We derive an analytic expression for the mean magnification due to strong gravitational lensing, using a simple lens model: a singular isothermal sphere embedded in an external shear field. We compute separate expressions for two-image and four-image lensing. For four-image lensing, the mean magnification takes a particularly simple form:, where is the external shear. We compare our analytic results with a numerical evaluation of the full magnification distribution. The results can be used to understand the magnification bias that favors the discovery of four-image systems over two-image systems in fluxlimited lens surveys.

We explore the connections between various coordinate systems associated with observers moving inwardly along radial geodesics in the Schwarzschild geometry. Painlevé-Gullstrand (PG) time is adapted to freely falling observers dropped from rest from infinity; Lake-Martel-Poisson (LMP) time coordinates are adapted to observers who start at infinity with non-zero initial inward velocity; Gautreau-Hoffmann time coordinates are adapted to observers dropped from rest from a finite distance from the black hole horizon. We construct from these an LMP family and a proper-time family of time coordinates, the intersection of which is PG time. We demonstrate that these coordinate families are distinct, but related, one-parameter generalizations of PG time, and show linkage to Lemaître coordinates as well.

The Painlevé-Gullstrand coordinates provide a convenient framework for presenting the Schwarzschild geometry because of their flat constant-time hypersurfaces, and the fact that they are free of coordinate singularities outside r=0. Generalizations ofPainlevé-Gullstrand coordinates suitable for the Kerr geometry have been presented by Doran and Natário. These coordinate systems feature a time coordinate identical to the proper time of zero-angular-momentum observers that are dropped from infinity. Here, the methods of Doran and Natário are extended to the five-dimensional rotating black hole found by Myers and Perry. The result is a new formulation of the Myers-Perry metric. The properties and physical significance of these new coordinates are discussed. † tehani.k.finch (at) nasa.gov

Abstract:The low velocity scattering of a D0-F1 supertube in the background of a BMPV black hole has been considered by Marolf and Virmani. Here we extend the analysis to the case of the D0-D4-F1 supertube of Bena and Kraus. We find that, similarly to the twocharge case, there is a critical value of the supertube circumferential angular momentum; above this value an adiabatic merger with the black hole cannot occur. By reconsidering the calculation of supertube angular momentum in the transverse direction, correspondence between the worldvolume and supergravity descriptions is established. We also examine dynamical mergers and discuss their implications.