<p>The paper is Dias et al (2023), Phys. Rev. Lett. 131, 131401 (<a href="https://doi.org/10.1103/PhysRevLett.131.131401" rel="nofollow noreferrer">DOI</a>, <a href="https://arxiv.org/abs/2303.07361" rel="nofollow noreferrer">arXiv</a>). From the abstract:</p>
<blockquote>
<p>We construct the first four-dimensional multiple black hole solution of general relativity with a positive cosmological constant. The solution consists of two static black holes whose gravitational attraction is balanced by the cosmic expansion.</p>
</blockquote>
<p>A positive cosmological constant behaves like a repulsive force that is proportional to distance. If you release two objects at relative rest, they will attract each other gravitationally if close enough, but beyond a certain distance they will fly apart instead. At some intermediate distance there must be an (unstable) equilibrium where they neither gravitate together nor apart. These authors have found an approximate numerical solution of GR describing two black holes at that distance. The holes don't orbit each other, they just &quot;hover&quot;.</p>
<p>This is not related to the Hubble expansion, which doesn't exist in this vacuum solution.</p>
<p>The claim that they are the first to find a <span class="math-container">$Λ&gt;0$</span> multi-black-hole solution seems to be wrong (even if you ignore that it's only approximate). Kastor and Traschen, Phys.Rev. D47 (1993) 5370-5375 (<a href="https://doi.org/10.1103/PhysRevD.47.5370" rel="nofollow noreferrer">DOI</a>, <a href="https://arxiv.org/abs/hep-th/9212035" rel="nofollow noreferrer">arXiv</a>) apparently beat them to it.</p>

CC BY-SA 4.0
2024-08-03T02:30:13.207Z
Is this because the black hole companions are not extensive objects but rather singularities (does this work for point particles)?
civitas
CC BY-SA 4.0
2024-08-03T13:15:13.900Z
But, it is an unstable equilibrium point so quantum fluctuations will disturb both black holes and they would not remain there forever.  Hawking radiation would also disturb it.
eshaya
CC BY-SA 4.0
2024-08-03T16:59:22.307Z
@civitas No, black holes are extensive objects, effectively the size of their event horizons. In principle you could find a numeric solution like this involving ordinary massive objects. There isn't any good treatment of point particles in classical GR.
benrg
CC BY-SA 4.0
2024-08-03T17:00:02.123Z
@DaveTheWave Already as a classical solution, this is unstable to arbitrarily small perturbations, so I'm sure that adding quantum mechanics would only make things worse.
benrg
CC BY-SA 4.0
2024-08-02T00:20:16.933Z
2024-08-03T16:56:48.533Z
2024-08-03T16:56:48.533Z
benrg
<p>I have always read that the accelerated expansion of the universe only affects structures that are not gravitationally bound.</p>
<p>However, there is a recent paper <a href="https://www.sciencedaily.com/releases/2023/10/231019111255.htm" rel="nofollow noreferrer">explained here</a> which says that pairs of black holes orbiting each other could stay like that as long as the universe keeps expanding as if some kind of force going outwards (similar to a centrifugal force) balanced the gravitational force between each other.</p>
<p>So how is this possible? Is it merely a hypothesis or can it occur according to what we know about physics and cosmology?</p>

<black-hole><gravity><cosmology><expansion><dark-energy>
In an expanding universe could black hole pairs keep orbiting each other forever?
vengaq
# In an expanding universe could black hole pairs keep orbiting each other forever?

(Asked by: username_0 on 2024-08-01)

I have always read that the accelerated expansion of the universe only affects structures that are not gravitationally bound.

However, there is a recent paper [explained here](https://www.sciencedaily.com/releases/2023/10/231019111255.htm) which says that pairs of black holes orbiting each other could stay like that as long as the universe keeps expanding as if some kind of force going outwards (similar to a centrifugal force) balanced the gravitational force between each other.

So how is this possible? Is it merely a hypothesis or can it occur according to what we know about physics and cosmology?

**Tags:** black-hole, gravity, cosmology, expansion, dark-energy


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## 1 answers

### Answer by username_1 on 2024-08-02. Score: 13

The paper is Dias et al (2023), Phys. Rev. Lett. 131, 131401 ([DOI](https://doi.org/10.1103/PhysRevLett.131.131401), [arXiv](https://arxiv.org/abs/2303.07361)). From the abstract:

> We construct the first four-dimensional multiple black hole solution of general relativity with a positive cosmological constant. The solution consists of two static black holes whose gravitational attraction is balanced by the cosmic expansion.

A positive cosmological constant behaves like a repulsive force that is proportional to distance. If you release two objects at relative rest, they will attract each other gravitationally if close enough, but beyond a certain distance they will fly apart instead. At some intermediate distance there must be an (unstable) equilibrium where they neither gravitate together nor apart. These authors have found an approximate numerical solution of GR describing two black holes at that distance. The holes don't orbit each other, they just "hover".

This is not related to the Hubble expansion, which doesn't exist in this vacuum solution.

The claim that they are the first to find a $Λ>0$ multi-black-hole solution seems to be wrong (even if you ignore that it's only approximate). Kastor and Traschen, Phys.Rev. D47 (1993) 5370-5375 ([DOI](https://doi.org/10.1103/PhysRevD.47.5370), [arXiv](https://arxiv.org/abs/hep-th/9212035)) apparently beat them to it.

> **Comments:**
> **username_2**: Is this because the black hole companions are not extensive objects but rather singularities (does this work for point particles)?  
> **username_3**: But, it is an unstable equilibrium point so quantum fluctuations will disturb both black holes and they would not remain there forever.  Hawking radiation would also disturb it.  
> **username_1**: @username_2 No, black holes are extensive objects, effectively the size of their event horizons. In principle you could find a numeric solution like this involving ordinary massive objects. There isn't any good treatment of point particles in classical GR.  
> **username_1**: @DaveTheWave Already as a classical solution, this is unstable to arbitrarily small perturbations, so I'm sure that adding quantum mechanics would only make things worse.  

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