# Oscillating Shells and Oscillating Balls in AdS

## TL;DR

This paper investigates oscillatory behaviors of shells and balls in Anti-de Sitter space, analyzing their effects on two-point functions and energy conditions, revealing new dynamical solutions with physical viability.

## Contribution

It introduces new oscillatory solutions for shells and balls in AdS, analyzing their properties and effects on two-point functions, and confirms physical energy conditions are satisfied.

## Key findings

- Two-point functions oscillate following shell motion
- Oscillatory solutions satisfy weak energy condition
- Ball configurations can be smoothly matched externally

## 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.