# Spectra of gravitational waves

In Jim Arnold’s blog, we have been having an occasionally enlightening, occasionally exasperating discussion about whether gravitational waves (GWs) exist.

The evidence strongly supports the interpretation of the mathematics of general relativity that says gravitational waves do indeed exist and are, in principle if not yet in practice, observable.

That leads to a question that hasn’t come up in Jim’s blog but I’d like to raise here: What is the spectrum of gravitational radiation?

Burt Jordaan and SL, aka Scruffy, clearly know the mathematics better than I. Jim Arnold does, too, but I don’t think he’ll have anything useful to say here because he disputes the very existence of GWs.

I think my question is shared by many of the people who have been reading the discussion at Jim’s blog, and I hope some of them will chime in with related questions.

My understanding is that any accelerated mass changes the geometry of (perturbs) spacetime, and that perturbation propagates in all directions from that mass at the speed of light. If we want to visualize it, it is like a ripple in a pond. If we want to describe it strictly mathematically, that propagation fits the pattern of a wave. It has a wavelength and frequency. In fact, unless the disturbance is strictly sinusoidal, it has multiple frequencies, each of which with a different intensity–i.e., a spectrum.

Light spectra are typically described as continuous or line spectra. That’s a convenient distinction although we know that a continuous spectrum is just a set of line spectra with too small a spacing between wavelengths to distinguish between the lines. Or we could talk about its being made up of photons with energies at a continuum of values.

In any case, I have not seen any discussion of what the expected spectra are for GWs.

In the other discussion, we were focusing on a case of a pair of neutron stars in a tight orbit which is getting tighter due to the emission of GWs. Burt noted that the propagating GW is periodic in character, and that made me wonder about its period. Does its spectrum have a narrow peak at the orbital frequency (and smaller peaks–harmonics–at multiples of that frequency)? Or does it have a spectrum more like blackbody radiation in thermodynamics?

What about the spectra in these other cases:

• An apple falls to Earth?
• A supernova ignites?
• Two black holes merge?
• Other phenomena that create huge gamma-ray bursts?

Will the new GW detectors being planned be able to give us much information about the spectra of such events? Will we ever be able to see a spectrum in enough detail to show the need for gravitons, just as Planck proposed the quanta we now call photons to explain the shape of the blackbody spectrum at high frequencies?

As you can see, this post is more about questions than answers. I hope the comments will lead us toward some answers as well as to some more questions.

Fred Bortz,
Author of Physics: Decade by Decade, a history of Physics in the 20th century

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