Quantum gravity in the region very near the horizon of an extreme Kerr black hole ( whose angular momentum and mass are related by J = GM ^ { 2 } ) is considered .
It is shown that consistent boundary conditions exist , for which the asymptotic symmetry generators form one copy of the Virasoro algebra with central charge c _ { L } = { 12 J \over \hbar } .
This implies that the near-horizon quantum states can be identified with those of ( a chiral half of ) a two-dimensional conformal field theory ( CFT ) .
Moreover , in the extreme limit , the Frolov-Thorne vacuum state reduces to a thermal density matrix with dimensionless temperature T _ { L } = { 1 \over 2 \pi } and conjugate energy given by the zero mode generator , L _ { 0 } , of the Virasoro algebra .
Assuming unitarity , the Cardy formula then gives a microscopic entropy S _ { micro } = { 2 \pi J \over \hbar } for the CFT , which reproduces the macroscopic Bekenstein-Hawking entropy S _ { macro } = { { Area } \over 4 \hbar G } .
The results apply to any consistent unitary quantum theory of gravity with a Kerr solution .
We accordingly conjecture that extreme Kerr black holes are holographically dual to a chiral two-dimensional conformal field theory with central charge c _ { L } = { 12 J \over \hbar } , and in particular that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with c _ { L } \sim 2 \times 10 ^ { 79 } .