<p><strong>Disclaimer:</strong> I'm Dr. Kevin Croker, lead author on the ApJ series in question.  I work on formal aspects of relativistic perturbation theory.  I think the best way to answer your question is to just address all of the commenters' responses.  I just made this SE account to respond to you, so I don't have sufficient reputation to reply as a comment yet.</p>
<p>(For ELNJ)
Dark energy solutions are ubiquitous in GR, though the only mainstream one came from Mottola (LANL) &amp; Mazur (South Carolina) and is called a &quot;gravastar.&quot;  Such solutions were primarily of theoretical interest until LIGO's detections raised the posibility of experimental differentiation from classical black holes.</p>
<p>My advisor had asked me to weigh in on a cosmological backreaction debate between Nick Kaiser and Istvan Szapudi at the Institute for Astronomy (IfA). During this investigation, given the right properties, I realized that these sorts of dark energy objects could become cosmologically coupled.  Because it seemed that the specific gravastar solution of Mottola &amp; Mazur would not couple, but other solutions could, I needed a new name for the larger class of &quot;objects containing dark energy.&quot;  So my co-author and I came up with GEODE in Section 3.4 of <a href="https://iopscience.iop.org/article/10.3847/1538-4357/ab32da" rel="noreferrer">https://iopscience.iop.org/article/10.3847/1538-4357/ab32da</a></p>
<p>The name is meant to be a play on geological geodes, though in hindsight maybe this was stupid.  Geological geodes don't look special on the outside (c.f. GEODEs look like classical BHs), are empty in the middle (c.f. GEODEs contain dark energy, which used to be called &quot;heavy vacuum&quot;), and have beautiful crystals on the inside edge (c.f. GEODEs a transition layer that may hold extreme amounts of spin).</p>
<p>There is the technical distinction that a GEODE is a cosmological solution.  So DE objects that are asymptotically flat are to be understood as GEODE models restricted to an amount of time short compared to <span class="math-container">$1/H(a)$</span>, where <span class="math-container">$H(a)$</span> is the Hubble rate at scale factor <span class="math-container">$a$</span>.</p>
<p>(For uhoh)</p>
<p><a href="https://www.npr.org/2020/08/27/906835155/space-week-the-mystery-of-dark-energy" rel="noreferrer">This</a> podcast does not discuss GEODEs, only the cosmological constant.  An ancient GEODE scenario (more technically, a Population III GEODE scenario) mimics a cosmological constant, but can be observationally distinguished.  Signatures include a correlation of the lookback time with the peak in cosmic star formation rate, essentially Figure 4 of <a href="https://arxiv.org/abs/1612.07245" rel="noreferrer">https://arxiv.org/abs/1612.07245</a> , and an altered Integrated Sachs-Wolfe signal (we're writing the paper now).</p>
<p>(For antispinwards)
As jmh suspects, the name is not from '66.  As far as I've been able to tell from the literature, the idea dates from Gliner's 1966 paper &quot;Algebraic properties of the energy-momentum tensor and vacuum-like states of matter.&quot;  This paper is freakishly lucid and short.  I quote it:</p>
