Abstract
We study aspects of entanglement and extremal surfaces in various families of spacetimes exhibiting cosmological, Big-Crunch, singularities, in particular isotropic AdS Kasner. The classical extremal surface dips into the bulk radial and time directions. Explicitly analysing the extremization equations in the semiclassical region far from the singularity, we find the surface bends in the direction away from the singularity. In the 2-dim cosmologies obtained by dimensional reduction of these and other singularities, we have studied quantum extremal surfaces by extremizing the generalized entropy. The resulting extremization shows the quantum extremal surfaces to always be driven to the semiclassical region far from the singularity. We give some comments and speculations on our analysis.
Highlights
In this paper we investigate aspects of entanglement and quantum extremal surfaces in certain classes of spacetimes exhibiting cosmological singularities studied first in [18]–[20]
In the 2dim cosmologies obtained by dimensional reduction of these and other singularities, we have studied quantum extremal surfaces by extremizing the generalized entropy
First we study aspects of classical extremal RT/HRT surfaces in the higher dimensional backgrounds: due to the time dependence the surfaces dip in the time direction
Summary
We review some aspects of the cosmological spacetimes discussed in [25]. The higher dimensional backgrounds were studied long back as time-dependent deformations of AdS/CF T in [18]–[20] towards gaining insights via gauge/gravity duality into cosmological (Big-Bang or -Crunch) singularities: further investigations on some of these appear in e.g. [26]–[29]: some reviews of cosmological singularities in string theory appear in e.g. [30, 31]. Certain aspects of generic dilaton gravity theories of this kind (and these 2-dim cosmological backgrounds), dimensional reduction and holography are discussed in [32]. Taking the time derivative terms to be dominant (dropping all the other terms) gives the near singularity behaviour described by This appears “universal”: the dilaton potential U governing the asymptotic behaviour of the background has disappeared. Using (2.5), various families of nontrivial 2-dim cosmologies can be found as exact classical solutions: in the vicinity of the singularity they vindicate this universal behaviour but far from this region exhibit various kinds of asymptotic data which is encoded by the dilaton potential U. In the following it will be useful to note the general cosmological solutions in the form (2.5), with the 2-dim fields on the left, and the higher dimensional spacetime on the right
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