Discrete spectrum of the quantum Reissner-Nordström geometry

Abstract

We start from a static, spherically symmetric space-time in the presence of an electrostatic field and construct the mini-superspace Lagrangian that reproduces the well known Reissner -Nordström solution. We identify the classical integrals of motion that are to be mapped to quantum observables and which are associated with the mass and charge. Their eigenvalue equations are used as supplementary conditions to the Wheeler-DeWitt equation and a link is provided between the existence of an horizon and to whether the spectrum of the observables is fully discrete or not. For each case we provide an orthonormal basis of states as emerges through the process of canonical quantization. *

Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field

“…from which we observe that Q Cas < 0. This latter condition is not necessarily true for the Reissner -Nordström case in [45] where Q Cas could also assume positive values. The negativity of the Casimir invariant implies that at a quantum level we should also expect ℓ(ℓ + 1) < 0.…”

“…In [45] the case of the Reissner-Nordström geometry has been considered. The classical solution found there is obtained by a Lagrangian strikingly similar to (3.16) with r as the dynamical variable.…”

“…At this point a comment is in order. The quantization of a mini-superspace with a metric similar to (5.2) has been considered in [45]. It is interesting to note, that in general the LRS Bianchi type III possesses a familiar mini-superspace structure to that of a static spherically symmetric line element.…”

Integrability of the mixmaster model

“…The physically relevant constants (or the appropriate combinations of them) would be those that are essential for the space-time geometry and which cannot be absorbed by any diffeomorphisms. A particular example where four constants of integration emerging from conserved mini-superspace charges are reduced to just two that are physically relevant can be seen in the classical part of the analysis performed in [50].…”

Θεωρία Νηματικών Δεσμών Και Η Εφαρμογή Τους Στις Συμμετρίες

“…Οι συμμετρίες, δηλαδή οι μετασχηματισμοί κάτω απο την δράση των οποίων ένας αριθμός διαφορικών εξισώσεων παραμένει αναλλοίωτος, αποτελούν κύρια μεθοδολογία για τον προσδιορισμό των διατηρητικών νόμων και την εύρεση των λύσεων των εξισώσεων. Οι συμμετρίες Lie αποτελούν την πιο συνηθισμένη περίπτωση συμμετριών και έχουν εφαρμοστεί σε πληθώρα προβλημάτων με σκοπό την εύρεση των ακριβών λύσεων τόσο στο κλασικό, όσο και στο κβαντικό επίπεδο [118][119][120][121][122][123][124]. Στη περίπτωση των μοντέλων βαρύτητας, τα οποία περιγράφονται μέσω μια σημειακής Λαγκραντζιανής, υπάρχει ένας ειδικός τύπος συμμετριών Lie, η δράση των οποίων πάνω στο ολοκλήρωμα δράσης, το αφήνουν αναλλοίωτο.…”