1992/10/19 by K. Hamada, Kenji Hamada, Hamada, K.
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Relativity and Gravitational Theory #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9210101
14 pages. phyztex. UT-Komaba 92-9
arxiv created 1992/10/19 · openalex publication_date 1992/10/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the quantum theory of 1+1 dimensional dilaton gravity, which is an interesting toy model of the black hole dynamics. The functional measures of gravity part are explicitly evaluated and derive the Wheeler-DeWitt like equations as physical state conditions. In ADM formalism the measures are very ambiguous, but in our formalism they are explicitly defined. Then the new features which are not seen in ADM formalism come out. A singularity appears at \df2 =κ(>0) , where κ=(N-51/2)/12 and N is the number of matter fields. At the final stage of the black hole evaporation, the Liouville term becomes important, which just comes from the measures of the fields. Behind the singularity the quantum mechanical region κ> \df2 >0 extends, where the sign of the kinetic term in the Wheeler-DeWitt like equation changes. If κ<0 , the singularity disappears. We briefly discuss the possibility of gravitational tunneling and the issue of the information loss. (Talk given at "YITP Workshop on Theories of Quantum Fields -Beyond Perturbation-", Kyoto, Japan, 14-17 July 1992. Some misleading arguments in the preprint UT-Komaba 92-7 entitled "Quamtum Theory of Dilaton Gravity in 1+1 Dimensions" are corrected. The several remarks on the quantization are included. The difference from the other quantum theory is clarified.