Stationary Black Holes and Light Rings

Area of Science:

• Astrophysics
• General Relativity
• Theoretical Physics

Background:

• Light rings (LRs) are bound null orbits critical to understanding black hole (BH) phenomena like ringdown and shadow.
• The existence of LRs in generic equilibrium black hole spacetimes is a fundamental question in astrophysics.

Purpose of the Study:

• To prove that stationary, axisymmetric, asymptotically flat black holes with a nonextremal, topologically spherical Killing horizon must possess at least one standard light ring outside the horizon for each rotation sense.

Main Methods:

• A topological argument is employed, assuming C^2 smoothness and circularity.
• The proof is independent of the field equations, highlighting a fundamental geometric property.

Main Results:

• A theorem is proven establishing the existence of at least one standard light ring (LR) outside the event horizon for each rotation sense in a stationary, axisymmetric, asymptotically flat black hole spacetime.
• The method also recovers a prior result concerning horizonless ultracompact objects admitting an even number of nondegenerate LRs.

Conclusions:

• The existence of light rings is a general feature of stationary black holes, not exclusive to specific solutions.
• This finding deepens our understanding of black hole structure and dynamics, with implications for gravitational wave astrophysics.