Next-to-leading term of the renormalized stress-energy tensor of the quantized massive scalar field in Schwarzschild spacetime. The back reaction

Understand

The next-to-leading term of the renormalized stress-energy tensor of the quantized massive field with an arbitrary curvature coupling in the spacetime of the Schwarzschild black hole is constructed.

• It is achieved by functional differentiation of the DeWitt-Schwinger effective action involving coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficients $a_{3}$ and $a_{4}.$ The back reaction of the quantized field upon the Schwarzschild black hole is briefly discussed.