1,721,069 research outputs found
Extracting the Maxwell charge from the Wheeler-DeWitt equation
No full textWe 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
The Cosmological constant and the Wheeler-DeWitt Equation
Full text linkWe discuss how to extract information about the cosmological constant from theWheeler-DeWitt equation, considered as an eigenvalue of a Sturm-Liouville problem. The equation is approximated to one loop with the help of a variational approach with Gaussian trial wave functionals. A canonical decomposition of modes is used to separate transverse-traceless tensors (graviton) from ghosts and scalar. We show that no ghosts appear in the final evaluation of the cosmological constant. A zeta function regularization is used to handle with divergences. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation. A brief discussion on the extension to a f(R) theory is considered
Naked Singularity in a Modified Gravity Theory
Full text linkThe cosmological constant induced by qantum fluctuation of the graviton on a given background is considered as a tool for building a spectrum of different geometries. In particular, we apply the method to the Schwarzschild background with positive and negative mass parameter. In this way, we put on the same level of comparison the related naked singularity (?M) and the positive mass wormhole. We discuss how to extract information in the context of a f (R) theory. We use the Wheeler-De Witt equation as a basic equation to perform such an analysis regarded as a Sturm-Liouville problem. The application of the same procedure used for the ordinary theory, namely f (R) = R, reveals that to this approximation level, it is not possible to classify the Schwarzschild and its naked partner into a geometry spectrum
Effective action, massive gravitons and the Cosmological Constant
Full text linkThe one loop effective action in a Schwarzschild background is here used to compute the cosmological constant in presence of massive gravitons. It is shown that the expression of the Zero Point Energy (ZPE) is equivalent to the one computed by means of a variational approach. To handle with ZPE divergences, we use the zeta function regularization. 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
Self-sustained traversable wormholes and the equation of state
No full textWe compute the graviton one loop contribution to a classical energy in a traversable wormhole background. The form of the shape function considered is obtained by the equation of state p=ωρ. We investigate the size of the wormhole as a function of the parameter ω. The investigation is evaluated by means of a variational approach with Gaussian trial wave functionals. A zeta function regularization is involved to handle with divergences. A renormalization procedure is introduced and the finite one loop energy is considered as a self-consistent source for the traversable wormhole.The case of the phantom region is briefly discussed
Harnack's inequality on homogeneous spaces
No full textWe consider a homogeneous space X= (X, d, m) of dimension v&\ and a local regular Dirichlet form in L2(X, in). We prove that if a Poincaré inequality holds on every pseudo-ball B(x, R) of X, then an Harnack's inequality can be proved on the same ball with local characteristic constant c0 and c1
Casimir energy and variational methods in AdS spacetime
No full textFollowing the subtraction procedure for manifolds with boundaries, we calculate by variational methods, the Schwarzschild-anti-de Sitter and the anti-de Sitter space energy difference. By computing the one-loop approximation for TT (traceless and transverseless) tensors we discover the existence of an unstable mode at zero temperature, which can be stabilized by the boundary reduction method. Implications for a foam-like space are discussed
Space-time foam, casimir energy and black hole pair creation
No full textWe conjecture that the neutral black hole pair production is related to the vacuum fluctuation of pure gravity via the Casimir-like energy. Implications on the foam-like structure of space-time are discussed
Wormholes and black-hole pair creation
No full textWe analyze the possibility of black holes pair creation induced by three-dimensional wormholes. Although this spacetirne configuration is nowadays hard to suppose, it can be very important in the early universe, when the wormhole space-time foam representation can be meaningful. We compare our approach with the no-boundary prescription of Hartle-Hawking
A spacetime foam approach to the cosmological constant and entropy
Full text linkA simple model of spacetime foam, made by N wormholes in a semiclassical approximation, is taken under examination. The Casimir-like energy of the quantum fluctuation of such a model and its probability of being realized are computed. Implications on the Bekenstein-Hawking entropy and the cosmological constant are considered
- …