<blockquote>
<p>&quot;This raises the thought that in an ultradense state of matter, with
the baryons so compressed that the meson fields which provide the
interaction between them (repulsion!) cannot be produced, a continuous
medium is formed in which the conditions correspond to an attraction
between material elements and are described phenomenologically by a
negative pressure.... It would seem that a negative pressure should
lead to an internal instability, and that if there are no volume
forces of the type of the electrostatic repulsion it would lead to a
contraction without limit. This is not true, however.&quot;</p>
</blockquote>
<p>Gliner then proves it with the conservation conditions.  He finishes with,</p>
<blockquote>
<p>&quot;The hypothetical process we have considered is interesting in
connection with the problem of the final state of matter which has
undergone gravitational collapse. According to the ideas developed
here this state is a <span class="math-container">$\mu$</span>-vacuum.&quot;</p>
</blockquote>
<p><span class="math-container">$\mu$</span>-vacuum is what we would call &quot;dark energy&quot; today.</p>
<p>(for jmh)
These objects are &quot;less discovered&quot; than black holes.  The objects that LIGO sees are certainly spinning, which means they are Kerr-like solutions.  At present, there is no known Kerr-like GEODE.  That does not mean it does not exist, but it is harder to build.</p>
<p>Interestingly, unlike static black holes, there is no known source for a Kerr black hole, i.e. a matter solution that you can &quot;paste into&quot; the &quot;bad places&quot; and still have things work.  Afaik, the state of the art is described by e.g. Posada <a href="https://academic.oup.com/mnras/article/468/2/2128/3059158" rel="noreferrer">https://academic.oup.com/mnras/article/468/2/2128/3059158</a> . Here a slowly spinning gravastar (a specific type of GEODE, considered only for a short amount of time) agrees with Kerr at the first step of calculation.  In this sense, a GEODE provides the first plausible source for the inside of a Kerr solution.</p>
<p>Far away from a GEODE, you find yourself in a cosmological solution.  Far away from a black hole, you find yourself in empty space.  That makes black holes much easier to work with, as models.  In every other place that we astrophysically expect a black hole, you could replace it with a GEODE and upset nothing or actually relieve tensions (e.g. high z quasar masses, large masses observed by LIGO).  These properties are discussed in <a href="https://iopscience.iop.org/article/10.3847/1538-4357/ab5aff" rel="noreferrer">https://iopscience.iop.org/article/10.3847/1538-4357/ab5aff</a> Section 2.1.  Unlike black holes, stellar collapse GEODEs can naturally grow to hundreds of Msol, see Figure 2.  Incidentally, our team predicted systems like GW190521, 7 weeks before the event arrived at LIGO's detectors.  This can be found in arxiv preprint of ApJ paper @ <a href="https://arxiv.org/abs/1904.03781v1" rel="noreferrer">https://arxiv.org/abs/1904.03781v1</a> , text below Equation (15) &amp; Figure 2.</p>

