Phases of Phases of Higher-Dimensional Higher-Dimensional Black Holes Black Holes Roberto Emparan Roberto Emparan ICREA & U. ICREA & U. Barcelona Barcelona • Earlier work w/ R.Myers, H.Reall, H.Elvang, P.Figueras • To appear, w/ T.Harmark, N.Obers, V.Niarchos, M.J.Rodríguez Strings 07 Strings 07
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Phases of Higher-Dimensional Black Holes Roberto Emparan ICREA & U. Barcelona Earlier work w/ R.Myers, H.Reall, H.Elvang, P.Figueras To appear, w/ T.Harmark,
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Phases of Phases of Higher-Dimensional Higher-Dimensional
Black HolesBlack Holes
Roberto EmparanRoberto Emparan
ICREA & U. BarcelonaICREA & U. Barcelona
• Earlier work w/ R.Myers, H.Reall, H.Elvang, P.Figueras
• To appear, w/ T.Harmark, N.Obers, V.Niarchos, M.J.Rodríguez
Strings 07Strings 07
Phases of black holes• Find all stationary solutions
– of Einstein's equations R= 0– with specified boundary conditions Asymp Flat– non-singular on and outside event horizons
• What does the phase diagram look like?
• Which solutions maximize the total horizon area (ie entropy)?
• NB: Classical stability? Not today…
• Just the Kerr black hole: Uniqueness thm
No multi-bhs (eg multi-Kerr can't be stationary)
J
(fix scale: M=1)
1
extremal Kerr
Area
Phases of 4D black holes
Myers-Perry black holes in D dimensions
• Spherical topology
• Consider a single spin:
JD = 5
no upper limit on Jfor fixed M
SD ¡ 2
J
D 6
JD 6
J
D = 5
extremal, singular
5D: one-black hole phases
1
thin black ring
q2732
3 different black holes with the same value of M,J