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1 26 th July 2016 / 1991(M1)-1995(D3), 2005( )
2 26 th July 2016 /
3
4 . ( )
5 Kerr 1965 BH Penrose 1967 Hawking BH Israel 1971 (Carter)-75(Robinson) BH 1972 BH theorem(,, ) Hawk 1975 Hawking
6 Schoen&Yau, Witten 1983 Hartle & Hawking 1984 & Christodoulou 1986 Ashtekhar 1987 static multi-bhs Bunting & Masood-ul-Alam
7 Choptuik 1995 D-brane Polchinski 1996 Minkowski Christodoulou & Klainerman 1997 ads/cft Maldacena 1998 Large extra dimension Alkani-Hamed et al 1999 Warped extra dimension Randall and Sundrum
8 Black ring Emparan & Reall F. Pretorius, Schwarzchild BH Dafermos, Rodonianski, Holzegel 2006 Ryu & Takayanagi relation 2008 BH formation( ) Christodoulou 2015 Black ring Tunyasuvunakool!! 2016 Braneworld BH Wang & Choptuik
9 2.
10 R gd 4 x
11 Schoen&Yau 1981, Witten 1981 Einstein +dominant energy condition (i) ( ) 0 (ii) ( )=0 iff Minkowski
12
13 Lichinerowicz theorem Lichnerowicz 1955 Strictly stationary and vacuum spacetime is flat. Non-rotating black hole uniqueness Bunting & Masood-ul-Alam 1984 Gibbons, Ida & Shiromizu 2002 Static, asymptotically flat black hole is unique to be Schwarzschild solution in four and higher dimensions. Positive pressure theorem Shiromizu 1994 Black hole no hair theorem in higher dimensions Generalized Lichnerowicz theorem Emparan, Ohashi & Shiromizu 2010 Einstein, electromagnetic field, Shiromizu, Ohashi & Suzuki 2012
14 BH (+ ergoregion) BH ( ) Einstein Kerr-(Newman) No hair theorem
15
16 Gauge/Gravity ( )
17 t Hooft 1993, Susskind 1994 ads/cft Ryu-Takayanagi Entanglement entropy ( )Einstein Maldacena 1997
18 Anti-deSitter 1 R g R = Λg µν µν 2 µν, Λ < 0 ds 2 = dy 2 + e 2 y / η
19 ( ) String
20 ? K 1 2 ab a b σ 2 abσ Rabt t = K 3 1 = K 3 σ ab σ ab 8πG T ab 1 2 g ab T t K: trace of extrinsic curvature ~ a t b 0 / / string theory?(string landscape?)
21 / (?) ~string ~ Anti-deSitter BH
22 3
23 3 1 Braneworld BH
24 Randall-SundrumII Randall & Sundrum 1999 anti-desitter bulk y Minkowski brane ds = dy + e y / ηµν dx µ dx ν
25 BH?
26 BH Emparan, Fabbri & Kaloper 2002, Tanaka 2003 ads/cft 5 BH = 4 BH Hawking
27 Shiromizu, Maeda, Sasaki, 2000 R g R = E µν µν µν 2 1 E µν (5) := C µ aνb n a n b
28 ~ brane ~ Shiromizu & Shibata 2000, Tanahashi & Tanaka 2008 Kudoh,Tanaka & Nakamura,2003, Figueras & Wiseman 2011 Abbolrahimi, Cattoen, Page & Yaghoobpour-Tari 2013 Wang & Choptuik D BH BH ads black string
29
30 ads/cft
31 3 2 BH
32 ( ) BH BH Black string, Black ring, Black Saturn, Less symmetry New strategy Large D
33 Large D Emparan, Suzuki & Tanabe 2013 Newton potential Φ~ r r 0 D 3 Φ r Φ Φʹ r D 3 ~ 0 D r 0 << r D 0 r >> D 3 r0 / D ( r0 / r) 0 flat r r 0 << r 0 / D ( r 0 / r) D 3 ~ 1 : near - horizon
34 Emparan,Shiromizu,Suzuki,Tanabe &Tanaka 2015 Soap bubble equation K : trace of extrinsic curvature, κ :surface gravity g K = κ tt
35 Black droplet Emparan,Shiromizu,Suzuki,Tanabe &Tanaka 2015 ~ BH on brane
36 Fate of uniform black string in large D Emparan,Suzuki & Tanabe 2015
37 Black ring end point Figueras, Kunesch & Tunyasuvunakool thick~thin -thin
38 Large D
39 3 3 dark energy
40 dark energy/modified gravity
41 K-essence Nozawa & Shiromizu 2014 S 4 [ 2 ( φ, ) ] = d x g R + K X + Lmatter X 1 = g 2 µν µ φ ν φ ~ φ 2 Witten dw ( φ) K = X U ( φ) = X φ dφ 2 ( W ( )) 2 Anti-deSitter spinor
42 revisit Shiromizu & Nozawa, in preparation 2016 K = K X X 8( W 1φ K ( φ)) X ( ) 2 2 W ( φ) 12( W ( φ, X )) 1 2 desitter spinor
43 Witten spinor?? Modified gravity? Schoen-Yau
44 4
45
46
47 K.Thorne Black Holes & Time Warps 1994
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