2020/02/05 by Daniel Berkowitz, Berkowitz, Daniel
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2002.03800
openalex publication_date 2020/02/05 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
New non trivial solutions to the Lorentzian-signature symmetry reduced Bianchi VIII Wheeler DeWitt equation for Hartle Hawking ordering parameters ± 2√(33) are obtained using an Euclidean-signature semi classical method. Using the aforementioned method we define 'excited' states for the Bianchi VIII wave function and construct leading order 'excited' states which appear to be a hybrid of scattering and bound states. Also six new solutions for the Λ≠ 0 Bianchi VIII Euclidean-signature Hamilton Jacobi equation are presented which can be used to construct semi-classical states corresponding to the Lorentzian signature symmetry reduced Wheeler DeWitt equation. In addition, new solutions to the Euclidean-signature Hamilton Jacobi equation for the Bianchi VIII models are found when Λ≠ 0 and an aligned primordial magnetic field is present. Furthermore, we find eight new complex solutions to the Euclidean-signature Hamilton Jacobi equation for the case when matter is not present, which can be used to construct additional semi-classical states. We also study the leading order wave functions which result from our aforementioned solutions when they are restricted to the β+ axis. Prior to presenting these results we explain the Euclidean-signature semi classical method and discuss how to solve the resultant equations this method generates when it is applied to the Lorentzian-signature symmetry reduced Bianchi VIII Wheeler DeWitt equation. The Euclidean-signature semi-classical method used here is applicable to other field theories as well. The work presented throughout this paper further shows the power Eulclidean-signature semi classical methods possess for solving problems in quantum cosmology and solving Lorentzian signature problems in general.