Evaporating firewalls
HJE
Evaporating firewalls
Mark Van Raamsdonk 0 1
0 6224 Agricultural Road, Vancouver , B.C., V6T 1W9 , Canada
1 Department of Physics and Astronomy, University of British Columbia
In this note, we begin by presenting an argument suggesting that large AdS black holes dual to typical high-energy pure states of a single holographic CFT must have some structure at the horizon, i.e. a fuzzball/firewall, unless the procedure to probe physics behind the horizon is state-dependent. By weakly coupling the CFT to an auxiliary system, such a black hole can be made to evaporate. In a case where the auxiliary system is a second identical CFT, it is possible (for specific initial states) that the system evolves to precisely the thermofield double state as the original black hole evaporates. In this case, the dual geometry should include the “late-time” part of the eternal AdS black hole spacetime which includes smooth spacetime behind the horizon of the original black hole. Thus, if a firewall is present initially, it evaporates. This provides a specific realization of the recent ideas of Maldacena and Susskind that the existence of smooth spacetime behind the horizon of an evaporating black hole can be enabled by maximal entanglement with a Hawking radiation system (in our case the second CFT) rather than prevented by it. For initial states which are not finely-tuned to produce the thermofield double state, the question of whether a late-time infalling observer experiences a firewall translates to a question about the gravity dual of a typical high-energy state of a two-CFT system.
Black Holes in String Theory; AdS-CFT Correspondence
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2
3
4
5
1 Introduction
Generic case
Discussion
Fuzzballs/firewalls for black hole microstates in AdS
Evaporating large AdS black holes
3.1
Gravity duals for CFTs with changing Hamiltonians
that an infalling observer will experience a firewall (if the assumptions hold).1
Firewalls were also proposed in a different context in [43], following [
44–53
]. There, in
the nonperturbative setting of AdS/CFT, it was argued that the existence of any spacetime
at all behind a general horizon (including Rindler horizons in pure AdS) requires
entanglement between the degrees of freedom associated with the region outside the horizon and
some other independent degrees of freedom (see figure 1). Based on these observations,
it was proposed in the context of hyperbolic AdS black holes that black hole microstates
(typical pure states of a CFT on Hd) are dual to black holes with no spacetime past the
horizon, i.e. with a lightlike singularity or firewall at the would-be horizon. As we review in
section 2, very similar arguments suggest that large AdS black hole microstates described
by typical high-energy states of a single CFT have firewalls (or fuzzballs). An alternative
argument for this has been given recently in [37]; our argument seems independent of this
1See also the closely related earlier work [
2–5
]. Since [
1
], there have been many arguments for and
against the firewall proposal, including [
6–42
].
– 1 –
ρ
B
W
ρ
A
Entanglement
Ψ
Β
Ψ
Α
and in particular does not make reference to perturbative quantum field theory modes in
the bulk.2
Since these large AdS microstate black holes are not maximally entangled with their
Hawking radiation, they are young black holes in the sense of AMPS. Thus, their firewalls
are not forced upon us by the original AMPS argument. To study “old” black holes in
the context of AdS/CFT, and thus to evaluate the AMPS argument in a non-perturbative
setting, we need to make our large AdS black holes evaporate. To achieve this, we consider
in section 3 a thought experiment in which we weakly couple the CFT to an auxiliary
“radiation” system.3 Specifically, we imagine that the CFT (originally in a high-energy
pure state) is coupled weakly to another identical CFT, for example by placing a wire
between the two spheres on which the CFTs live.
Through this weak interaction, the two-CFT system evolves from a disentangled
product state to a state where the two CFTs are nearly maximally entangled (given the
constraints of energy conservation). In the dual gravity picture, the interaction allows radiation
from the original black hole to leak out at the AdS boundary and enter a second
asymptotically AdS spacetime where it collects and eventually forms a second black hole. For a
specific choice of initial state, it is possible that the entangled state that the CFTs evolve
to is precisely the thermofield double state. In this case, we argue that the gravity dual to
the two-CFT system includes a “late-time” region of the eternal AdS black hole spacetime.
Thus, an observer falling into the original black hole will find smooth spacetime behind
the horizon.
3
A similar construction was considered in [37].
At least for the specific initial states that lead to the thermofield double state, our
conclusions are that the black hole starts with a firewall but ends wi (...truncated)