CC BY-SA 4.0
2020-09-09T21:06:57.347Z
Thank you very much for your answer.  I know you must be extremely busy and I appreciate you taking the time to give "the" answer.
Natsfan
CC BY-SA 4.0
2020-09-09T22:43:34.230Z
If you're going to thank me, I'm going to thank you.  Its your interest and curiosity that has given me the opportunity to provide more information to a wider audience, for example @ELNJ
kwurtechog
CC BY-SA 4.0
2020-09-10T10:58:53.317Z
Thank you for the reply, I'll have a look. Yes that pesky 50 reputation points threshold is sometimes frustrating
uhoh
CC BY-SA 4.0
2020-09-09T20:56:13.753Z
2020-09-09T21:09:09.967Z
2020-09-09T21:09:09.967Z
kwurtechog
<p>Phys.org's <a href="https://phys.org/news/2020-09-candidate-mysterious-dark-energy.html" rel="nofollow noreferrer">Researchers predict location of novel candidate for mysterious dark energy</a> says that GEODEs may explain the dark energy problem. I'm not an astronomer but I've never heard of GEODEs. I know what the letters mean but what is a GEODE physically. GEODE is Generic Objects of Dark Energy (GEODE).</p>

CC BY-SA 4.0
2020-09-02T02:29:28.900Z
Can you give a link or some further background information?  I *am* an astronomer and have never heard of these - at least telling people where you encountered this idea would be helpful.
Eric Jensen
CC BY-SA 4.0
2020-09-02T03:06:43.157Z
GEODE stands for Generic Objects of Dark Energy (GEODEs). They are very similar to Black Holes. I read the article on Phys.org.  It was from this link: https://phys.org/news/2020-09-candidate-mysterious-dark-energy.html?utm_source=nwletter&utm_medium=email&utm_campaign=daily-nwletter
Natsfan
CC BY-SA 4.0
2020-09-02T03:54:57.093Z
you can also read and/or hear an astronomer discuss this in NPR's podcast [SPACE WEEK: The Mystery Of Dark Energy](https://www.npr.org/2020/08/27/906835155/space-week-the-mystery-of-dark-energy) Also note that the Phys.org article links to the *open access* (Croker et al. 2020) [Implications of Symmetry and Pressure in Friedmann Cosmology. III. Point Sources of Dark Energy that Tend toward Uniformity](https://iopscience.iop.org/article/10.3847/1538-4357/abad2f)
uhoh
CC BY-SA 4.0
2020-09-02T14:54:24.627Z
yes, I noticed that too.  I guess the idea occurred in the 1960s and the name came later.  Or maybe the objects were discovered in the 1960s.
Natsfan
<cosmology><dark-matter><dark-energy>
What are GEODEs?
Natsfan
# What are GEODEs?

(Asked by: username_0 on 2020-09-01)

Phys.org's [Researchers predict location of novel candidate for mysterious dark energy](https://phys.org/news/2020-09-candidate-mysterious-dark-energy.html) says that GEODEs may explain the dark energy problem. I'm not an astronomer but I've never heard of GEODEs. I know what the letters mean but what is a GEODE physically. GEODE is Generic Objects of Dark Energy (GEODE).

**Tags:** cosmology, dark-matter, dark-energy

> **Comments:**
> **username_1**: Can you give a link or some further background information?  I *am* an astronomer and have never heard of these - at least telling people where you encountered this idea would be helpful.  
> **username_0**: GEODE stands for Generic Objects of Dark Energy (GEODEs). They are very similar to Black Holes. I read the article on Phys.org.  It was from this link: https://phys.org/news/2020-09-candidate-mysterious-dark-energy.html?utm_source=nwletter&utm_medium=email&utm_campaign=daily-nwletter  
> **username_2**: you can also read and/or hear an astronomer discuss this in NPR's podcast [SPACE WEEK: The Mystery Of Dark Energy](https://www.npr.org/2020/08/27/906835155/space-week-the-mystery-of-dark-energy) Also note that the Phys.org article links to the *open access* (Croker et al. 2020) [Implications of Symmetry and Pressure in Friedmann Cosmology. III. Point Sources of Dark Energy that Tend toward Uniformity](https://iopscience.iop.org/article/10.3847/1538-4357/abad2f)  
> **username_0**: yes, I noticed that too.  I guess the idea occurred in the 1960s and the name came later.  Or maybe the objects were discovered in the 1960s.  

---

## 1 answers

### Answer by username_3 on 2020-09-09. Score: 8 | Accepted answer

**Disclaimer:** I'm Dr. Kevin Croker, lead author on the ApJ series in question. I work on formal aspects of relativistic perturbation theory. I think the best way to answer your question is to just address all of the commenters' responses. I just made this SE account to respond to you, so I don't have sufficient reputation to reply as a comment yet.

(For ELNJ)
Dark energy solutions are ubiquitous in GR, though the only mainstream one came from Mottola (LANL) & Mazur (South Carolina) and is called a "gravastar." Such solutions were primarily of theoretical interest until LIGO's detections raised the posibility of experimental differentiation from classical black holes.

My advisor had asked me to weigh in on a cosmological backreaction debate between Nick Kaiser and Istvan Szapudi at the Institute for Astronomy (IfA). During this investigation, given the right properties, I realized that these sorts of dark energy objects could become cosmologically coupled. Because it seemed that the specific gravastar solution of Mottola & Mazur would not couple, but other solutions could, I needed a new name for the larger class of "objects containing dark energy." So my co-author and I came up with GEODE in Section 3.4 of <https://iopscience.iop.org/article/10.3847/1538-4357/ab32da>

The name is meant to be a play on geological geodes, though in hindsight maybe this was stupid. Geological geodes don't look special on the outside (c.f. GEODEs look like classical BHs), are empty in the middle (c.f. GEODEs contain dark energy, which used to be called "heavy vacuum"), and have beautiful crystals on the inside edge (c.f. GEODEs a transition layer that may hold extreme amounts of spin).

