We study the propagation of neutrinos in gravitational fields using wave functions that are exact to first order in the metric deviation. For illustrative purposes, the geometrical background is represented by the Lense-Thirring metric. We derive explicit expressions for neutrino deflection, helicity transitions, flavor oscillations and oscillation Hamiltonian.

Area metric manifolds emerge as effective classical backgrounds in quantum string theory and quantum gauge theory, and present a true generalization of metric geometry. Here, we consider area metric manifolds in their own right, and develop in detail the foundations of area metric differential geometry. Based on the construction of an area metric curvature scalar, which reduces in the metric-induced case to the Ricci scalar, we re-interpret the Einstein-Hilbert action as dynamics for an area metric spacetime. In contrast to modifications of general relativity based on metric geometry, no continuous deformation scale needs to be introduced; the extension to area geometry is purely structural and thus rigid. We present an intriguing prediction of area metric gravity: without dark energy or fine-tuning, the late universe exhibits a small acceleration. INVITATIONA new theoretical concept which, once formulated, naturally emerges in many related contexts, deserves further study. Even more so, if it makes us view well-established theories in a novel way, and meaningfully points beyond standard theory.Area metrics, we argue in this paper, are such an emerging notion in fundamental physics.An area metric may be defined as a fourth rank tensor field which allows to assign a measure to two-dimensional tangent areas, in close analogy to the way a metric assigns a measure to tangent vectors. In more than three dimensions, area metric geometry is a true generalization of metric geometry; although every metric induces an area metric, not every area metric comes from an underlying metric. The mathematical constructions, and physical conclusions, of the present paper are then based on a single principle:Spacetime is an area metric manifold.We will be concerned with justifying this rather bold idea by a detailed construction of the geometry of area metric manifolds, followed by providing an appropriate theory of gravity, which finally culminates in an application of our ideas to cosmology. In the highly symmetric cosmological area metric spacetimes, we can compare our results easily to those of Einstein gravity. We obtain the interesting result that the simplest type of area metric cosmology, namely a universe filled with non-interacting string matter, may be solved exactly and is able to explain the observed [1,2] very small late-time acceleration of our Universe, see the figure on page 40, without introducing any notion of dark energy, nor by invoking fine-tuning arguments.It may come as a surprise, but standard physical theory itself predicts the departure from metric to true area metric manifolds. More precisely, the quantization of classical theories based on metric geometry generates, in a number of interesting cases, area metric geometries: back-reacting photons in quantum electrodynamics effectively propagate in an area metric background [3]; the massless states of quantum string theory give rise to the Neveu-Schwarz two-form potential and dilaton besides the graviton, producing a generalized geometry which may be neatly...

The propagation of light in area metric spacetimes, which naturally emerge as refined backgrounds in quantum electrodynamics and quantum gravity, is studied from first principles. In the geometric-optical limit, light rays are found to follow geodesics in a Finslerian geometry, with the Finsler norm being determined by the area metric tensor. Based on this result, and an understanding of the nonlinear relation between ray vectors and wave covectors in such refined backgrounds, we study light deflection in spherically symmetric situations and obtain experimental bounds on the non-metricity of spacetime in the solar system.

We study the global structure of Lorentzian manifolds with partial sectional curvature bounds. In particular, we prove completeness theorems for homogeneous and isotropic cosmologies as well as static spherically symmetric spacetimes. The latter result is used to rigorously prove the absence of static spherically symmetric black holes in more than three dimensions. The proofs of these new results are preceded by a detailed exposition of the local aspects of sectional curvature bounds for Lorentzian manifolds, which extends and strengthens previous constructions.Comment: 50 pages, 2 figure

The Lorentzian spacetime metric is refined to an area metric which naturally emerges as a generalized geometry in quantum string and gauge theory. Employing the area metric curvature scalar, the EinsteinHilbert gravitational action is reinterpreted as dynamics for an area metric. The area metric cosmology of the radiation-dominated early universe does not depart from general relativity, enabling successful nucleosynthesis. But intriguingly, without the need for dark energy or fine-tuning, area metric cosmology explains the observed small acceleration of the late universe.