Weak-Field Limit of Gravitational Radiation and the Equivalence Principle?

[Alexrey]

I was just wondering if our use of a flat Minkowski background metric when looking at gravitational radiation in the weak-field limit is essentially done so that locally, for example with detectors on Earth, we can treat spacetime as being flat, but on a larger scale we use the equivalence principle to patch all of these flat background perturbed spacetimes together to create a curved spacetime. Or am I wrong and we actually treat our whole solar system as being a flat spacetime? This little question has been bothering me for some time as I thought that I would have been forced to use a Schwarzschild background when dealing with detection of GWs on Earth.

 

[tom.stoer]

Afaik the source of the gravitational waves is always treated non-perturbatively, e.g. for black hole merger or (close) binary systems. But then there is a kind of far field approximation and I think there it is save to use Minkwoski background geometry plus gravitational waves propagating on this background. The most experiments are sensitive to a certain frequency of gravitational waves and there you always assume plane wave approximation (I am not sure about polarization).

But I am not an expert and I do not know whether corrections due to Schwarzschild geometry of the gravitational field of Earth orsune are required.

 

[bcrowell]

Afaik the source of the gravitational waves is always treated non-perturbatively, e.g. for black hole merger or (close) binary systems. But then there is a kind of far field approximation and I think there it is save to use Minkwoski background geometry plus gravitational waves propagating on this background.

Yeah, I think this is right. In linearized gravity you can't even get masses to orbit one another, so I don't think you can describe the source using linearized gravity.

 

[bcrowell]

This little question has been bothering me for some time as I thought that I would have been forced to use a Schwarzschild background when dealing with detection of GWs on Earth.

Suppose, for example, that a given gravitational wave event is detected by both a detector on the Earth's surface and a space-based detector. Then I'm sure that the frequencies measured by the two detectors will, at least in theory, differ by the usual time dilation factors that we see when communicating with a space probe.

However, I really doubt that the analysis requires a full treatment of a gravitational plane wave encountering a Schwarzschild field. You'd probably need that, for example, if you wanted to describe the analogs of refraction and diffraction, but I'm pretty sure those effects are much too weak to matter in practical gravitational wave experiments.

 

[Alexrey]

Awesome, thanks for your help guys, I appreciate it.