92,159 research outputs found
On the relation between 2+1 Einstein gravity and Chern Simons theory
A simple example is given to show that the gauge equivalence classes of
physical states in Chern Simons theory are not in one-to-one correspondence
with those of Einstein gravity in three spacetime dimensions. The two theories
are therefore not equivalent. It is shown that including singular metrics into
general relativity has more, and in fact a quite counter-intuitive, impact on
the theory than one naively expects.Comment: 14 pages, LaTeX2e, 3 eps figure
Generalised model-independent characterisation of strong gravitational lenses IV: formalism-intrinsic degeneracies
Based on the standard gravitational lensing formalism with its effective,
projected lensing potential in a given background cosmology, we investigate
under which transformations of the source position and of the deflection angle
the observable properties of the multiple images, i.e. the time delay
differences, the relative image positions, relative shapes, and magnification
ratios, remain invariant. As these observables only constrain local lens
properties, we derive general, local invariance transformations in the areas
covered by the multiple images. We show that the known global invariance
transformations, e.g. the mass sheet transformation or the source position
transformation, are contained in our invariance transformations, when they are
restricted to the areas covered by the multiple images and when
lens-model-based degeneracies are ignored, like the freedom to add or subtract
masses in unconstrained regions without multiple images. Hence, we have
identified the general class of invariance transformations that can occur, in
particular in our model-independent local characterisation of strong
gravitational lenses.Comment: 10 pages, 4 figures, in press in A&A, comments very welcome (update
to accepted and improved version
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