2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35026Exhaustive ghost solutions to Einstein-Weyl equations for two dimensional spacetimes are obtained, where the ghost neutrinos propagate in the background spacetime, but do not influence the background spacetime due to the vanishing stress-energy-momentum tensor for the ghost neutrinos. Especially, those non-trivial ghost solutions provide a counterexample to the traditional claim that the Einstein-Hilbert action has no meaningful two dimensional analogue.10 pages, errors in Section 1 and typos in Appendix correctedGeneral Relativity and Quantum Cosmologytext