Separability of Rotational Effects on a Gravitational Lens.pdfVIP

Separability of Rotational Effects on a Gravitational Lens Hideki Asada,∗ Masumi Kasai† and Tatsuya Yamamoto Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan (February 2, 2008) 2 We derive the deflection angle up to O(m a) due to a Kerr gravitational lens with mass m and specific angular momentum a. It is known that at 3 the linear order in m and a the Kerr lens is observationally equivalent to the 0 0 Schwarzschild one because of the invariance under the global translation of 2 n the center of the lens mass. We show, however, nonlinear couplings break a J the degeneracy so that the rotational effect becomes in principle separable for 7 1 multiple images of a single source. Furthermore, it is distinguishable also for v 9 each image of an extended source and/or a point source in orbital motion. 9 0 2 −10 1 In practice, the correction at O(m a) becomes O(10 ) for the supermassive 0 3 black hole in our galactic center. Hence, these nonlinear gravitational lensing 0 / h effects are too small to detect by near-future observations. p - o r PACS Number(s); 95.30.Sf, 98.62.Sb, 04.70.Bw t s a : v i I. INTRODUCTION X r a It is of great importance to elucidate the nature of compact objects like black holes and neutron stars. In particular, the general relativity predicts the frame-dragging effect around