field theory (a fact which, incidentally, has already been demonstrated by the Hawking- and Unruh-effects).

Another complication needs to be addressed: Anomalies of the quantized stress energy tensor. It is not only that the value of the (expectation value of) the quantized stress energy tensor isn’t fixed on curved spacetime due to the appearance of metric- or curvature-dependent renormalization ambiguities, but there are also curvature-induced anomalies. Recall that in quantum field theory one generally says that a certain quantity is subject to an anomaly if the quantized/renormalized quantity fails to feature a property — mostly, a symmetry property — which is fulfilled for the counterpart of that quantity in classical field theory. In the case of the stress energy tensor, this is the trace anomaly or conformal anomaly. Suppose that $\phi$ is a $C^\infty$ solution of the conformally coupled, massless linear scalar wave equation, i.e.  $$(\nabla^a \nabla_a + \frac{1}{6} R)\phi = 0$$ on a globally hyperbolic spacetime $\boldsymbol{M}$ with scalar curvature $R$. Then the classical stress energy tensor of $\phi$ has vanishing trace, $T^{a}{}_{a} = 0$. This expresses the conformal invariance of the equation of motion. However, as was shown by Wald [@WaldTrAn], it is not possible to have the 