Math @ Duke

Publications [#243999] of Arlie O. Petters
Papers Published
 Frittelli, S; Petters, AO, Wavefronts, caustic sheets, and caustic surfing in gravitational lensing,
Journal of Mathematical Physics, vol. 43 no. 11
(November, 2002),
pp. 55785611, AIP Publishing, ISSN 00222488 [0208135], [doi]
(last updated on 2019/06/15)
Abstract: Very little attention has been paid to the properties of optical wavefronts and caustic surfaces due to gravitational lensing. Yet the wavefrontbased point of view is natural and provides insights into the nature of the caustic surfaces on a gravitationally lensed lightcone. We derive analytically the basic equations governing the wavefronts, lightcones, caustics on wavefronts, and caustic surfaces on lightcones in the context of weakfield, thinscreen gravitational lensing. These equations are all related to the potential of the lens. In the process, we also show that the standard singleplane gravitational lensing map extends to a new mapping, which we call a wavefront lensing map. Unlike the standard lensing map, the Jacobian matrix of a wavefront lensing map is not symmetric. Our formulas are then applied to caustic "surfing." By surfing a caustic surface, a spaceborne telescope can be fixed on a gravitationally lensed source to obtain an observation of the source at very high magnification over an extended time period, revealing structure about the source that could not otherwise be resolved. Using our analytical expressions for caustic sheets, we present a scheme for surfing a caustic sheet of a lensed source in rectilinear motion. Detailed illustrations are also presented of the possible types of wavefronts and caustic sheets due to nonsingular and singular elliptical potentials, and singular isothermal spheres, including an example of caustic surfing for a singular elliptical potential lens. © 2002 American Institute of Physics.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

