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Register a new userAnalytical Kerr black hole lensing in the weak deflection limit
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M. Sereno Univ. Zurich
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We present an analytical treatment of gravitational lensing by a Kerr black hole in the weak deflection limit. Lightlike geodesics are expanded as a Taylor series up to and including third-order terms in m/b and a/b, where m is the black hole mass, a the angular momentum and b the impact parameter of the light ray. Positions and magnifications of individual images are computed with a perturbative analysis. At this order, the degeneracy with the translated Schwarzschild lens is broken. The critical curve is still a circle displaced from the black hole position in the equatorial direction and the corresponding caustic is point-like. The degeneracy between the black hole spin and its inclination relative to the observer is broken through the angular coordinates of the perturbed images.
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We present a new upper limit on the energy that may be extracted from a Kerr black hole by means of particle collisions in the ergosphere (i.e., the collisional Penrose process). Earlier work on this subject has focused largely on particles with critical values of angular momentum falling into an extremal Kerr black hole from infinity and colliding just outside the horizon. While these collisions are able to reach arbitrarily high center-of-mass energies, it is very difficult for the reaction products to escape back to infinity, effectively limiting the peak efficiency of such a process to roughly $130%$. When we allow one of the initial particles to have impact parameter $b > 2M$, and thus not get captured by the horizon, it is able to collide along outgoing trajectories, greatly increasing the chance that the products can escape. For equal-mass particles annihilating to photons, we find a greatly increased peak energy of $E_{rm out} approx 6times E_{rm in}$. For Compton scattering, the efficiency can go even higher, with $E_{rm out} approx 14times E_{rm in}$, and for repeated scattering events, photons can both be produced {it and} escape to infinity with Planck-scale energies.
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