We show that vacuum fluctuations of the stress-energy tensor in two-dimensional dilaton gravity lead to a sharp focusing of light cones near the Planck scale, effectively breaking space up into a large number of causally disconnected regions. This phenomenon, called "asymptotic silence" when it occurs in cosmology, might help explain several puzzling features of quantum gravity, including evidence of spontaneous dimensional reduction at short distances. While our analysis focuses on a simplified two-dimensional model, we argue that the qualitative features should still be present in four dimensions.

The spinless Ba\~nados-Teiltelboim-Zanelli (BTZ) spacetime is considered in the quantum theory context. Specially, we study the case of negative mass parameter using quantum test particles obeying the Klein-Gordon and Dirac equations. We study if this classical singular spacetime, with a naked singularity at the origin, remains singular when tested with quantum particles. The need of additional information near the origin is confirmed for massive scalar particles and all the possible boundary conditions necessary to turn the spatial portion of the wave operator self-adjoint are found. When tested by massless scalar particles or fermions, the singularity is ``healed'' and no extra boundary condition are needed. Near infinity, no boundary conditions are necessary.Comment: 6 pages, rvtex, accepted for publication in PR

The behavior of a massive scalar particle on the spacetime surrounding a monopole is studied from a quantum mechanical point of view. All the boundary conditions necessary to turn the spatial portion of the wave operator self-adjoint are found and their importance to the quantum interpretation of singularities is emphasized.

The recently proposed Hořava-Lifshitz (HL) theory of gravity is analyzed from the quantum cosmology point of view. By employing usual quantum cosmology techniques, we study the quantum Friedmann-Lemaître-Robertson-Walker (FLRW) universe filled with radiation in the context of HL gravity. We find that this universe is quantum mechanically nonsingular in two different ways: the expectation value of the scale factor a (t) never vanishes and, if we abandon the detailed balance condition suggested by Hořava, the quantum dynamics of the universe is uniquely determined by the initial wave packet and no boundary condition at a = 0 is indeed necessary.

Initial conditions given on a spacelike, static slice of a non-globally hyperbolic spacetime may not define the fates of classical and quantum fields uniquely. Such lack of global hyperbolicity is a well-known property of the anti-de Sitter solution and led many authors to question how is it possible to develop a quantum field theory on this spacetime. Wald and Ishibashi took a step towards the healing of that causal issue when considering the propagation of scalar fields on AdS. They proposed a systematic procedure to obtain a physically consistent dynamical evolution. Their prescription relies on determining the self-adjoint extensions of the spatial component of the differential wave operator. Such a requirement leads to the imposition of a specific set of boundary conditions at infinity. We employ their scheme in the particular case of the four-dimensional AdS spacetime and compute the expectation values of the field squared and the energy-momentum tensor, which will then bear the effects of those boundary conditions. We are not aware of any laws of nature constraining us to prescribe the same boundary conditions to all modes of the wave equation. Thus, we formulate a physical setup in which one of those modes satisfy a Robin boundary condition, while all others satisfy the Dirichlet condition. Due to our unusual settings, the resulting contributions to the fluctuations of the expectation values will not respect AdS invariance. As a consequence, a back-reaction procedure would yield a nonmaximally symmetric spacetime. Furthermore, we verify the violation of weak energy condition as a direct consequence of our prescription for dynamics.