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  1. A bstract We study the near-zone symmetries of a massless scalar field on four-dimensional black hole backgrounds. We provide a geometric understanding that unifies various recently discovered symmetries as part of an SO(4 , 2) group. Of these, a subset are exact symmetries of the static sector and give rise to the ladder symmetries responsible for the vanishing of Love numbers. In the Kerr case, we compare different near-zone approximations in the literature, and focus on the implementation that retains the symmetries of the static limit. We also describe the relation to spin-1 and 2 perturbations. 
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  2. We utilize the coset construction to derive the effective field theory of magnon-phonon interactions in (anti)-ferromagnetic and ferrimagnetic insulating materials. The action is used to calculate the equations of motion which generalize theLandau-Lifshitz and stress equations to allow for magneto-acoustic couplings to all orders in the fields at lowest order in the derivative expansion. We also include the symmetry breaking effects due to Zeeman, and Dzyaloshinsky-Moriya interactions. This effective theory is a toolbox for the study of magneto-elasticphenomena from first principles. As an example we use this theory to calculate the leading order contribution to the magnon decay width dueto its the decay into phonons. 
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  3. Abstract It is well known that asymptotically flat black holes in generalrelativity have a vanishing static, conservative tidal response. We show that this is a result of linearly realized symmetries governingstatic (spin 0,1,2)perturbations around black holes. The symmetries have a geometric origin: in the scalar case, they arise from the (E)AdS isometries of a dimensionally reduced black hole spacetime. Underlying the symmetries is a ladder structure which can be used to construct the full tower of solutions,and derive their general properties: (1) solutions that decay withradius spontaneously break the symmetries, and mustdiverge at the horizon;(2) solutions regular at the horizon respect the symmetries, andtake the form of a finite polynomial that grows with radius.Taken together, these two properties imply that static response coefficients — and in particular Love numbers — vanish. Moreover, property (1) is consistent with the absence of black holes with linear (perturbative) hair. We also discuss the manifestation of these symmetries in the effective point particle description of a black hole, showing explicitly that for scalar probesthe worldline couplings associated with a non-trivial tidal response and scalar hair must vanish in order for the symmetries to be preserved. 
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