Extracting the Maxwell charge from the Wheeler-DeWitt equation
arXiv:0807.0082 · doi:10.1016/j.physletb.2008.06.070
Abstract
We consider the Wheeler-De Witt equation as a device for finding eigenvalues of a Sturm-Liouville problem. In particular, we will focus our attention on the electric (magnetic) Maxwell charge. In this context, we interpret the Maxwell charge as an eigenvalue of the Wheeler-De Witt equation generated by the gravitational field fluctuations. A variational approach with Gaussian trial wave functionals is used as a method to study the existence of such an eigenvalue. We restrict the analysis to the graviton sector of the perturbation. We approximate the equation to one loop in a Schwarzschild background and a zeta function regularization is involved to handle with divergences. The regularization is closely related to the subtraction procedure appearing in the computation of Casimir energy in a curved background. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation.
6 pages. Accepted for publication in Physics Letters B
References in corpus (10)
- New Developments in the Casimir Effect
- Self sustained phantom wormholes in semi-classical gravity
- Spectrum of Charged Black Holes - The Big Fix Mechanism Revisited
- A Quantum Mechanical Model of the Reissner-Nordstrom Black Hole
- Quantum Mechanics of Charged Black Holes
- Gauge Dependence of the Effective Average Action in Einstein Gravity
- Self Sustained Traversable Wormholes?
- The Quantum States and the Statistical Entropy of the Charged Black Hole
- Self sustained traversable wormholes and the equation of state
- Statistical Mechanics of Charged Black Holes in Induced Einstein-Maxwell Gravity
Cited by in corpus (7)
- Cosmological Constant from a Deformation of the Wheeler-DeWitt Equation
- Distorting General Relativity: Gravity's Rainbow and f(R) theories at work
- Naked Singularities are not Singular in Distorted Gravity
- Electric Charges and Magnetic Monopoles in Gravity's Rainbow
- Gravity's Rainbow induces Topology Change
- Topological Defects in a Deformed Gauge Theory
- Wheeler-DeWitt equation and the late gravitational collapse: effects of factor ordering and the tunneling scenario