General structure of the graviton self-energy

The graviton self-energy at finite temperature depends on 14 structure functions. We show that, in the absence of tadpoles, the gauge invariance of the effective action imposes three non-linear relations among these functions. The consequences of such constraints, which must be satisfied by the thermal graviton self-energy to all orders, are explicitly verified in general linear gauges to one loop order. [S0556-2821(99)06112-3].