ATRONOMY – BLACK HOLE & RELATIVITY (38) CALCULATOR
Photon Sphere Radius
A precise tool.
What is the Photon Sphere Radius & How does it work?
A photon sphere is a spherical region of space where gravity is strong enough that photons can travel in circular orbits. It exists just outside the event horizon of a non‑rotating (Schwarzschild) black hole.
The radius of this sphere depends only on the mass of the black hole. In General Relativity the exact solution gives a radius that is 1.5 times the Schwarzschild radius, or three times the gravitational radius (GM/c²).
Because the photon sphere marks the innermost stable orbit for light, it plays a crucial role in the appearance of black‑hole shadows and in the lensing of background radiation.
r_{ph}=frac{3GM}{c^{2}}
r_{ph} = photon‑sphere radius, G = gravitational constant, M = black‑hole mass, c = speed of light
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Frequently Asked Questions
What is a photon sphere?
A photon sphere is a region in space around a black hole where gravity is strong enough that light can travel in circular orbits.
How do you calculate the photon sphere radius?
The photon sphere radius is 1.5 times the Schwarzschild radius, or three times the gravitational radius (GM/c²), where G is the gravitational constant, M is the mass of the black hole, and c is the speed of light.
Why is the photon sphere significant?
The photon sphere marks the innermost stable orbit for light, making it a critical boundary in understanding black hole physics.
Does the photon sphere exist around all black holes?
Yes, the photon sphere exists around non-rotating (Schwarzschild) black holes. Rotating black holes have different properties.
Can anything escape from a photon sphere?
No, once inside the photon sphere, even light cannot escape due to the extreme gravitational pull of the black hole.
Results are for informational purposes only and do not constitute professional advice.