6.1 Speed of gravitational waves

Association of a gravitational wave event with an electromagnetic event, such as the observation of a gamma or X-ray burst coincidentally with a gravitational wave event, would help to deduce the speed of gravitational waves to a phenomenal accuracy. The best candidate sources for the simultaneous observations of both are the well-known extra-galactic gamma-ray bursts (GRBs). Depending on the model that produces the GRB, the delay between the emission of a GRB and gravitational waves might be either a fraction of a second (as in GRBs generated by internal shocks in a fireball [308]) or 100’s of seconds (as in GRBs generated when the fireball is incident on an external medium [258]). It is unlikely that high-redshift gamma-ray observations will be visible in the gravitational wave band, since the amplitude of gravitational waves might be rather low. However, advanced detectors might see occasional low-redshift events, especially if the GRB is caused by black-hole–neutron-star mergers. Third generation detectors would be sensitive to such events up to z = 2. A single unambiguous association can verify the speed of gravitational waves relative to light to a fantastic precision.

For instance, even a day’s delay in the arrival times of gravitational and electromagnetic radiation from a source at a distance of one giga light year (distance to a low-redshift GRB detectable by advanced detectors) would determine the relative speeds to better than one part in 1011 (1 day/109 yr ∼ 3 × 10–12). Coincident detection of GRBs and gravitational waves would require good timing accuracy to determine the direction of the source so that astronomical observations of associated gamma rays (and afterglows in other spectral bands) can be made. Consequently, gravitational wave antennas around the globe will have to make a coincident detection of the event.

If the speed of gravitational waves is less than that of light, then this could indicate that the graviton has an effective nonzero mass.

This would have other observable effects, in particular dispersion; different frequencies should move at different speeds. Will [393] pointed out that LISA’s observations of coalescences of SMBHs at high redshifts will place extremely tight constraints on dispersion, and may, therefore, indirectly set the best available limits on the speed of gravitational waves. This and other bounds on the graviton mass are discussed in Section 6.6.1.

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