neutron stars - Black Hole Photon Sphere

The photon sphere is a spherical region in space where photons are forced to travel in an orbit at $r = \frac{3GM}{c^{2}}$.

1. 
   

   Is it possible to detect these spheres?

   
   
   


2. 
   

   What happens if I fall through it?

   
   


3. 
   

   What happens to a photon that tangentially hits the event horizon, wouldn't this also lead to a photon orbiting the black hole?

   
   


4. 
   

   EDIT Since neutron stars also might have a photon sphere, do we know neutron stars that should have such a sphere?

   
   

Answer

1. 
   

   The photon sphere is of theoretical interest only- the photon orbits are unstable [a boulder at the top of a hill, instead of the bottom of a valley], so in the real world there isn't going to be some huge herd of photons to detect or crash through or anything like that.

   
   


2. 
   

   In the same vein, if you fall through it, you fall through it. Nothing special happens to you. Other than the fact that you are almost certainly going to have a bad experience very soon, if you are not already.

   
   


3. 
   
   

   No. The photon is captured if its impact parameter (that is, the distance "of closest approach" to the black hole) is any less than the radius of the photon sphere. That's the definition of the photon sphere. In other words, any photon that approaches from distant space will be captured if its path goes inside the photon sphere at all. However, a photon emitted on a radial trajectory from an object between the event horizon and the photon sphere can escape. A photon emitted by an object inside the event horizon has nowhere to go but towards the singularity.

   
   


4. 
   

   Neutron stars do not have a photon sphere. The Schwarzschild radius of a neutron star is about 3 km, which means you have to compress it within that size to create a black hole. This means that the photon sphere radius would be about 4.5 km, so to have a photon sphere you would need to cram the neutron star smaller than that. [Warning: Do not try this at home. You will create a supernova, with a black hole remnant.] Neutron stars are actually more like 10-15 km in radius, so they do not have strong enough gravity to do any of that.