Exhaustive Ghost Solutions to Einstein-Weyl Equations for Two Dimensional Spacetimes

摘要

Exhaustive ghost solutions to Einstein-Weyl equations for two dimensionalspacetimes are obtained, where the ghost neutrinos propagate in the backgroundspacetime, but do not influence the background spacetime due to the vanishingstress-energy-momentum tensor for the ghost neutrinos. Especially, thosenon-trivial ghost solutions provide a counterexample to the traditional claimthat the Einstein-Hilbert action has no meaningful two dimensional analogue.