Analytical derivation of second-order deflection in the equatorial plane of a radially moving Kerr–Newman black hole

In this work, we base ourselves on the second-order post-Minkowskian equations of motion, and apply an iterative technique to analytically derive the gravitational deflection of the relativistic particles in the equatorial plane of a Kerr–Newman black hole with a radial (or longitudinal) and constant velocity. We find that the kinematically correctional effects on the second-order contributions to the deflection can be expressed in a very compact form, which are valid for both the massive particle and photon. Our result reduces to the previous formulation for the first-order deflection caused by a moving Schwarzschild black hole when the second-order contributions are dropped.

[1]  Wenbin Lin,et al.  Second post-Minkowskian order harmonic metric for a moving Kerr-Newman black hole , 2015 .

[2]  Wenbin Lin,et al.  Exact and unique metric for Kerr-Newman black hole in harmonic coordinates , 2014 .

[3]  Michael Shao,et al.  High precision astrometry mission for the detection and characterization of nearby habitable planetary systems with the Nearby Earth Astrometric Telescope (NEAT) , 2011, 1107.3643.

[4]  M. Shao,et al.  Sub-Microarcsecond Astrometry with SIM-Lite: A Testbed-based Performance Assessment , 2008, 0812.1530.

[5]  Ulrich Bastian,et al.  The Gaia mission: science, organization and present status , 2007, Proceedings of the International Astronomical Union.

[6]  V. Makarov,et al.  Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers , 2006, Proceedings of the International Astronomical Union.

[7]  Robert A. Laskin,et al.  Successful completion of SIM-PlanetQuest technology , 2006, SPIE Astronomical Telescopes + Instrumentation.

[8]  E. Fomalont,et al.  Gravimagnetism, causality, and aberration of gravity in the gravitational light-ray deflection experiments , 2005, gr-qc/0510077.

[9]  M. Sereno.  On gravitational lensing by deflectors in motion , 2005, astro-ph/0501605.

[10]  D. Heyrovský.  Velocity Effects on the Deflection of Light by Gravitational Microlenses , 2004, astro-ph/0410183.

[11]  Hideo Matsuhara,et al.  JASMINE: Japan Astrometry Satellite Mission for INfrared Exploration , 2004, Proceedings of the International Astronomical Union.

[12]  O. Wucknitz,et al.  Deflection of light and particles by moving gravitational lenses , 2004, astro-ph/0401362.

[13]  S. Ragusa,et al.  CORRIGENDUM: Gravitational deflection of massive particles in classical and semiclassical general relativity , 2003 .

[14]  S. Frittelli.  Aberration by gravitational lenses in motion , 2003, astro-ph/0311189.

[15]  S. Frittelli.  On bending angles by gravitational lenses in motion , 2002, astro-ph/0212207.

[16]  Astronomy,et al.  Determining Tangential Peculiar Velocities of Clusters of Galaxies Using Gravitational Lensing , 2002, astro-ph/0211227.

[17]  S. Frittelli,et al.  Fermat potentials for nonperturbative gravitational lensing , 2002, gr-qc/0205014.

[18]  B. Mashhoon,et al.  Gravitomagnetic effects in the propagation of electromagnetic waves in variable gravitational fields of arbitrary-moving and spinning bodies , 2001, gr-qc/0110101.

[19]  M. G. Lattanzi,et al.  GAIA: Composition, formation and evolution of the Galaxy , 2001, astro-ph/0101235.

[20]  S. Kopeikin,et al.  Lorentz covariant theory of light propagation in gravitational fields of arbitrary moving bodies , 1999, gr-qc/9902030.

[21]  M. Birkinshaw,et al.  Null Geodesics in Perturbed Spacetimes , 1993, astro-ph/9303020.

[22]  R. Wagoner,et al.  Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity , 1973 .