I am studying gravitational waves and I am trying to understand two types of wave solutions I have seen for the metric. In various texts (Carroll, Wald, etc.), they discuss the gravitational wave solutions in the transverse traceless (TT) gauge (linearized gravity). This involves a solution which consists of a superposition of plane waves and has two degrees of freedom which define the plus and cross polarization.

In my search through the literature, I keep finding papers that discuss "pp-waves." I have seen enough theorems and analysis to see that they are useful in describing things like "sandwich waves" and "impulsive waves," but I really want to know if these pp-waves are different than the wave solutions in the TT gauge shown in the text books.

Are pp-waves simply the waves in the TT gauge, but transformed via Brinkmann coordinates? I haven't read through Brinkmanns paper yet, but everyone seems to just cite him and not show this transformation if this is the case.

Any help would be appreciated!

  • $\begingroup$ When you say gravitational wave solutions in the TT gauge, do you mean exact solutions to Einstein's equations or the GW solutions in linearized gravity? $\endgroup$ Aug 25, 2022 at 23:35
  • $\begingroup$ The latter, linearized gravity. Sorry I did not clarify. $\endgroup$
    – user41178
    Aug 26, 2022 at 0:37

1 Answer 1


pp-waves are (a class of) exact solutions to the Einstein equation. Among other things, they can describe the exact solutions for gravitational plane waves.

When you solve the linearized Einstein equation in the TT-gauge, the solutions you find are not solutions of the full non-linear Einstein equation, but only approximate solution. Of course, it should be true that plane wave solutions of the linearized Einstein equation in a Minkowski background approximate the corresponding exact pp-wave solutions.


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