# Would gravitational waves detected at GW150914 have been redshifted?

Would the gravitational waves detected in September 2015 (announced Feb 2016) have been gravitationally redshifted as they escaped from a black hole of 62 solar masses?

If so, how would that have been taken into account in any of the conclusions formed by studying that set of waves? Would it affect how far apart we think the two blackholes were when they merged, for example?

The GW150914 'chirp' signal ranged in frequency from 35 Hz to 250 Hz. (So, at speed c, wavelength = 9000 km to /1200 km?).

Would that signal have been redshifted as it escaped the gravitational well of a mass of 62 solar masses?

I figure a combined 62 solar-mass black hole would have a radius of ~180km ($R_s=\tfrac{2GM}{c^2}$), so using $\tfrac{\Delta f}{f}=\tfrac{GM}{Rc^2}$, the frequency of an escaping wave should be shifted by ~50%.

(Please let me know if these are the right equations. It looks like mass cancels out, so same redshift from any blackhole??)

• How do I close this question? – Errol Hunt Feb 23 '17 at 23:19

The main source of red shifted gravitational radiation is from the fact the two BHs were $1.3$ billion light years distant. This means with the Hubble constant $H~=~70km/s-mpc$ and $v~=~Hd$ that the BHs are expanding away from us at $v~=~2.8\times 10^4km/s$. This results in a red shift factor of $z~\simeq~.1$. This has to be added into the result.