Comment on "Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions"

In a recent paper (Phys. Rev. D 94, 125016 (2016)), the authors argued that the singularities of the two-point functions on the Poincar\'e domain of the $n$-dimensional anti-de Sitter spacetime ($\text{PAdS}_n$) have the Hadamard form, regardless of which (Robin) boundary condition is chosen at the conformal boundary. However, the argument used to prove this statement was based on an incorrect expression for the two-point function $G^{+}(x,x')$, which was obtained by demanding $\text{AdS}$ invariance for the vacuum state. In this comment I show that their argument works only for Dirichlet and Neumann boundary conditions and that the full $\text{AdS}$ symmetry cannot be respected by nontrivial Robin conditions (i.e., those which are neither Dirichlet nor Neumann). By studying the conformal scalar field on $\text{PAdS}_2$, I find the correct expression for $G^{+}(x,x')$ and show that, notwithstanding this problem, it still have the Hadamard form.Comment: 3 page

Quantum Singularities in Static Spacetimes

We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets satisfying Klein-Gordon and Dirac equations. We show that in many cases the classical singularities are excluded when tested by quantum particles but unfortunately there are other cases where the singularities remain from the quantum mechanical point of view. When it is possible we also find, for spacetimes where quantum mechanics does not exclude the singularities, the boundary conditions necessary to turn the spatial portion of the wave operator into self-adjoint and emphasize their importance to the interpretation of quantum singularities.Comment: 14 pages, section Quantum Singularities has been improve

Quantum Cosmology In (1+1)-dimensional Hořava-lifshitz Theory Of Gravity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)In a recent paper [Phys. Rev. D 92, 084012 (2015)], the author studied the classical (1+1)-dimensional Friedmann-Robertson-Walker (FRW) universe filled with a perfect fluid in the Hořava-Lifshitz (HL) theory of gravity. This theory is dynamical due to the anisotropic scaling of space and time. It also resembles the Jackiw-Teitelboim model, in which a dilatonic degree of freedom is necessary for dynamics. In this paper, I will take one step further in the understanding of (1+1)-dimensional HL cosmology by means of the quantization of the FRW universe filled with a perfect fluid with the equation of state (EoS) p=wρ. The fluid will be introduced in the model via Schutz formalism and Dirac's algorithm will be used for quantization. It will be shown that the Schrödinger equation for the wave function of the universe has the following properties: for w=1 (radiation fluid), the characteristic potential will be exponential, resembling Liouville quantum mechanics; for w≠1, a characteristic inverse square potential appears in addition to a regular polynomial that depends on the EoS. Explicit solutions for a few cases of interest will be found and the expectation value of the scale factor will be calculated. As in usual quantum cosmology, it will be shown that the quantum theory smooths out the big-bang singularity, but the classical behavior of the universe is recovered in the low-energy limit. © 2016 American Physical Society.93102013/09357-9, FAPESP, São Paulo Research FoundationFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

Vacuum Fluctuations and the Small Scale Structure of Spacetime

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.Comment: 4 pages, revte

Boundary conditions and renormalized stress-energy tensor on a Poincar\'e patch of AdS2\textrm{AdS}_2

Quantum field theory on anti-de Sitter spacetime requires the introduction of boundary conditions at its conformal boundary, due essentially to the absence of global hyperbolicity. Here we calculate the renormalized stress-energy tensor $T_{\mu\nu}$ for a scalar field $\phi$ on the Poincar\'e patch of $\text{AdS}_2$ and study how it depends on those boundary conditions. We show that, except for the Dirichlet and Neumann cases, the boundary conditions break the maximal $\textrm{AdS}$ invariance. As a result, $\langle\phi^2\rangle$ acquires a space dependence and $\langle T_{\mu\nu}\rangle$ is no longer proportional to the metric. When the physical quantities are expanded in a parameter $\beta$ which characterizes the boundary conditions (with $\beta=0$ corresponding to Dirichlet and $\beta=\infty$ corresponding to Neumann), the singularity of the Green's function is entirely subtracted at zeroth order in $\beta$. As a result, the contribution of nontrivial boundary conditions to the stress-energy tensor is free of singular terms.Comment: 7 pages. Minor Correction. Matches published versio