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  • $\begingroup$ But couldn't the linearised Weyl tensor also not vanish if the metric is a vacuum solution that doesn't represent gravitational waves such as the Schwarzschild metric? $\endgroup$
    – Moguntius
    Commented Mar 6 at 22:35
  • $\begingroup$ Electric fields also don’t vanish when there is point charge, but we have no problem distinguishing Coulomb electric fields from electromagnetic waves. Why wouldn’t the same approach apply to gravitational waves? $\endgroup$
    – Dexter Kim
    Commented Mar 8 at 6:02
  • $\begingroup$ Because gravitational waves, in contrast to electromagnetic waves, carry the charge they couple to. Gravity couples to mass/energy/stress and grav. waves carry energy, whereas elm. waves, which couple to electric charge, are not charged themselves and, therefore, do not (directly, i.e. if we neglect high order quantum effects) interact with each other. $\endgroup$
    – Moguntius
    Commented Mar 13 at 19:12
  • $\begingroup$ I don’t see the relevance of nonlinearities in determination of the existence of gravitational waves. If the Weyl tensor doesn’t vanish and if it has wavelike propagating modes (w.r.t. the background metric) what would force us to conclude that gravitational waves are not actually present? $\endgroup$
    – Dexter Kim
    Commented Mar 14 at 20:12
  • $\begingroup$ If you are thinking of full nonlinear solutions of GR then yes, it’s a completely different beast, but apart from numerical simulations almost all calculations are done in the weak field regime where linearised equations make sense. $\endgroup$
    – Dexter Kim
    Commented Mar 14 at 20:20