Recent research has proposed that some black holes are the astrophysical origin of dark energy.  Is this true and what exactly does this mean?  What is dark energy in the first place?  These are all complex questions, and this short report is just a thin film on top of deep dark unknown waters.  The truth is that astrophysicists have many hypotheses about what dark energy is and are not at all certain, but the proposal found in the paper that prompted this blog post (1) is intriguing in that it does not require any new fundamental fields or forces of nature.  Instead, we need to better understand General Relativity.

A short oversimplified answer to these questions is that Black holes are not emitting energy that causes the universe to expand.  They are not some sort of giant dark energy stars.  Emitting that energy analogous to how the Sun emits light.  It's more complicated than that.  The research shows that black holes may grow in size due to the universes expansion.  That dark energy arises from the coupling of black holes to that expansion.  There is an analogy between the evolution of the planets and the evolution of the Sun one cannot understand the solar system without understanding the whole system and how they interact. Dark energy is in a sense just a way we account for all the details typically ignored in solving Einstein's Field Equations in which we pretend space is a featureless vacuum etc.

Metrics:Distance in Space-Time

To understand what is to come we need one concept from general relativity that is the “metric”.  General Relativity is Einstein’s theory of gravity and space time.  It is summarized in the form of a tensor differential equation that tells us how space time curves due to a given distribution of matter.  The metric in general relativity is an expression of this curvature.  If the space time is not curved, then the metric is just a fancy version of the Pythagorean theorem you learned in middle school or high school.

$\300dpi a^2+b^2=c^2$

In four-dimensional space time this becomes the Minkowski metric.

$\300dpi ds^2=-dt^2+dx^2+dy^2+dz^2$

The exact solutions of the Einstein Field Equations which give us Black holes assume that space time will become the Minkowski metric at large distances (and hence long times).  These solutions all have a singularity at the center of the Black hole.  This singularity is a point where the math breaks down.

The exact solution of the Einstein Field Equations which gives us the expanding universe and the big bang is also flat but not Minkowski. This solution is called the Friedman-Lemaître-Robertson-Walker metric, the real big bang theory.  In addition to that this universe wide metric is locally perturbed by a background of random gravitational waves.  The standard solutions to the Einstein Field Equations don’t account for this background and don’t have realistic boundary or initial conditions.   They are static and steady state.   The real universe is dynamic and changing.

In a sense this proposal would make dark energy merely a way that we account for all of these dynamics this cosmological coupling, which have up to this point been ignored.

So, what is my humble opinion on this proposal?  This is as good as or better than anything else that has been proposed.  This is an idea worthy of consideration and the authors of this paper raise interesting questions in their consideration of future tests and theoretical directions. According to the paper what they propose would have an effect on the Cosmic Microwave background, observations of gamma ray burst, the rate of stellar mass black hole mergers, measurement of orbital period decay, and the evolution of stars and black holes.  Some of the effects they propose a search for would also be informative to other models.  For example, if dark matter is real (a different not necessarily related phenomena) then looking for it accumulate in the strong gravity of black holes and for effects that would have on the orbits of objects spiraling into them would be a good thing to check for among another good test to perform.  These are all things which could be searched for at little or no added cost.

Better Exact Solutions To Einsteins Field Equations Are Needed?
They also propose that theorist should attempt to come up with solutions to the Einstein field equations that quote

As described in Section 1, there are known exact solutions with each of the following properties: strong spin, arbitrary RW asymptotics, dynamical mass, and interior vacuum energy equation of state. Our result implies the existence, within GR, of an exact solution with all of these properties. Currently, there is no known solution that possesses all four, though there are known solutions with various combinations of two (e.g., Guariento et al. 2012; Dymnikova&Galaktionov 2016). Finding solutions that feature all four properties is an important theoretical step forward.

Later on they state

Realistic astrophysical BH models must become cosmological at large distance from the BH. Non-singular cosmological BH models can couple to the expansion of the universe, gaining mass proportional to the scale factor raised to some power k.

I don’t really disagree with these statements.  However, I think it is more likely that either General Relativity is not complete or our set of fundamental forces of nature is not complete.

It would not surprise me if we were either ignoring or simply unaware of a 5th or 6th fundamental force of nature that plays an important role in dark energy and/or in what they have observed.  Something that explains dark matter, dark energy and does so without sacrificing the solutions to the equations of general relativity that have passed every test ever given to them so far.  Indeed so called test of General Relativity are test of the various exact solutions of Einstein's Field Equations even with all their shortcomings.  Any solution that proposes to replace them needs to also meet these test. Challenge accepted.

An interesting interview with Dr Chris Pearson conducted by science journalist Fraser Cain.

The study of dark matter and dark energy is the opposite of settled science.  Until we know what dark energy is and can write its Lagrangian equation (an equation that describes the energy and interactions in a field theory) and do repeatable experiments, or make observations, that verify that Lagrangian we will not know what dark energy is for certain.

That said, this paper raises particularly important points and makes especially important observations.

References

Duncan Farrah et al 2023 ApJL 944 L31DOI 10.3847/2041-8213/acb704