$〈T_{\nu }^{\mu }{〉}_{\mathrm{ren}}$ of the quantized conformal fields in the Unruh state in Schwarzschild spacetime

The renormalized expectation value of the stress-energy tensor of the conformally invariant massless fields in the Unruh state in Schwarzschild spacetime is constructed. It is achieved through solving the conservation equation in the optical space with a polynomial ansatz, utilizing the regularity conditions and expected asymptotic behavior of the stress-energy tensor in a physical metric, and performing a fit to the results of the numerical calculations. It is shown that the adopted method, which is based on the conformal transformations of the one-loop effective action, is complementary to that of Visser.