Infinite black hole entropies at infinite distances and tower of states

AdS2 type-IIA solutions and scale separation

“…We will see that scale separation L 2 = L 2 L 6 is possible within the validity regime of the supergravity approximation. We also compare these results with those of [13]. In section 4, we discuss various generalizations of spaces M 6 and show that scale separation works in a different way than before.…”

“…However these modes cannot be given in terms of the internal KK modes of M (6) . This was already seen in [13] from the so-called attractor equations, since, as a function of the electric and magnetic black hole charges, S can be made large, while keeping the internal scale L 6 small. Here we will confirm this result by investigating the supergravity solutions of the corresponding intersecting D-branes, and reading off from the supergravity solutions the corresponding length scales.…”

“…As it was recently discussed in [13], the limit of large entropy, S → ∞, is at infinite distance in the space of 4D black hole metrics. Therefore, similarly to the ADC, a black hole entropy conjecture (BHEC) was put forward in [13], stating that the large entropy limit of black holes is also accompanied by a tower of light modes. However these modes cannot be given in terms of the internal KK modes of M (6) .…”

“…(3.19), corresponds to m KK (S N =2 ) 1/2 of [13], up to a numerical factor of order one. We find agreement with [13], cf. eq.…”

The Black Hole Entropy Distance Conjecture and Black Hole Evaporation

“…This implies that the near‐flat limit of pure AdS is accompanied by an infinite tower of light states. The distance between background metrics was further applied to space‐times with a single horizon in [6]. The analysis shows that the limit of infinite entropy is at infinite distance in field space.…”