Oscillating shells and oscillating balls in AdS

Abstract

It has recently been reported that certain thin timelike shells undergo oscillatory motion in AdS. In this paper, we compute two-point function of a probe field in the geodesic approximation in such an oscillating shell background. We confirm that the two-point function exhibits an oscillatory behaviour following the motion of the shell. We show that similar oscillatory dynamics is possible when the perfect fluid on the shell has a polytropic equation of state. Moreover, we show that certain ball like configurations in AdS also exhibit oscillatory motion and comment on how such a solution can be smoothly matched to an appropriate exterior solution. We also demonstrate that the weak energy condition is satisfied for these oscillatory configurations.

Out-of-Time-Order correlators in driven conformal field theories

“…While, generically, a black hole state is expected in the Holographic context, it is less intuitive how one may obtain an oscillatory correlation function. Note that, as far as an oscillatory behaviour is concerned, thin time-like shells can undergo an oscillatory motion in AdS, which yields a corresponding behaviour in real-time for two point functions [70]. It was further noted that such oscillating configurations rely on when the perfect fluid on the shell is described by a polytropic equation of state.…”

Out-of-Time-Order correlators in driven conformal field theories

“…Related to the existence of oscillatory correlation functions (e.g. an oscillating OTOC), note that thin time-like shells can undergo an oscillatory motion in AdS, which yields a corresponding behaviour in real-time for two point functions [96]. It was further noted that such oscillating configurations rely on when the perfect fluid on the shell is described by a polytropic equation of state.…”