Quantum field theory and the antipodal identification of black-holes

Abstract

The antipodal points ( U, V, θ, ϕ) and (− U, − V, π − θ, ϕ + π) of the Schwarzchild-Kruskal manifold, usually interpreted as two different events (in two different worlds) are considered here as physically identified (to give one single world). This has fundamental consequences for the QFT formulated on this manifold. The antipodal symmetric fields have (globally) zero norm. The usual particle-antiparticle Fock space definition breaks down. There is no quantum operator (unitary, antiunitary or projection) giving antipodal symmetric states from the usual Kruskal ones. The antipodal symmetric Green functions have the same periodicity β = 8 π M in imaginary (Schwarzschild) time as the usual (non-symmetric) ones. (Identification with “conical singularity” would give a period 1 2 β ). In any case, no usual thermal interpretation is possible for T = β −1 (nor for T 0 = 2 β or any other value) in the theory. In the light of these results we discuss “old” ideas and more recent ones on identification.