What is the photon sphere and where is the singularity in a black hole?

[AbsoluteZer0]

Hi,

I somewhat know the basics about black holes. Tell me if I'm wrong.

--A black hole is formed when a supermassive star (one of many theories of the formation of black holes) burns out due to exhausted fusion reactions. It can no longer support its own mass and the core collapses in on itself. The radius of the core must be compressed to a value known as the Schwarzschild Radius before it can become a black hole.--

So far is that correct?
I've heard a bit about the Photon Sphere of the singularity. What is the photon sphere? And is the singularity the center of a black hole?

Thanks,

 

[Nabeshin]

Hi,

I somewhat know the basics about black holes. Tell me if I'm wrong.

--A black hole is formed when a supermassive star (one of many theories of the formation of black holes) burns out due to exhausted fusion reactions. It can no longer support its own mass and the core collapses in on itself. The radius of the core must be compressed to a value known as the Schwarzschild Radius before it can become a black hole.--

So far is that correct?

Essentially, yes.

I've heard a bit about the Photon Sphere of the singularity. What is the photon sphere?

The photon sphere is the radius at which photons can perform circular orbits around the black hole. Note that the Schwarzschild radius occurrs at r=2M, while the photon sphere is at r=3M. Another interesting point you might be curious about is the radius of the innermost circular orbit, which occurs at r=6M. If you imagine you're a ship orbiting a black hole, what this is saying is that in closer than r=6M, you can't orbit in a stable circle (small perturbations will either throw you into the hole or out of the system).

And is the singularity the center of a black hole?

In a rough sense, yes.

 

[Chronos]

The unit conventions used by Nabeshin may be a little confusing. In terms of size, the photon sphere is defined by r = 3R/2, where r = photon sphere radius and R = schwarzschild radius. It cannot be less than this size because the photon would cross the event horizon at aphelion. Note as well this is an unstable orbit and can only be achieved by a massless partice. For anything massive, the possible orbits are more distant, as also noted by Nabeshin. Note also this formula applies only to the simple Schwarzschild [non-rotating] black hole. It gets ugly when a black hole is rotating [e.g., Kerr].