Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1999-10-12
Class.Quant.Grav. 17 (2000) 189-199
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
16 pages LaTex, to appear in Class. Quant. Gravity
Scientific paper
10.1088/0264-9381/17/1/313
Every (1 polarization) cylindrical wave solution of vacuum general relativity is completely determined by a corresponding axisymmetric solution to the free scalar wave equation on an auxilliary 2+1 dimensional flat spacetime. The physical metric at radius R is determined by the energy, $\gamma (R)$, of the scalar field in a box (in the flat spacetime) of radius R. In a recent work, among other important results, Ashtekar and Pierri have introduced a strategy to study the quantum geometry in this system, through a regularized quantum counterpart of $\gamma (R)$. We show that this regularized object is a densely defined symmetric operator, thereby correcting an error in their proof of this result. We argue that it admits a self adjoint extension and show that the operator, unlike its classical counterpart, is not positive.
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