Massless Black Holes & Black Rings as Effective Geometries of the D1-D5 System. September 2005 Masaki Shigemori (Caltech). hep-th/0508110: Vijay Balasubramanian, Per Kraus, M.S. 1. Introduction. AdS/CFT. Can study gravity/string theory in AdS using CFT on boundary. CFT on boundary.
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September 2005Masaki Shigemori (Caltech)
hep-th/0508110: Vijay Balasubramanian, Per Kraus, M.S.
CFT on boundary
string theory in AdS (bulk)
thermal ensemble in CFT
AdS black hole
Thermal ensemble = weighted collection of microstates
Nothing stops one from consideringindividual microstates in CFT
Cf. gas of molecules is well described bythermodynamics, although it’s in pure microstate
1-to-1 correspondence between bulk and CFT microstates
There must be bulk microstategeometries (possibly quantum)
Ensemble in CFT
cf. Mathur’s conjecture
decay at early stage= thermal correlator= particle absorbed in BH
quasi-periodic behavior at late times= particle coming back after exploring inside BH= Hawking radiation
R ground state of D1-D5 sys
BPS state of FP sys
Classical profile of F1
FP sys geometry
is not physical temp
has BE condensed (J>0)
whole J is carried by
* How about bulk side? Why not “coarse-grain” bulk metric?
Probe the bulk geometry corresponding toR ground state
General non-twist bosonic correlator for
For , correlator is indep. of details of microstates:
Correlator for M=0 BTZ black hole
Plug in profile F(v) corresponding to typical distribution
If one assumes that F(v) is randomly fluctuating, for r¿l,
This is M=0 BTZ black hole!
probe particle details of microstates:
“fuzzball”Consistency check:where are we probing?
For bosonic correlator for probe with
Bulk geometry is “weight sum” ofAdS3 and M=0 BTZ black hole??
Profile: (ring) + (fluctuation)
black ring with vanishing horizon
A black hole geometry should be understood as an effective coarse-grained description that accurately describes the results of “typical” measurements, but breaks down in general.