# Are there black body-like thermal emissions of gravitational waves?

In this answer, I'm interpreting the question like this: Does a blackbody excite thermal gravitational radiation, like it excites thermal electromagnetic radiation? And can this ever be significant in the real world?

(For some clarifications regarding thermal radiation, see ProfRob's answer.)

From both theory and observation, we know that gravitational radiation can carry energy away from a system,$$^\dagger$$ such as a system of two compact objects orbiting each other, but those gravitational waves never reached equilibrium with the system that produced them, so this is not a blackbody.

$$^\dagger$$ Defining the "energy" of gravitational disturbances in general relativity can be problematic, but I won't try to address that here. This answer is long enough already.

Reaching equilibrium takes time. The weaker the interaction, the longer it takes. And if the radiation escapes too quickly after it is produced, then equilibrium may never be reached.

According to ref 1, that's exactly what happens in the case of gravitational radiation. Gravitational radiation is hard to contain in a bounded region even temporarily (this post addresses a related issue), and gravity is very weak, so gravitational radiation tends to escape long before reaching equilibrium with the rest of the system. The same paper proposes a range of conditions under which gravitational radiation could theoretically reach equilibrium, but the paper does not show numeric estimates, and I don't know if the proposed conditions correspond to anything realistic.

Hawking radiation from black holes is special. I'll say more about that below, but first, here are a few miscellaneous comments:

• Cosmology: According to ref 2, the current temprature of the gravitational wave background (resulting from gravitational radiation that may have been in thermal equilibrium with other entities in the very early universe) is expected to be much lower than the already-low temperature of the cosmic microwave background. Regarding the not-so-early universe: as far as I know, gravitational waves being produced today can't reach equilibrium on cosmological scales (even electromagnetic radiation isn't doing that, and it interacts much more strongly), but I don't know enough about cosmology to say anything enlightened.

• If equilibrium is reached, then the resulting properties of blackbody radiation can be calculated without worrying about the how strong or weak the interactions are. The Boltzmann distribution, where the probability of a state of energy $$E$$ being occupied is $$e^{-E/kT}$$, can be used for gravitational radiation just like it's used for electromagnetic radiation, using a quantum version of linearized general relativity to define the "energy" of a graviton.

• Gravitons in quantum physics: Whether or not a full theory of quantum gravity would have gravitons is a question that has been debated in the literature, but we can say this: string theory, the most-studied theory of quantum gravity by far, does have gravitons at least in its perturbative expansion(s). Gravitons can also be included in quantum field theory in a perturbative expansion (ref 3). The resulting quantum field theory theory is not renormalizable, but that's okay as long as we treat it perturbatively as a low-energy effective theory with a high-energy cutoff to hide the deeper physics that quantum field theory (probably) doesn't know about.

• Gravitationally bound systems: The thermodynamics of systems that are held together by gravity is interesting, because such systems have negative heat capacity: their temperature increases when they lose energy, and putting more energy into them makes them colder. This is true whether or not gravitational radiation plays any role. It's true even in Newton's model of gravity, which doesn't have gravitational waves. But the negative heat capacity does have an interesting consequence in one type of system where (quantum) gravitational radiation does play a role: black holes. That brings us to the subject of Hawking radiation...

Hawking radiation is a quantum effect that all black holes are expected to exhibit. Hawking radiation has the characteristics of blackbody radiation. Hawking's original derivation of Hawking radiation did not use a full theory of quantum gravity, and the process that produces the radiation in Hawking's original approach is different than an ordinary blackbody. A full theory of quantum gravity undoubtedly has something interesting to say about the actual process, which is probably something like thermalization except that it must involve spacetime geometry in a novel way. Significant recent progress has been made in understanding how this probably works (ref 4), but I'm only barely beginning to study that subject, so I won't try to say anything else about it here.

Regardless of exactly how it is produced, the temperature of Hawking radiation is predicted to be exceedingly low for black holes of stellar mass or more. (Remember: gravitationally-bound systems have negative heat capacity, so larger black holes are colder.) As a result, the radiation is expected to be dominated by massless entities — photons and gravitons — even though it can contain anything in principle (ref 5). Even neutrinos might be too massive to make a significant contribution. The quantitative details are reviewed in ref 6, which says that the power emitted as gravitons is expected to be roughly ten times less than the power emitted as photons, according to the text above equation (1) in ref 6.

1. Padmanabhanan and Singh, "A note on the thermodynamics of gravitational radiation" (https://arxiv.org/abs/gr-qc/0305030)

2. Press and Thorne (1972), "Gravitational-wave astronomy", Annual Rev. Astron Astrophys 10:355-374 (https://www.annualreviews.org/doi/pdf/10.1146/annurev.aa.10.090172.002003)

3. Donoghue, "Introduction to the Effective Field Theory Description of Gravity" (https://arxiv.org/abs/gr-qc/9512024)

4. Raju, "Lessons from the Information Paradox", (https://arxiv.org/abs/2012.05770)

5. Harlow and Ooguri, "Symmetries in Quantum Field Theory and Quantum Gravity" (https://arxiv.org/abs/1810.05338)

6. Don Page, "Time Dependence of Hawking Radiation Entropy" (https://arxiv.org/abs/1301.4995)

I'm adding this rather than extending the discussion below Chiral Anomaly's answer. I think that answer is correct, but I do think some clarification is required.

The requirements for black body radiation (which is not a radiation mechanism in itself) are that the radiation emitted by the body is "thermal", which means that the emission spectrum could be characterised by a temperature; that the object absorbs all radiation incident upon it; and that the object described as a blackbody is in equilibrium at a single temperature.

The second of these conditions is very unlikely to apply anywhere in the present-day universe. Matter is almost transparent to gravitational waves which is why they are so difficult to detect.

However, conditions are considerably different in the early universe. There are indeed predictions that the relic gravitational waves arising from the epoch of inflation will have a thermal spectrum and could have been characterised by a temperature $$T > 10^{28}$$ eV (!) in the pre-inflationary universe and subsequently has a blackbody spectrum of frequencies (e.g. Bhattacharaya et al. 2006; Zhao et al. 2009; Wang et al. 2017). This radiation will have decoupled from the rest of the universe after inflation and will have cooled to an extremely low temperature today ($$\sim 10^{-26}$$) K, but with wavelengths that may have been sufficiently large to imprint subtle signatures on the cosmic microwave background.

But is there any way in which the gravitational wave emission process could be described as "thermal" or be assigned a "temperature" in the present day? I don't think you can ascribe a gravitational wave temperature to single macroscopic objects, or even to binary systems because the microscopic components of these systems are behaving in concert. It would be akin to trying to assign a temperature to a single atom or molecule.

Chiral Anomaly suggests (in comments) a cluster of neutron stars. Clusters can be assigned a "temperature" that is essentially proportional to the rms speed of the component stars, in much the same way that molecules in a gas have a temperature. There could be some merit in this. Undoubtedly the cluster as a whole would emit low frequency gravitational wave radiation (with wavelengths that could be larger than the cluster) that had a spectrum that could be connected with this rms speed.