<p>I know that the photon circle or photon sphere is located at around 1.5 times the radius of the Schwarzschild event horizon, but wouldn't it be comparatively further out for smaller black holes?</p>
<p>After all, less massive black holes are actually denser than larger ones, correct?</p>
<p>And the 'worldlines' (spacetime pathways, ds2) around supermassive black holes, just outside of the event horizon, are less curved or bent than around a much smaller black hole?</p>
<p>So, for instance, an ultramassive smbh has a photon sphere just outside of its event horizon?</p>

CC BY-SA 4.0
2023-04-18T21:06:28.190Z
I'm not clear on your question you seem so say "I know the photon sphere is at 3/2 r_s, but I think that's wrong".  Take a look at https://en.wikipedia.org/wiki/Photon_sphere it has a mathematical proof of the 3/2 figure.  So "No, an ultramassive black hole has a photon sphere at 3/2 of its schwatzchild radius" (although actual black holes be rotating so thing are more complicated)  Does the wikipage answer your question completely?
James K
CC BY-SA 4.0
2023-04-19T02:26:56.993Z
What James said. And presumably you know that $r_s=\frac{2GM}{c^2}$, i.e., the Schwarzschild radius is proportional to the mass. FWIW, I have a derivation for the photon sphere radius = $\frac32r_s$ [here](https://physics.stackexchange.com/a/680961/123208), but it does require a little calculus.
PM 2Ring
CC BY-SA 4.0
2023-04-19T07:07:38.737Z
Note that the Schwarzschild $r$ coordinate is defined in terms of the area or circumference of a sphere. See https://physics.stackexchange.com/q/222550/123208
PM 2Ring
CC BY-SA 4.0
2023-04-19T15:43:12.223Z
As you say, it is1.5 times the Schwarzschild radius
ProfRob
<black-hole><general-relativity><space-time><supermassive-black-hole><photons>
Does the (relative) distance of the photon sphere from the center of a black hole vary according its mass?
Kurt Hikes
# Does the (relative) distance of the photon sphere from the center of a black hole vary according its mass?

(Asked by: username_0 on 2023-04-18)

I know that the photon circle or photon sphere is located at around 1.5 times the radius of the Schwarzschild event horizon, but wouldn't it be comparatively further out for smaller black holes?

After all, less massive black holes are actually denser than larger ones, correct?

And the 'worldlines' (spacetime pathways, ds2) around supermassive black holes, just outside of the event horizon, are less curved or bent than around a much smaller black hole?

So, for instance, an ultramassive smbh has a photon sphere just outside of its event horizon?

**Tags:** black-hole, general-relativity, space-time, supermassive-black-hole, photons

> **Comments:**
> **username_1**: I'm not clear on your question you seem so say "I know the photon sphere is at 3/2 r_s, but I think that's wrong".  Take a look at https://en.wikipedia.org/wiki/Photon_sphere it has a mathematical proof of the 3/2 figure.  So "No, an ultramassive black hole has a photon sphere at 3/2 of its schwatzchild radius" (although actual black holes be rotating so thing are more complicated)  Does the wikipage answer your question completely?  
> **username_2**: What username_1 said. And presumably you know that $r_s=\frac{2GM}{c^2}$, i.e., the Schwarzschild radius is proportional to the mass. FWIW, I have a derivation for the photon sphere radius = $\frac32r_s$ [here](https://physics.stackexchange.com/a/680961/123208), but it does require a little calculus.  
> **username_2**: Note that the Schwarzschild $r$ coordinate is defined in terms of the area or circumference of a sphere. See https://physics.stackexchange.com/q/222550/123208  
> **username_3**: As you say, it is1.5 times the Schwarzschild radius  

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## 0 answers

