Relationship between Hawking Radiation and Gravitational Anomalies

We show that in order to avoid a breakdown of general covariance at the quantum level the total flux in each outgoing partial wave of a quantum field in a black hole background must be equal to that of a $(1+1)$-dimensional blackbody at the Hawking temperature.

Figure 1

Part of the causal diagram of a black hole spacetime, with inset detail of a region near the horizon. Dashed arrows indicate unoccupied modes, while solid arrows indicate occupied modes. The white region is the infinitesimal slab near the horizon where outgoing modes are eliminated.