Geometric Approach to Circular Photon Orbits and Black Hole Shadows

TL;DR

This paper introduces a purely geometric method to calculate circular photon orbits and black hole shadow radii, providing an alternative to the traditional effective potential approach and confirming their equivalence.

Contribution

A novel geometric approach for determining photon orbits and black hole shadows, offering a new perspective and validation against conventional methods.

Findings

Geometric approach is equivalent to effective potential method

Successfully calculates black hole shadow radius

Provides a new framework for analyzing photon orbits

Abstract

Circular photon orbit and black hole shadow are significantly important issues in physics and astronomy, and a number of breakthroughs have been witnessed in recent years. Conventionally, the stable and unstable circular photon orbits are obtained using the effective potential of test particles moving in black hole spacetime. In this work, a pure geometric approach is developed to calculate these circular photon orbits and black hole shadow radius. Furthermore, it can be proved that our geometric approach is completely equivalent to the conventional approach based on effective potentials of test particles.