<p>Adding to @Guillochon's answer, there are even a number of <a href="http://en.wikipedia.org/wiki/Tests_of_general_relativity" rel="nofollow">general relativistic tests</a> in our solar system, the most famous being the <a href="http://en.wikipedia.org/wiki/Tests_of_general_relativity#Perihelion_precession_of_Mercury" rel="nofollow">precession of the perihelion of Mercury</a>. </p>

<p>In short, the location of the point of closest approach to the Sun (perihelion) for the planet Mercury is a changing quantity. Essentially, given one full revolution, it doesn't trace out a closed shape. The distance this point moves per Julian year is <strong>not</strong> well predicted by simply assuming a simple 2-body system evolving under Newtonian mechanics (the Sun and Mercury being these two bodies). Other things which are taken into account are the gravitational influences of other planets (most importantly Jupiter) on this 2-body system, and the fact that the sun is not perfectly spherical in shape (it's an <a href="http://en.wikipedia.org/wiki/Oblate_spheroid" rel="nofollow">Oblate Spheroid</a>).
It turns out that if you include a correction due to GR, its precession can be completely accounted for. </p>

<p>The other notable GR test was the deflection of light from a star by the Sun in a <a href="http://en.wikipedia.org/wiki/Tests_of_general_relativity#Deflection_of_light_by_the_Sun" rel="nofollow">1919 solar eclipse</a>, proving only a few years its formulation that GR was a viable theory.</p>

CC BY-SA 3.0
2013-10-25T18:54:50.953Z
It is definitely true. But I wonder then, in which systems could perihellion precession be dynamically important? In fact, for Mercury the GR part is significantly smaller than other effects, which are causing the precession.
Alexey Bobrick
CC BY-SA 3.0
2013-10-25T19:02:28.750Z
Well, it's an order of magnitude smaller than the gravitational influences of other planets. The point is it's still **required** to correctly predict its motion. The simple answer is systems which are much more massive (i.e. very massive stars or clusters of stars orbiting closely around black holes).
astromax
CC BY-SA 3.0
2013-10-25T19:10:54.667Z
Stars orbiting close to black holes tend to get disrupted. In fact, stellar mass black holes do not really make the effect stronger for stellar companions apart from being more massive than typical stars. The stars cannot come closer to these black holes than they would be able to for a normal companion. For supermassive black holes, though, the effect possibly could be present. However, it would be nice to outline and substantiate the dynamical importance of GR effects in this case.
Alexey Bobrick
CC BY-SA 3.0
2013-10-25T20:18:59.547Z
@AlexeyBobrick The super massive kind is implied in my previous statement. Also, GR becomes incredibly important when super massive black holes orbit around one another.
astromax
CC BY-SA 3.0
2013-10-25T21:57:13.503Z
I guess you mean GW radiation effects on binary evolution of SBHs. GW radiation in general actually could be a good answer, though it is about binaries. Or do you mean something else?
Alexey Bobrick
CC BY-SA 3.0
2013-10-26T12:58:57.403Z
Yea - gravitational waves just sort of fall out of GR by making it linearized. The original question is regarding stellar systems/environments in which relativity becomes important, so binary black hole systems are probably not what he was looking for. Gravitational waves are produced by any massive objects, we just hope to measure them from orbiting black holes because the signal would be the strongest.
astromax
CC BY-SA 3.0
2013-10-26T17:11:29.303Z
Yes and yes. It would be really interesting to know multi-star systems for which GW effects could be as important as they are for binaries. However, one reason why such systems possibly don't exist is because binaries are dynamically stable and bound at small separations, whereas most N-body systems are not.
Alexey Bobrick
CC BY-SA 3.0
2013-10-25T18:22:07.127Z
2013-10-25T18:22:07.127Z
astromax
<p>Stellar clusters around supermassive black holes are systems in which relativity likely plays a role. Currently, only bright stars can be seen in our own galactic center because there is a ton of neutral gas between us and the galactic center that obscures it. As a result, we only have a few "test particles" out of the many stars that actually orbit the black hole at close distances.</p>

<p>Nevertheless, measuring <a href="http://en.wikipedia.org/wiki/Relativistic_Precession">relativistic precession</a> may be possible for a star with one of the closest-known pericenter distances to Sagittarius A* (the central black hole in our galaxy), <a href="http://en.wikipedia.org/wiki/S2_%28star%29">S2</a>, potentially within the next few years once enough data has been collected.</p>

<p>As to how relativistic effects can affect dynamics of the cluster, the precession induced by general relativity can suppress resonant interactions, including three-body resonances such as the <a href="http://en.wikipedia.org/wiki/Kozai_resonance">Kozai</a>. Depending on if these sorts of resonances are important compared to other relaxation processes, the relaxation time can increase significantly, resulting in the cluster evolving more-slowly over time. This can affect things such as the rate of <a href="http://en.wikipedia.org/wiki/Mass_segregation">mass segregation</a>, <a href="http://adsabs.harvard.edu/abs/2009ApJ...697L.149C">tidal disruptions</a>, and production of <a href="http://en.wikipedia.org/wiki/Stellar_kinematics#Hypervelocity_stars">hypervelocity stars</a>/<a href="http://adsabs.harvard.edu/abs/2008ApJ...683L.151L">S-stars</a>.</p>

