Remarks on the thermofield double state in 4D black hole background

Recently, it was shown that there is an anomalous singularity of propagators in spacetimes with horizons for thermal states noncanonical temperatures. In this paper, I extend these observations to the situation when background geometry given by four-dimensional Schwarzschild and Reissner-Nordstr\"om black holes. Namely, demonstrate two-point function free scalar field theory acquires two points are located on horizon. This sense coefficient before divergent term differs from canonical one depends explicitly temperature state. As previously shown, leads explosive behavior regularized stress-energy tensor horizon state does not coincide