AdS黑洞的演化與火墻悖論

Abstract

Harlow-Hayden 猜想指出，解讀霍金輻射中隱藏的資訊需要遠比該黑洞壽命更長的時間, 從而解決黑洞的火墻悖論。為了解此猜想，我們研究AdS 時空中的帶電平坦黑洞。在AdS/CFT 對應中，此類黑洞對應與一種類似誇克膠子電漿的場論，對於帶電黑洞來說可謂最為人所理解之量子重力系統。值得強調的是，研究帶電黑洞是黑洞蒸發課題裏不可或缺的一環，畢竟即使原本不帶電的黑洞也必然會在蒸發過程中吸收電荷。我們把Hiscock-Weems 的微分方程模型加以推廣，發現帶電平坦黑洞必然趨向其幾何的極端值，並被Seiberg-Witten 不穩定性所摧毀或相變為某種孤立子。這發現支持Harlow-Hayden 猜想。 另外，廣義相對論裏極度扭曲的時空幾何容許黑洞內部存在無上限的體積，理論上 可以積存掉入黑洞的所有資訊。我們研究具有類似性質，被昵稱為「怪獸」[“monsters”]的非黑洞幾何。假設怪獸存在，那或許它們就會塌縮成內部無上限體積的黑洞。然而，研究結果顯示量子重力極有可能不允許怪獸存在。這間接支持了黑洞內部並不存在無上限體積的看法。

We investigate the Harlow-Hayden conjecture [that it takes a vastly longer time to decode Hawking radiation than the lifetime of a black hole] in the context of charged black holes with flat event horizon in AdS spacetime. This is motivated by the fact that in the application of the anti-de Sitter/conformal field theory [AdS/CFT] correspondence, such black holes are dual to a field theory that behaves very much like a Quark-Gluon Plasma [QGP], and are thus arguably the most well-understood quantum gravity system, especially when charged black holes are concerned. It is essential to study charged black holes because even neutral black holes inevitably pick up electrical charges as they evaporate. By modeling Hawking evaporation using an extension of the Hiscock and Weems analysis, we show that charged flat black holes inevitably evolve towards the extremal limit, and are destroyed either by brane pair production induced by the Seiberg-Witten instability, or by a phase transition into a type of soliton. The lifetime of such black holes is thus cut short as Harlow and Hayden require, in order to evade the firewall argument. In a curved geometry, a small area can bound an arbitrarily large volume, so we also investigate the possibility that black holes can store a huge amount of information behind its horizon. Since black holes are formed from gravitational collapse, it would be interesting to see if non-black hole configurations can behave in such a manner. Such a “monster”, if it exists, could be the stage that leads to a black hole with arbitrarily large interior. Again, by investigating the issue in AdS, we found that monsters most probably don’t exist in quantum gravity. This suggests – although it does not prove – that realistic black holes formed from collapse do not have arbitrarily large interior volume.