The cosmological constant as an eigenvalue of the Hamiltonian constraint in Horava-Lifshits theory

In the framework of Horava-Lifshitz theory, we study the eigenvalues associated with the Wheeler-DeWitt equation representing the vacuum expectation values associated with the cosmological constant. The explicit calculation is performed with the help of a variational procedure with trial wave functionals of the Gaussian type. We analyze both the case with the detailed balanced condition and the case without it. In the case without the detailed balance, we find the existence of an eigenvalue depending on the set of coupling constants (g2,g3) and (g4,g5,g6), respectively, and on the physical scale.Comment: RevTeX,11 Pages, Substantial Improvements. References added. To appear in Phys.Rev.

Self sustained traversable wormholes and the equation of state

We compute the graviton one loop contribution to a classical energy in a \textit{traversable} wormhole background. The form of the shape function considered is obtained by the equation of state $p=\omega\rho$. We investigate the size of the wormhole as a function of the parameter $\omega$. 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 \textit{self-consistent} source for the traversable wormhole.The case of the phantom region is briefly discussed.Comment: Uses RevTeX 4. 21 pages. Submitted to Classical and Quantum Gravity. Extended version of the talk given at ERE2006 (Palma de Mallorca, September 4-8, 2006) and of the talk given at MG11-GT5, Berlin, 23-29 July, 200

The Cosmological Constant as an Eigenvalue of a Sturm-Liouville Problem and its Renormalization

We discuss the case of massive gravitons and their relation with the cosmological constant, considered as an eigenvalue of a Sturm-Liouville problem. A variational approach with Gaussian trial wave functionals is used as a method to study such a problem. 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.Comment: 8 pages, Talk given at "QFEXT'05", the 7-th workshop on quantum field theory under the influence of external conditions, Barcelona, Spain, Sept. 5-9, 200

Casimir energy and black hole pair creation in Schwarzschild-de Sitter spacetime

Following the subtraction procedure for manifolds with boundaries, we calculate by variational methods, the Schwarzschild-de Sitter and the de Sitter space energy difference. By computing the one loop approximation for TT tensors we discover the existence of an unstable mode even for the non-degenerate case. This result seems to be in agreement with the sub-maximal black hole pair creation of Bousso-Hawking. The instability can be eliminated by the boundary reduction method. Implications on a foam-like space are discussed.Comment: 19 pages,RevTeX with package epsf and four eps figures. Added other references. Accepted for publication in Classical and Quantum Gravit

Casimir energy and variational methods in AdS spacetime

Following 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 tensors we discover the existence of an unstable mode at zero temperature, which can be stabilized by the boundary reduction method. Implications on a foam-like space are discussed.Comment: Submitted to Classical and Quantum Gravit

Naked Singularity in a Modified Gravity Theory

The cosmological constant induced by quantum 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.Comment: 8 Pages. Contribution given to DICE 2008. To appear in the proceeding

Black hole pair creation and the stability of flat space

We extend the Gross-Perry-Yaffe approach of hot flat space instability to Minkowski space. This is done by a saddle point approximation of the partition function in a Schwarzschild wormhole background which is coincident with an eternal black hole. The appearance of an instability in the whole manifold is here interpreted as a black hole pair creation.Comment: 11 pages,RevTeX4, 2 figures. Accepted for publication in Int. J. Mod. Phys.

Spacetime Foam Model of the Schwarzschild Horizon

We consider a spacetime foam model of the Schwarzschild horizon, where the horizon consists of Planck size black holes. According to our model the entropy of the Schwarzschild black hole is proportional to the area of its event horizon. It is possible to express geometrical arguments to the effect that the constant of proportionality is, in natural units, equal to one quarter.Comment: 16 pages, 2 figures, improved and extended version with some significant changes. Accepted for publication in Phys.Rev.

Extracting the Cosmological Constant from the Wheeler DeWitt Equation in a Modified Gravity Theory

We discuss how to extract information about the cosmological constant from the Wheeler-DeWitt equation, considered as an eigenvalue of a Sturm-Liouville problem. A generalization to a f(R)theory is taken under examination. The equation is approximated to one loop with the help of a variational approach with Gaussian trial wave functionals. We use a zeta function regularization to handle with divergences. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation.Comment: Talk given at QFEXT 07, Workshop on Quantum Field Theory Under the Influence of External Conditions, Leipzig, 17-21 Sep 2007 and talk given at 9th International Conference on Path Integrals - New Trends and Perspectives, Dresden, 23-28 September 2007. 8 pages, accepted for publication in Journal of Physics

Phantom stars and topology change

In this work, we consider time-dependent dark energy star models, with an evolving parameter $\omega$ crossing the phantom divide, $\omega=-1$. Once in the phantom regime, the null energy condition is violated, which physically implies that the negative radial pressure exceeds the energy density. Therefore, an enormous negative pressure in the center may, in principle, imply a topology change, consequently opening up a tunnel and converting the dark energy star into a wormhole. The criteria for this topology change are discussed, in particular, we consider the Morse Index analysis and a Casimir energy approach involving quasi-local energy difference calculations that may reflect or measure the occurrence of a topology change. We denote these exotic geometries consisting of dark energy stars (in the phantom regime) and phantom wormholes as phantom stars. The final product of this topological change, namely, phantom wormholes, have far-reaching physical and cosmological implications, as in addition to being used for interstellar shortcuts, an absurdly advanced civilization may manipulate these geometries to induce closed timelike curves, consequently violating causality.Comment: 19 pages, 13 figures. V2: Extended version of the paper accepted for publication in Physical Review