Complete classification of photon escape in the Kerr black hole spacetime

Abstract

We consider necessary and sufficient conditions for photons emitted from an arbitrary spacetime position of the extremal Kerr black hole to escape to infinity. The radial equation of motion determines necessary conditions for photons emitted from r = r * to escape to infinity, and the polar angle equation of motion further restricts the allowed region of photon motion. From these two conditions, we provide a method to visualize a two-dimensional photon impact parameter space that allows photons to escape to infinity, i.e., the escapable region. Finally, we completely identify the escapable region for the extremal Kerr black hole spacetime. This study has generalized our previous result [K. Ogasawara and T. Igata, Phys. Rev. D 103, 044029 (2021)], which focused only on light sources near the horizon, to the classification covering light sources in the entire region.

A generalization of photon sphere based on escape/capture cone

“…Let us review a condition for a null geodesic to reach future null infinity in a static and spherically symmetric spacetime [29][30][31]. Due to these symmetries, the impact parameter b := −k φ /k t is conserved along the geodesic.…”

“…In a Kerr spacetime, each null geodesic possesses the conserved quantities, the energy E, the angular momentum L, and Carter's constant Q [30] (we follow the notation of Ref. [29] for Carter's constant). Their values are determined by the initial condition (i.e., the information at the point p), and for the energy and angular momentum, we have E = −k t | p and L = k φ p , respectively.…”

Nonradial neutrino emission upon black hole formation in core collapse supernovae

“…The escape conditions for the Kerr metric are more complicated than those for the Schwarzschild metric and entail a number of cases which are tabulated in [25] for a full Kerr space and [22] for a disc model.…”

Electromagnetic signatures of strong-field gravity from accreting black holes

“…There have been several arguments in favour of exploring this region in more detail especially if the medium is magnetized (Krolik et al, 2005;Abramowicz et al, 2010;Noble et al, 2011;Zhu et al, 2012). The plunging region is directly adjacent to the event horizon, and so the GR effects on photons originating here should be most prominent, assuming that the signal from that region can be detected and disentangled (Semerák, 1996;Stuchlík et al, 2018;Ogasawara & Igata, 2021). We will show hereafter that polarimetrical effects contain even more specific signatures of strong gravity if they arise in the plunging area (Karas, 2006;Schnittman & Krolik, 2009.…”