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Consider a spherically symmetric spacetime generated by a self-gravitating massless scalar field $\phi$ and let $\psi$ be a test (nonspherical) massless scalar field propagating on this dynamical background.
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P. Bizoń, T. Chmaj, and A. Rostworowski, Class. Quantum Grav. 26
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P. Bizoń, T. Chmaj, A. Rostworowski, and S. Zaja̧c, Class. Quantum Grav. 26
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