CC BY-SA 3.0
2013-11-07T21:50:58.390Z
Dear @Guillochon, could you consider extending your already nice answer to a complete form, so that I could accept it and the readers could enjoy its beautiful completeness?
Alexey Bobrick
CC BY-SA 3.0
2013-09-26T22:38:27.053Z
Nice answer, thank you! Could you give a reference or an estimate to a few qualitative statements you make: concerning the presence of many stars closer than 1000 AU for our system, concerning the possibility of measuring precession and the fact, that GR corrections can be relevant to Kozai mechanism. Also, three-body interactions of which kind are mentioned here? Binaries and field stars, binaries and SBH, or SBH+star and field stars?
Alexey Bobrick
CC BY-SA 3.0
2013-09-26T22:50:14.780Z
@AlexeyBobrick I updated my answer only a little to specify that there are other resonant interactions that may be affected, but I'll add some more info later.
Guillochon
CC BY-SA 3.0
2013-09-26T21:44:37.527Z
2013-09-26T22:49:01.260Z
2013-09-26T22:49:01.260Z
Guillochon
<p>I am curious, if anybody knows of any stellar dynamical systems/environments, where relativistic effects could play a dynamical role on the motion of these stellar systems? As a subquestion - are there any known important weak, but cumulatively strong effects?</p>

<p>In other words, when can relativistic effects invalidate the applicability of N-Body/Collisionless Boltzman/Gas/.. models based on newtonian gravity.</p>

<p>From these systems I would like to exclude the simplest well known case of compact binaries.</p>

CC BY-SA 3.0
2013-09-26T21:28:29.787Z
@Guillochon: For our galactic center, the stars approach the supermassive black hole at some 1000AU at best, whereas its gravitational radius is barely 1AU. One definitely doesn't need more than 1-order postnewtonian dynamics for that (if at all). This is a relativistic effect, but the theory is essentially that of a special relativistic tensor field. Though, maybe, indeed for some more massive black holes in other galaxies the effects may be more pronounced.
Alexey Bobrick
CC BY-SA 3.0
2013-09-26T21:29:51.920Z
@Guillochon, nevertheless, thank you for your answer! I would be very much happy to see it a bit more substanciated.
Alexey Bobrick
CC BY-SA 3.0
2013-09-26T21:33:53.360Z
@AlexeyBobrick That is for the *observed* galactic center stars, which are a small fraction of the total. And even among the observed stars, [S2](http://en.wikipedia.org/wiki/S2_(star)) may show some detectable precession (despite being many gravitational radii away).
Guillochon
<general-relativity><stellar-dynamics><newtonian-gravity>
Relativistic effects in stellar dynamical systems
Alexey Bobrick
# Relativistic effects in stellar dynamical systems

(Asked by: username_0 on 2013-09-26)

I am curious, if anybody knows of any stellar dynamical systems/environments, where relativistic effects could play a dynamical role on the motion of these stellar systems? As a subquestion - are there any known important weak, but cumulatively strong effects?

In other words, when can relativistic effects invalidate the applicability of N-Body/Collisionless Boltzman/Gas/.. models based on newtonian gravity.

From these systems I would like to exclude the simplest well known case of compact binaries.

**Tags:** general-relativity, stellar-dynamics, newtonian-gravity
> **Comments:**
> **username_0**: @Guillochon: For our galactic center, the stars approach the supermassive black hole at some 1000AU at best, whereas its gravitational radius is barely 1AU. One definitely doesn't need more than 1-order postnewtonian dynamics for that (if at all). This is a relativistic effect, but the theory is essentially that of a special relativistic tensor field. Though, maybe, indeed for some more massive black holes in other galaxies the effects may be more pronounced.  
> **username_0**: @Guillochon, nevertheless, thank you for your answer! I would be very much happy to see it a bit more substanciated.  
> **username_1**: @AlexeyBobrick That is for the *observed* galactic center stars, which are a small fraction of the total. And even among the observed stars, [S2](http://en.wikipedia.org/wiki/S2_(star)) may show some detectable precession (despite being many gravitational radii away).  

---

## 2 answers

### Answer by username_1 on 2013-09-26. Score: 8 | Accepted answer

Stellar clusters around supermassive black holes are systems in which relativity likely plays a role. Currently, only bright stars can be seen in our own galactic center because there is a ton of neutral gas between us and the galactic center that obscures it. As a result, we only have a few "test particles" out of the many stars that actually orbit the black hole at close distances.

