A universal lower bound on the specific temperatures of AdS-Reissner–Nordström black holes with flat event horizons

Abstract

We show that, in a gravitational theory [in any number of dimensions greater than 3] which admits BPS branes and AdS-Reissner-Nordström black holes with flat event horizons, the specific [dimensionless] temperature of such a black hole is bounded below by ≈ 0.156875. This confirms the recent suggestion by Hartnoll and Tavanfar, to the effect that no such black hole can be arbitrarily cold, since from the AdS/CFT dual point of view the low-temperature degrees of freedom should not be concealed by the equivalent of an event horizon.

Stringy stability of charged dilaton black holes with flat event horizon

“…(3.10) the mass of flat uncharged black hole is, with our normalization condition, M = 3π 2 K 3 /2. For consistency check, we note that the flat uncharged black hole has metric [21] Thus with our normalization condition, and L = 1, we get indeed Eq. (5.16).…”

“…Embedding the black hole into string theory however, exposes it to the menace of Seiberg-Witten instability [18,19], which is induced by uncontrolled brane pair production, analogous to the Schwinger mechanism of vacuum polarization [20]. Indeed, it has been shown that Reissner-Nordström black holes do "universally" become unstable in the Seiberg-Witten sense for all spacetime dimensions above 3 [21]. It is therefore interesting to study whether charged dilaton black holes are also vulnerable to Seiberg-Witten instability.…”

Cold black holes in the Harlow–Hayden approach to firewalls

“…Seiberg and Witten stressed that the situation is particularly delicate when the boundary geometry is [scalar-]flat -which is precisely the case here. In [65] [85] it was shown that electrically neutral AdS black holes with flat event horizons are stable in this sense, and in fact this remains true for most values of the electric charge below the extremal value. However, when the electric charge becomes sufficiently large but still sub-extremal, the distortion of the branes does become large enough to trigger the instability.…”

“…It turns out that the addition of small amounts of electric charge to a black hole with a flat event horizon has no ill-effects, that is, the brane action remains positive everywhere. But [for four-dimensional black holes] when the charge reaches about 92% of the extremal charge [85] -that is, when the temperature is low, but not zero -the brane action becomes negative at a certain distance from the black hole, triggering a pair-production instability. In short, we have exactly what we need, supplied by basic objects in string theory.…”

“…16 In the case of an (n + 2)-dimensional black hole, the instability is triggered when the electric charge exceeds n−1 n+1 n n−1 2n n+1 × Q extremal . See [85] for detailed discussions. Since T c is controlled by K, we see that, for lower values of K, the black hole tends to be destroyed by a phase transition into a soliton, instead of by Seiberg-Witten instability: see for example Figure (10), with M (0) = 5.6 × 10 20 cm, Q(0) = 6 × 10 −34 cm.…”