Will gravitational waves decay into photons? (and by how much?)

We know intense regions of curvature, for example near a black hole horizon, induce a flow of electromagnetic waves (and, less so, other particles). aka Hawking radiation.

By contrast, curvature in one direction which is equivalent to acceleration in flat space induces photons in random directions (Unruh effect).

Gravitational waves are ripples in space time, which create regions of local curvature as they pass by.

By analogy, one would expect that, although very weak, these should also induce a flow of photons. For a linear gravitational wave (from a distant source) one might expect to experience the Unruh effect if it passed through you. i.e. the gravitational wave should have a small (i.e. practically unmeasurable) temperature.

For a gravitational wave from a spherical source, by analogy I would expect to see some kind of weak Hawking radiation flow with average direction away from the source as they passed by.

Following the logic, a gravitational wave emitted from a spherical source should slowly turn into an electromagnetic wave. The question becomes, as time goes to infinity, what percent of the gravitational wave will have turned into an electromagnetic wave (or photons)? Will all of it? Or will it reach some equilibrium. Is there a back-of-the-envelope calculation that one can do?

(I can't see a process in which an electromagnetic wave decays into a gravitational wave so I think this is only a one way process - but then again photons also induce a gravitational field so this suggest to me that some equilibrium might be reached).

Or is there a counter argument which says gravitational waves won't decay into photons?

If there is such a process it must be very slow otherwise gravitational waves couldn't travel such long distances and be detected on Earth.

(Also, perhaps if the gravitational wave did all decay into photons, perhaps these collection of photons couldn't be described in terms of waves?)

• Commented Feb 17, 2023 at 18:35
• This says something about it but I didn't understand it much: commons.erau.edu/cgi/….
– user84158
Commented Feb 17, 2023 at 18:43
• Gravitational waves are described by General Relativity, which is not definitively quantized. Photons are quantum mechanical entities and appear in quantum mechanical interactions. The article you do not understand goes into possible quantization of GR which would result in the type of graviton+graviton interactions which could go into two photons, leading to the decay of the classical gravitational wave. Primary research goal is quantization of GR, and then speculations about gravitational waves. Commented Feb 17, 2023 at 18:52
• @zooby your 1st paragraph is true only if the BH is charged. Hawking in his calculation for Schwarz. BH assumed a simple renormalized scalar field STE to find the total outgoing flux of radiation. Likewise, if its a charged BH, you will need a renormalized Maxwell STE. The UD Detector in your linked article relies on the existence of an outgoing Maxwell radiation, so the BH must be charged to make any measurements. I'm not sure why this implies graviton decaying into photons etc Commented Feb 17, 2023 at 20:00
• However, mathematically there are close correspondence b/w calculations of gauge fields and similar calculations for spin 2 fields. See for instance, the classical double copy prescription by Prof. Tim Adamo et al Commented Feb 17, 2023 at 20:04

I would say that title question mixes paradigms: “gravitational wave” usually implies classical gravitational radiation while “photons” are quantum entities.

Gravitational radiation can convert into electromagnetic radiation, or (in quantum terms) gravitons can convert into photons. Not “decay” as such, which implies spontaneity without external influences, but “convert” where some external cause facilitates such transition. For example, decay of a single graviton into one or several photons is forbidden by conservation laws (of energy, momentum, angular momentum). Similarly, in purely classical theory, initial data of purely gravitational radiation would never lead to formation of EM wave ($$F_{\mu\nu}=0$$ on a Cauchy surface ensures that $$F_{\mu\nu}\equiv0$$ at all times everywhere). But with some external cause the conversion is possible. E.g. gravitational wave can undergo conversion into EM radiation in the presence of a charged object, or in external magnetic fields. In quantum realm at least one additional particle is needed for conversion.

gravitational wave emitted from a spherical source should slowly turn into an electromagnetic wave. The question becomes, as time goes to infinity, what percent of the gravitational wave will have turned into an electromagnetic wave (or photons)?

Purely spherically symmetric systems do not produce gravitational radiation, OP probably meant “isolated source”? If we have an isolated radiating source in pure vacuum then only the fields associated with this source (e.g. its magnetic fields, its EM radiation etc.) can lead to gravitational to EM radiation conversion. The further from the source the smaller the fluxes, the smaller the nonlinearities, so there would not be some dynamical equilibrium between gravitational end EM radiation, instead the fractions of energy carried by different types of radiation are determined near the source and remain almost the same to infinite distances/times.

On the other hand, if we imagine an ideal box of finite volume fully reflective for both EM and gravitational radiation, then after a time we could expect that thermal equilibrium would be achieved inside it (since graviton/photon scattering/conversion cross-sections are very small at low energies the time required could be quite substantial). If the average energy density is small enough that massive particles do not form and total volume is small enough so that formation of the central black hole is unfavorable, then we can expect Planck spectra for gravitons and photons and since each species have two polarization states for each wave vector, the energy density of gravitational radiation would be the same as for the EM radiation.

• Interesting. You mention other particles are necessary for the conversion. I guess the 1 atom of hydrogen per cubic cm of empty space would have negligible effect. Also I guess graviton-graviton interactions in a wave far from the source would be small due to the wave being almost-linear.
– user84158
Commented Feb 19, 2023 at 4:06
• Yes, you are right. A spherical source is not the correct term. I suppose you can't call colliding black holes a spherical source! Although, nearly spherical as the resulting black hole settles into a sphere.
– user84158
Commented Feb 19, 2023 at 4:09

Gravitational waves are ripples in the fabric of spacetime caused by the acceleration of massive objects. They were predicted by Albert Einstein's theory of general relativity and were first detected by the Laser Interferometer Gravitational-Wave Observatory (LIGO) in 2015.

Gravitational waves are not expected to decay into photons, as they are not electromagnetic in nature. Unlike photons, which are the quanta of the electromagnetic force, gravitational waves are the quanta of the gravitational force. Therefore, they do not interact with charged particles or electromagnetic fields in the same way that photons do.

However, it is possible for gravitational waves to interact with particles through the weak force, which is responsible for certain types of radioactive decay. This interaction is very weak and would be difficult to detect in practice.

In summary, while gravitational waves are not expected to decay into photons, they can interact weakly with particles through the weak force. However, this interaction is very weak and is unlikely to have a significant effect on the propagation of gravitational waves.