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2017

Marginally bound (critical) geodesics of rapidly rotating black holes

Hod, Shahar

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One of the most important geodesics in a black-hole spacetime is the marginally bound spherical orbit.

This critical geodesic represents the innermost spherical orbit which is bound to the central black hole.
The radii $r_{\text{mb}}({\bar a})$ of the marginally bound {\it equatorial} circular geodesics of rotating Kerr black holes were found analytically by Bardeen {\it et.
al.} more than four decades ago (here $\bar a\equiv J/M^2$ is the dimensionless angular-momentum of the black hole).

Marginally bound (critical) geodesics of rapidly rotating black holes · Around

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See Fig. 2 of [ 6 ] for the characteristic form of the effective radial potential

Cited in the paper.

In obtaining the solution ( 25

Cited in the paper.

Note that one finds Δ ℓ = M ln ⁡ ( 1 + 2 ) \Delta\ell=M\ln(1+\sqrt{2}) for the prograde equatorial geodesic with cos ⁡ i = 1 \cos i=1 , in accord with the result of [ 2 ]

Cited in the paper.

Note that one finds L / M μ = 2 / cos ⁡ i L/M\mu=2/\cos i for extremal black holes with ϵ ≡ 0 \epsilon\equiv 0 , in accord with the result of [ 7 ]

Cited in the paper.

It is worth emphasizing again that the effective inclination angle i i is a constant

Cited in the paper.

S. Hod, Phys. Rev. D 84

2013

Later among the works it cites.