Observables in quantum field theory on a collapsing black hole background

We study the quantum radiation from a curved background using scalar observables constructed from the (1+1) dimensional renormalized stress-energy tensor (RSET). We compute energy density $\cal U$, flux $\cal F$ and pressure $\cal P$ for an arbitrary collapse scenario and an arbitrary observer. The results show a clear structure: $\cal F - \cal U$ represents the collapse-independent ingoing modes, $\cal F + \cal U$ represents the collapse-dependent outgoing modes and $\cal P - \cal U$ represents the trace anomaly. We also compute the observables constructed from the perception renormalized stress-energy tensor (PeRSET). We find they have the same collapse-dependent contribution comparing to their RSET-related counterparts. For free-falling observers, in particular, the PeRSET-related observables are the same as the corresponding RSET-related ones, except the energy densities differ by the trace anomaly.