<p>As already pointed out in <a href="https://physics.stackexchange.com/a/25658/170710">this answer</a>, it is most likely impossible for a Neutron star (NS) to have a Photon sphere (PS), simply because they can probably not become dense enough without collapsing into a black hole. This however can not be said with certainty as we do not know the precise equation of state of NSs. In other words we do not know what radius they take given a certain mass.</p>
<p>Additionally, there is a lower bound for the NS radius set by the condition that the sound speed is limited by the speed of light (causality). See <a href="https://ui.adsabs.harvard.edu/abs/2012ARNPS..62..485L/abstract" rel="nofollow noreferrer">this review</a> for a very detailed overview of the NS equation of state.</p>
<p>This all can be illustrated in a mass-radius diagram (taken from <a href="https://arxiv.org/abs/2007.07725" rel="nofollow noreferrer">here</a>), where I marked in dark-red the radius of the  photon sphere
<span class="math-container">$$ r = 3 GM/c^2.$$</span></p>
<p>So, a NS with a PS would have to be to the upper left of this line, but below the causality limit and on one of the lines denoting a specific equation of state. You see, such an NS would need to be rather heavy but there is not much parameter space left fulfilling all of these criteria. That makes it rather unlikely that such an NS actually exists.</p>
<p><a href="https://i.sstatic.net/i03mp.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/i03mp.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2022-07-14T14:13:48.147Z
2022-07-14T14:13:48.147Z
SpaceCore
<p>Just a simple question.</p>
<p>Has neutron stars photon sphere as black holes?</p>
<p>If the answer is yes, what is the radious and why?</p>

<black-hole><neutron-star>
Photon sphere in neutron stars
Gabriel Palau
# Photon sphere in neutron stars

(Asked by: username_0 on 2022-07-13)

Just a simple question.

Has neutron stars photon sphere as black holes?

If the answer is yes, what is the radious and why?

**Tags:** black-hole, neutron-star

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## 1 answers

### Answer by username_1 on 2022-07-14. Score: 4

As already pointed out in [this answer](https://physics.stackexchange.com/a/25658/170710), it is most likely impossible for a Neutron star (NS) to have a Photon sphere (PS), simply because they can probably not become dense enough without collapsing into a black hole. This however can not be said with certainty as we do not know the precise equation of state of NSs. In other words we do not know what radius they take given a certain mass.

Additionally, there is a lower bound for the NS radius set by the condition that the sound speed is limited by the speed of light (causality). See [this review](https://ui.adsabs.harvard.edu/abs/2012ARNPS..62..485L/abstract) for a very detailed overview of the NS equation of state.

This all can be illustrated in a mass-radius diagram (taken from [here](https://arxiv.org/abs/2007.07725)), where I marked in dark-red the radius of the photon sphere
$$ r = 3 GM/c^2.$$

So, a NS with a PS would have to be to the upper left of this line, but below the causality limit and on one of the lines denoting a specific equation of state. You see, such an NS would need to be rather heavy but there is not much parameter space left fulfilling all of these criteria. That makes it rather unlikely that such an NS actually exists.

[![enter image description here](https://i.sstatic.net/i03mp.png)](https://i.sstatic.net/i03mp.png)


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