Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1997-06-09
Class.Quant.Grav. 15 (1998) 1315-1321
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
8 pages, LaTex. Title altered. One reference added. A few typos esp. eq.(7),(38) corrected. To appear in Class.Q.Grav
Scientific paper
10.1088/0264-9381/15/5/013
We propose a scheme for quantizing a scalar field over the Schwarzschild manifold including the interior of the horizon. On the exterior, the timelike Killing vector and on the horizon the isometry corresponding to restricted Lorentz boosts can be used to enforce the spectral condition. For the interior we appeal to the need for CPT invariance to construct an explicitly positive definite operator which allows identification of positive and negative frequencies. This operator is the translation operator corresponding to the inexorable propagation to smaller radii as expected from the classical metric. We also propose an expression for the propagator in the interior and express it as a mode sum.
Narayan K.
Yajnik Urjit A.
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