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2009

Light's Bending Angle in the Equatorial Plane of a Kerr Black Hole

Iyer, Savitri V., Hansen, Edward C.

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We present here a detailed derivation of an explicit spin-dependent expression for the bending angle of light as it traverses in the equatorial plane of a spinning black hole.

We show that the deflection produced in the presence of the black hole angular momentum explicitly depends on whether the motion of the light ray is in the direction, or opposite to the spin.
Compared to the zero-spin Schwarzschild case, the bending angle is greater for direct orbits, and {\em smaller} for retrograde orbits, confirming our physical intuition about the loss of left-right symmetry from a lensing perspective.
In addition, we show that for higher spins, the effect is more pronounced resulting in tighter winding of direct orbits with respect to the axis of rotation, and a higher degree of unwinding of retro orbits.

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Built on

C. Darwin, Proc. R. Soc. London A249
1958
Earlier work this paper cites.
R. D. Atkinson, Astron. J. 70
1965
Earlier work this paper cites.
R. H. Boyer, R. W. Lindquist, J. Math. Phys, 8
1967
Earlier work this paper cites.

Similar

P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Scientists
1971
Cited alongside, same era.
Misner, C., Thorne, K., & Wheeler, J., Gravitation
1973
Cited alongside, same era.
J.-P. Luminet, Astron. Astrophys. 75
1979
Cited alongside, same era.
S. V. Iyer and E. C. Hansen, “Strong and Weak Deflection of Light in the Equatorial Plane of a Kerr Black Hole,” in preparation
Cited in the paper.

Then

H. Ohanian, Am. J. Physics 55
1987
Later among the works it cites.
S. Chandrasekhar, The Mathematical Theory of Black Holes
1992
Later among the works it cites.
S. V. Iyer and A. O. Petters, General Relativity and Gravitation 39
2007
Later among the works it cites.

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