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

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Discussion Overview

The discussion revolves around the use of a flat Minkowski background metric in the weak-field limit of gravitational radiation and its relationship with the equivalence principle. Participants explore whether the entire solar system can be treated as flat spacetime or if a Schwarzschild background is necessary for gravitational wave detection on Earth.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions if the flat Minkowski background is used locally for detectors on Earth while the equivalence principle is applied to create a curved spacetime on a larger scale.
  • Another participant suggests that gravitational wave sources are treated non-perturbatively, particularly in cases like black hole mergers, and mentions a far field approximation allowing for the use of Minkowski background geometry.
  • A different participant agrees that linearized gravity does not adequately describe mass interactions, implying that a Schwarzschild background may be necessary for certain analyses.
  • Concerns are raised about the potential differences in frequencies measured by Earth-based and space-based detectors due to time dilation, but doubts are expressed regarding the necessity of a full treatment of gravitational plane waves in a Schwarzschild field for practical experiments.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the necessity of a Schwarzschild background versus a flat spacetime approach, indicating that multiple competing views remain without a clear consensus.

Contextual Notes

Participants note limitations in their understanding of the effects of Schwarzschild geometry on gravitational wave detection and the implications of linearized gravity on mass interactions.

Alexrey
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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.
 
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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.
 
tom.stoer said:
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.
 
Alexrey said:
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.
 
Awesome, thanks for your help guys, I appreciate it.
 

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