Approximate stress-energy tensor of the massless spin-1/2field in Schwarzschild spacetime

Abstract

The approximate stress-energy tensor of the conformally invariant massless spin-1/2 field in the Hartle-Hawking state in the Schwarzschild spacetime is constructed. It is shown that by solving the conservation equation in conformal space and utilizing the regularity conditions in a physical metric one obtains the stress-energy tensor that is in a good agreement with the numerical calculations.The back reaction of the quantized field upon the spacetime metric is briefly discussed. * Electronic address: matyjase@tytan.umcs.lublin.pl, jurek@kft.umcs.lublin.pl 1

Ingoing Eddington-Finkelstein metric of an evaporating black hole

“…These effects induce a nonzero expectation value for the stress-energy tensor. The renormalized expectation value of the complete quantum stress-energy tensor outside the classical event horizon has been calculated by various authors [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], usually using a framework established by Christensen and Fulling [3]. In this framework, the assumptions are that the stress-energy tensor is time independent, satisfies local stress-energy conservation, and has a trace determined solely by the conformal anomaly, both for the fields that are classically conformally invariant (such as a massless scalar field and the electromagnetic field) and for the gravitational field.…”

“…There have been many calculations of the quantum stress-energy tensor in the Unruh state in the Schwarzschild spacetime, both for a massless scalar field and for the electromagnetic field [5-7, 9-13, 15-17]. A method for computing the stress-energy tensor for the quantized massless spin-1/2 field in a general static spherically symmetric spacetime was presented in [18][19][20]. The canonical quantization of the electromagnetic field has also been investigated in the Kerr metric [21].One of the important questions that one wants to answer concerns the effect of quantized matter on the geometry of black holes.…”