Hot Attractors

Understand

The product of the areas of the event horizon and the Cauchy horizon of a non-extremal black hole equals the square of the area of the horizon of the black hole obtained from taking the smooth extremal limit.

• We establish this result for a large class of black holes using the second order equations of motion, black hole thermodynamics, and the attractor mechanism for extremal black holes.
• This happens even though the area of each horizon generically depends on the moduli, which are asymptotic values of scalar fields.
• The conformal field theory dual to the BTZ black hole facilitates a microscopic interpretation of the result.