Analytic nondegenerate shift-symmetric Horndeski theories admit no static spherical regular black holes with a time-independent scalar; the unique marginal nonanalytic completion is sGB, whose hairy solutions remain centrally singular.
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In Einstein-scalar-Maxwell theories, charged compact binaries produce gravitational waveforms containing a leading -1 post-Newtonian dipole correction controlled by one deviation parameter b.
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Static regular black holes in Horndeski theories: analytic no-go and nonanalytic obstructions
Analytic nondegenerate shift-symmetric Horndeski theories admit no static spherical regular black holes with a time-independent scalar; the unique marginal nonanalytic completion is sGB, whose hairy solutions remain centrally singular.
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Inspiral gravitational waveforms from charged compact binaries with scalar hair
In Einstein-scalar-Maxwell theories, charged compact binaries produce gravitational waveforms containing a leading -1 post-Newtonian dipole correction controlled by one deviation parameter b.