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Creators/Authors contains: "Disconzi, M."

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  1. We show that linear superpositions of plane waves involving a single-valued, covariantly stable dispersion relation $$\omega(k)$$ always propagate outside the lightcone, unless $$\omega(k) =a+b k$$. This implies that there is no notion of causality for individual dispersion relations, since no mathematical condition on the function $$\omega(k)$$ (such as the front velocity or the asymptotic group velocity conditions) can serve as a sufficient condition for subluminal propagation in dispersive media. Instead, causality can only emerge from a careful cancellation that occurs when one superimposes all the excitation branches of a physical model. This is shown to happen automatically in local theories of matter that are covariantly stable. 
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  2. We consider a (very) simple version of the restricted three body problem in general relativity. The background geometry is given by a Schwarzschild solution governing the motion of two bodies of masses $$m_1$$ and $$m_2$$. We assume that corrections to the trajectory of the body of mass $$m_1$$ due to the presence of the mass $$m_2$$ are given by a Newtonian approximation where Poisson's equation is solved with respect to the Schwarzschild background geometry. Under these assumptions, we derive approximate equations of motion for the corrections to the trajectory of the body of mass $$m_1$$. 
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