Iosif Bena, Pierre Heidmann, Ruben Monten, Nicholas P. Warner
SciPost Phys. 7, 063 (2019) ·
published 14 November 2019

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We develop a new hybrid WKB technique to compute boundarytoboundary scalar
Green functions in asymptoticallyAdS backgrounds in which the scalar wave
equation is separable and is explicitly solvable in the asymptotic region. We
apply this technique to a family of sixdimensional $\frac{1}{8}$BPS
asymptotically AdS$_3\,\times\,$S$^3$ horizonless geometries that have the same
charges and angular momenta as a D1D5P black hole with a large horizon area.
At large and intermediate distances, these geometries very closely approximate
the extremalBTZ$\,\times\,$S$^3$ geometry of the black hole, but instead of
having an event horizon, these geometries have a smooth highlyredshifted
globalAdS$_3\,\times\,$S$^3$ cap in the IR. We show that the response function
of a scalar probe, in momentum space, is essentially given by the pole
structure of the highlyredshifted globalAdS$_3$ modulated by the BTZ response
function. In position space, this translates into a sharp exponential
blackholelike decay for times shorter than $N_1 N_5$, followed by the
emergence of evenly spaced "echoes from the cap," with period $\sim N_1 N_5$.
Our result shows that horizonless microstate geometries can have the same
thermal decay as black holes without the associated information loss.
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