Exact description of black holes on branes

Explicit tests of the proposal include the exact localized AdS4 braneworld black holes discovered by Emparan, Horowitz, and Myers, with their projection onto the brane being reinterpreted as three-dimensional quantum black holes.

“Explicit tests of this proposal include the exact localized AdS 4 braneworld black holes discovered by Emparan, Horowitz, and Myers [23,24], with their projection onto the brane being reinterpreted as three-dimensional quantum black holes.”

From the mass identification (4.27), M takes values in the finite range -1/(8G3) ≤ M ≤ 1/(24G3), where l is held fixed.

“From the mass identification (4.27), M takes values in the finite range [23,24],”

Setting n = q = 0 in the metric functions (D.10) recovers the form of the C-metric used in [23,24].

“Setting n = q = 0 in the metric functions (D.10) recovers the form of the C-metric used in [23,24] (cf.Eq. ( 5.1) of [24]).”

The form function F(M) is purely a function of mass M because it depends on M only through x1 and is otherwise independent of ν = l/l3.

“Lastly, 25 Evidence of the G3 identification in (4.27) is that the relation can be derived exactly by integrating the bulk volume in the action with a bulk IR cutoff as r → ∞ [23].”

For μ ≫ 1 the black hole extends a distance l off of the brane, looking like a 'flattened pancake'.

“Alternatively, for µ ≫ 1 the black hole extends a distance ℓ off of the brane, looking like a 'flattened pancake' [23].”