Abstract
We continue the programme of exploring the means of holographically decoding
the geometry of spacetime inside a black hole using the gauge/gravity
correspondence. To this end, we study the behaviour of certain extremal
surfaces (focusing on those relevant for equal-time correlators and
entanglement entropy in the dual CFT) in a dynamically evolving asymptotically
AdS spacetime, specifically examining how deep such probes reach. To highlight
the novel effects of putting the system far out of equilibrium and at finite
volume, we consider spherically symmetric Vaidya-AdS, describing black hole
formation by gravitational collapse of a null shell, which provides a
convenient toy model of a quantum quench in the field theory. Extremal surfaces
anchored on the boundary exhibit rather rich behaviour, whose features depend
on dimension of both the spacetime and the surface, as well as on the anchoring
region. The main common feature is that they reach inside the horizon even in
the post-collapse part of the geometry. In 3-dimensional spacetime, we find
that for sub-AdS-sized black holes, the entire spacetime is accessible by the
restricted class of geodesics whereas in larger black holes a small region near
the imploding shell cannot be reached by any boundary-anchored geodesic. In
higher dimensions, the deepest reach is attained by geodesics which (despite
being asymmetric) connect equal time and antipodal boundary points soon after
the collapse; these can attain spacetime regions of arbitrarily high curvature
and simultaneously have smallest length. Higher-dimensional surfaces can
penetrate the horizon while anchored on the boundary at arbitrarily late times,
but are bounded away from the singularity. We also study the details of length
or area growth during thermalization. While the area of extremal surfaces
increases monotonically, geodesic length is neither monotonic nor continuous.
Users
Please
log in to take part in the discussion (add own reviews or comments).