There is the technical distinction that a GEODE is a cosmological solution. So DE objects that are asymptotically flat are to be understood as GEODE models restricted to an amount of time short compared to $1/H(a)$, where $H(a)$ is the Hubble rate at scale factor $a$.

(For username_2)

[This](https://www.npr.org/2020/08/27/906835155/space-week-the-mystery-of-dark-energy) podcast does not discuss GEODEs, only the cosmological constant. An ancient GEODE scenario (more technically, a Population III GEODE scenario) mimics a cosmological constant, but can be observationally distinguished. Signatures include a correlation of the lookback time with the peak in cosmic star formation rate, essentially Figure 4 of <https://arxiv.org/abs/1612.07245> , and an altered Integrated Sachs-Wolfe signal (we're writing the paper now).

(For antispinwards)
As jmh suspects, the name is not from '66. As far as I've been able to tell from the literature, the idea dates from Gliner's 1966 paper "Algebraic properties of the energy-momentum tensor and vacuum-like states of matter." This paper is freakishly lucid and short. I quote it:

> "This raises the thought that in an ultradense state of matter, with
> the baryons so compressed that the meson fields which provide the
> interaction between them (repulsion!) cannot be produced, a continuous
> medium is formed in which the conditions correspond to an attraction
> between material elements and are described phenomenologically by a
> negative pressure.... It would seem that a negative pressure should
> lead to an internal instability, and that if there are no volume
> forces of the type of the electrostatic repulsion it would lead to a
> contraction without limit. This is not true, however."

Gliner then proves it with the conservation conditions. He finishes with,

> "The hypothetical process we have considered is interesting in
> connection with the problem of the final state of matter which has
> undergone gravitational collapse. According to the ideas developed
> here this state is a $\mu$-vacuum."

$\mu$-vacuum is what we would call "dark energy" today.

(for jmh)
These objects are "less discovered" than black holes. The objects that LIGO sees are certainly spinning, which means they are Kerr-like solutions. At present, there is no known Kerr-like GEODE. That does not mean it does not exist, but it is harder to build.

Interestingly, unlike static black holes, there is no known source for a Kerr black hole, i.e. a matter solution that you can "paste into" the "bad places" and still have things work. Afaik, the state of the art is described by e.g. Posada <https://academic.oup.com/mnras/article/468/2/2128/3059158> . Here a slowly spinning gravastar (a specific type of GEODE, considered only for a short amount of time) agrees with Kerr at the first step of calculation. In this sense, a GEODE provides the first plausible source for the inside of a Kerr solution.

Far away from a GEODE, you find yourself in a cosmological solution. Far away from a black hole, you find yourself in empty space. That makes black holes much easier to work with, as models. In every other place that we astrophysically expect a black hole, you could replace it with a GEODE and upset nothing or actually relieve tensions (e.g. high z quasar masses, large masses observed by LIGO). These properties are discussed in <https://iopscience.iop.org/article/10.3847/1538-4357/ab5aff> Section 2.1. Unlike black holes, stellar collapse GEODEs can naturally grow to hundreds of Msol, see Figure 2. Incidentally, our team predicted systems like GW190521, 7 weeks before the event arrived at LIGO's detectors. This can be found in arxiv preprint of ApJ paper @ <https://arxiv.org/abs/1904.03781v1> , text below Equation (15) & Figure 2.

> **Comments:**
> **username_0**: Thank you very much for your answer.  I know you must be extremely busy and I appreciate you taking the time to give "the" answer.  
> **username_3**: If you're going to thank me, I'm going to thank you.  Its your interest and curiosity that has given me the opportunity to provide more information to a wider audience, for example @ELNJ  
> **username_2**: Thank you for the reply, I'll have a look. Yes that pesky 50 reputation points threshold is sometimes frustrating  

---