Nevertheless, measuring [relativistic precession](http://en.wikipedia.org/wiki/Relativistic_Precession) may be possible for a star with one of the closest-known pericenter distances to Sagittarius A\* (the central black hole in our galaxy), [S2](http://en.wikipedia.org/wiki/S2_%28star%29), potentially within the next few years once enough data has been collected.

As to how relativistic effects can affect dynamics of the cluster, the precession induced by general relativity can suppress resonant interactions, including three-body resonances such as the [Kozai](http://en.wikipedia.org/wiki/Kozai_resonance). Depending on if these sorts of resonances are important compared to other relaxation processes, the relaxation time can increase significantly, resulting in the cluster evolving more-slowly over time. This can affect things such as the rate of [mass segregation](http://en.wikipedia.org/wiki/Mass_segregation), [tidal disruptions](http://adsabs.harvard.edu/abs/2009ApJ...697L.149C), and production of [hypervelocity stars](http://en.wikipedia.org/wiki/Stellar_kinematics#Hypervelocity_stars)/[S-stars](http://adsabs.harvard.edu/abs/2008ApJ...683L.151L).

> **Comments:**
> **username_0**: Nice answer, thank you! Could you give a reference or an estimate to a few qualitative statements you make: concerning the presence of many stars closer than 1000 AU for our system, concerning the possibility of measuring precession and the fact, that GR corrections can be relevant to Kozai mechanism. Also, three-body interactions of which kind are mentioned here? Binaries and field stars, binaries and SBH, or SBH+star and field stars?  
> **username_1**: @AlexeyBobrick I updated my answer only a little to specify that there are other resonant interactions that may be affected, but I'll add some more info later.  
> **username_0**: Dear @Guillochon, could you consider extending your already nice answer to a complete form, so that I could accept it and the readers could enjoy its beautiful completeness?  

---

### Answer by username_2 on 2013-10-25. Score: 3

Adding to @Guillochon's answer, there are even a number of [general relativistic tests](http://en.wikipedia.org/wiki/Tests_of_general_relativity) in our solar system, the most famous being the [precession of the perihelion of Mercury](http://en.wikipedia.org/wiki/Tests_of_general_relativity#Perihelion_precession_of_Mercury).

In short, the location of the point of closest approach to the Sun (perihelion) for the planet Mercury is a changing quantity. Essentially, given one full revolution, it doesn't trace out a closed shape. The distance this point moves per Julian year is **not** well predicted by simply assuming a simple 2-body system evolving under Newtonian mechanics (the Sun and Mercury being these two bodies). Other things which are taken into account are the gravitational influences of other planets (most importantly Jupiter) on this 2-body system, and the fact that the sun is not perfectly spherical in shape (it's an [Oblate Spheroid](http://en.wikipedia.org/wiki/Oblate_spheroid)).
It turns out that if you include a correction due to GR, its precession can be completely accounted for.

The other notable GR test was the deflection of light from a star by the Sun in a [1919 solar eclipse](http://en.wikipedia.org/wiki/Tests_of_general_relativity#Deflection_of_light_by_the_Sun), proving only a few years its formulation that GR was a viable theory.

> **Comments:**
> **username_0**: It is definitely true. But I wonder then, in which systems could perihellion precession be dynamically important? In fact, for Mercury the GR part is significantly smaller than other effects, which are causing the precession.  
> **username_2**: Well, it's an order of magnitude smaller than the gravitational influences of other planets. The point is it's still **required** to correctly predict its motion. The simple answer is systems which are much more massive (i.e. very massive stars or clusters of stars orbiting closely around black holes).  
> **username_0**: Stars orbiting close to black holes tend to get disrupted. In fact, stellar mass black holes do not really make the effect stronger for stellar companions apart from being more massive than typical stars. The stars cannot come closer to these black holes than they would be able to for a normal companion. For supermassive black holes, though, the effect possibly could be present. However, it would be nice to outline and substantiate the dynamical importance of GR effects in this case.  
> **username_2**: @AlexeyBobrick The super massive kind is implied in my previous statement. Also, GR becomes incredibly important when super massive black holes orbit around one another.  
> **username_0**: I guess you mean GW radiation effects on binary evolution of SBHs. GW radiation in general actually could be a good answer, though it is about binaries. Or do you mean something else?  
> **username_2**: Yea - gravitational waves just sort of fall out of GR by making it linearized. The original question is regarding stellar systems/environments in which relativity becomes important, so binary black hole systems are probably not what he was looking for. Gravitational waves are produced by any massive objects, we just hope to measure them from orbiting black holes because the signal would be the strongest.  
> **username_0**: Yes and yes. It would be really interesting to know multi-star systems for which GW effects could be as important as they are for binaries. However, one reason why such systems possibly don't exist is because binaries are dynamically stable and bound at small separations, whereas most N-body systems are not.  

---

