Abstract
The universal nature of black hole collapse in asymptotically AdS3 gravitational theories suggests that its holographic dual process, thermalization, should similarly be fixed by the universal features of 2d CFT with large central charge c. It is known that non-equilibrium states with scaling dimensions of order c can be sorted into states that eventually thermalize and those that fail to do so. By proving an equivalence between bounded Virasoro coadjoint orbits and certain (in)stability intervals of Hill’s equation it is shown that semi-classical CFTs possess a phase transition where a state that fails to thermalize can be promoted to a thermalizing state by preparing the system beforehand with an energy greater than an appropriate threshold energy. It is generally a difficult problem to ascertain whether a state will thermalize or not. As partial progress to this problem a set of lower bounds are presented for the threshold energy, which can alternatively be interpreted as criteria for thermalization.
Highlights
The key word in the CFT description of black hole collapse is thermalization, it is typically said that a state thermalizes if at asymptotic late times a certain class of sufficiently ‘simple’ correlators on the state approach the expectation values that would have been obtained if they had been computed on a thermal state instead
The distinguishing function determining whether a state thermalizes or not is the stress tensor expectation value of the state
In this paper it will be demonstrated that given a non-equilibrium state that would keep the system in an integrable phase, there exists a state associated energy scale such that one can trigger thermalization
Summary
One particular feature of asymptotically AdS3 gravity is that its black hole solutions, the BTZ black holes, possess a mass gap. One of the Virasoro descendants of the identity operator is the stress tensor, the AdS/CFT dictionary states that its dual field is the graviton field, the bulk interpretation is that Virasoro identity block resums all graviton exchanges between the probes and the geometry generated by the heavy state It was found through means closely related to the uniformization of punctured Riemann surfaces [3, 23] that the correlator A(z1, z2) could be written in the form. This concludes a condensed version of some of the results in [2]
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