866 research outputs found
Global properties of gravitational lens maps in a Lorentzian manifold setting
In a general-relativistic spacetime (Lorentzian manifold), gravitational
lensing can be characterized by a lens map, in analogy to the lens map of the
quasi-Newtonian approximation formalism. The lens map is defined on the
celestial sphere of the observer (or on part of it) and it takes values in a
two-dimensional manifold representing a two-parameter family of worldlines. In
this article we use methods from differential topology to characterize global
properties of the lens map. Among other things, we use the mapping degree (also
known as Brouwer degree) of the lens map as a tool for characterizing the
number of images in gravitational lensing situations. Finally, we illustrate
the general results with gravitational lensing (a) by a static string, (b) by a
spherically symmetric body, (c) in asymptotically simple and empty spacetimes,
and (d) in weakly perturbed Robertson-Walker spacetimes.Comment: 26 page
On the initial-value problem of the Maxwell-Lorentz equations.
We consider the Maxwell-Lorentz equations, i.e., the equation of motion of a charged dust coupled to Maxwell's equations, on an arbitrary general-relativistic spacetime. We decompose this system of equations into evolution equations and constraints, and we demonstrate that the evolution equations are strongly hyperbolic. This result guarantees that the initial-value problem of the Maxwell- Lorentz equations is well-posed. We illustrate this general result with a discussion of spherically symmetric solutions on Minkowski spacetime
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