An alternative well-posedness property and static spacetimes with naked singularities

In the first part of this paper, we show that the Cauchy problem for wave propagation in some static spacetimes presenting a singular time-like boundary is well posed, if we only demand the waves to have finite energy, although no boundary condition is required. This feature does not come from essential self-adjointness, which is false in these cases, but from a different phenomenon that we call the alternative well-posedness property, whose origin is due to the degeneracy of the metric components near the boundary. Beyond these examples, in the second part, we characterize the type of degeneracy which leads to this phenomenon.Comment: 34 pages, 3 figures. Accepted for publication in Class. Quantum Gra

Dynamics in Stationary, Non-Globally Hyperbolic Spacetimes

Classically, the dynamics in a non-globally hyperbolic spacetime is ill posed. Previously, a prescription was given for defining dynamics in static spacetimes in terms of a second order operator acting on a Hilbert space defined on static slices. The present work extends this result by giving a similar prescription for defining dynamics in stationary spacetimes obeying certain mild assumptions. The prescription is defined in terms of a first order operator acting on a different Hilbert space from the one used in the static prescription. It preserves the important properties of the earlier one: the formal solution agrees with the Cauchy evolution within the domain of dependence, and smooth data of compact support always give rise to smooth solutions. In the static case, the first order formalism agrees with second order formalism (using specifically the Friedrichs extension). Applications to field quantization are also discussed.Comment: 18 pages, 1 figure, AMSLaTeX; v2: expanded discussion of field quantization, new Proposition 3.1, revised Theorem 4.2, corrected typos, and updated reference

Critical Role of Macrophages and Their Activation via MyD88-NFκB Signaling in Lung Innate Immunity to Mycoplasma pneumoniae

Mycoplasma pneumoniae (Mp), a common cause of pneumonia, is associated with asthma; however, the mechanisms underlying this association remain unclear. We investigated the cellular immune response to Mp in mice. Intranasal inoculation with Mp elicited infiltration of the lungs with neutrophils, monocytes and macrophages. Systemic depletion of macrophages, but not neutrophils, resulted in impaired clearance of Mp from the lungs. Accumulation and activation of macrophages were decreased in the lungs of MyD88−/− mice and clearance of Mp was impaired, indicating that MyD88 is a key signaling protein in the anti-Mp response. MyD88-dependent signaling was also required for the Mp-induced activation of NFκB, which was essential for macrophages to eliminate the microbe in vitro. Thus, MyD88-NFκB signaling in macrophages is essential for clearance of Mp from the lungs