The spectral function in a strongly coupled, thermalising CFT

In relation to the fluctuation-dissipation theorem, we discuss a time-dependent notion of spectral function and effective temperature. Extending recent results from [1], we work out these quantities in a two-dimensional thermalising CFT dual to AdS3-Vaidya spacetime which interpolates between a black brane geometry at early times and a higher temperature black brane at late times. The computation is carried out in the gravitational holographic dual in the geodesic approximation and using a non-standard analytic continuation.