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Quadratic DHOST theories revisited

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arxiv 2012.10218 v1 pith:A2VIHN2U submitted 2020-12-18 gr-qc astro-ph.COhep-th

Quadratic DHOST theories revisited

classification gr-qc astro-ph.COhep-th
keywords theoriesdhostquadraticscalarfieldlagrangiantermdegenerate
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We present a novel and remarkably simple formulation of degenerate higher-order scalar-tensor (DHOST) theories whose Lagrangian is quadratic in second derivatives of some scalar field. Using disformal transformations of the metric, we identify a special "frame" (or metric) for which the Lagrangian of quadratic DHOST theories reduces to the usual Einstein-Hilbert term plus a few terms that depend on simple geometric quantities characterizing the uniform scalar field hypersurfaces. In particular, for quadratic DHOST theories in the physically interesting class Ia, the Lagrangian simply consists of the Einstein-Hilbert term plus a term proportional to the three-dimensional scalar curvature of the uniform scalar field hypersurfaces. The classification of all quadratic DHOST theories becomes particularly transparent in this geometric reformulation, which also applies to scalar-tensor theories that are degenerate only in the unitary gauge.

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Cited by 1 Pith paper

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  1. Radial Perturbations of Black Holes in DHOST Theories

    gr-qc 2026-06 unverdicted novelty 6.0

    Radial perturbations of black holes with primary hair in DHOST theories are rewritten as a flat radial wave equation whose positive self-adjoint extension guarantees stability of the monopole mode.