10.1093/ptep/ptx022
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Violation of cosmic censorship in the gravitational collapse of a dust cloud in five dimensions (2016)
  • Author(s): R. Mizuno, S. Ohashi, T. Shiromizu
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 2016 Issue: 10 Pages: 103E03-103E03
  • DOI: 10.1093/ptep/ptw147
  • NAID: 120006223579
  • Peer Reviewed
• [Presentation] A no-go theorem in strictly stationary spacetime (2019)
  • Author(s): 白水徹也
  • Organizer: Workshop on ``General relativity and partial differential equation"
  • Int'l Joint Research / Invited
• [Presentation] ブラックホール幾何 (2019)
  • Author(s): 白水徹也
  • Organizer: 第66回幾何学シンポジウム
  • Invited
• [Presentation] Can ghost have positive ADM mass? -theory compatible with Schoen-Yau's positive energy theorem- (2019)
  • Author(s): 白水徹也
  • Organizer: 3rd Korea-Japan bilateral workshop on string axion cosmology
  • Int'l Joint Research / Invited
• [Presentation] 時空特異点の数理～因果構造と最長曲線～ (2019)
  • Author(s): 白水徹也
  • Organizer: 日本物理学会
  • Invited
• [Presentation] On uniqueness of static black hole in Einstein-conformal scalar (2018)
  • Author(s): 白水徹也
  • Organizer: Workshop on "Essential next steps for gravity and cosmology"
  • Int'l Joint Research
• [Presentation] How to ``solve" Einstein equation -a review- (2018)
  • Author(s): 白水徹也
  • Organizer: Workshop on ``Partial differential equation and general relativity"
  • Int'l Joint Research / Invited
• [Presentation] Loosely trapped surface (2017)
  • Author(s): 白水徹也
  • Organizer: Gravitational Dynamics and Black Holes
  • Int'l Joint Research
• [Presentation] ブラックホール, 山なし谷なし (2017)
  • Author(s): 白水徹也
  • Organizer: 生物から宇宙までの非平衡現象
• [Presentation] いまさら一般相対論 (2016)
  • Author(s): 白水徹也
  • Organizer: 天文天体物理学夏の学校
  • Place of Presentation: 長野県 ホテル圓山荘
  • Year and Date: 2016-07-26
  • Invited
• [Book] ホーキング、最後に語る:多宇宙をめぐる博士のメッセージ (2018)
  • Author(s): スティーヴン・W・ ホーキング, トマス・ ハートッホ, 佐藤 勝彦, 白水 徹也
  • Total Pages: 96
  • Publisher: 早川書房
  • ISBN: 4152097884