Relativistic star perturbations in Horndeski theories with a gauge-ready formulation

Understand

We present a general framework for studying the relativistic star perturbations on a static and spherically symmetric background in full Horndeski theories.

• We take a perfect fluid into account as a form of the Schutz-Sorkin action.
• Our formulation is sufficiently versatile in that the second-order actions of perturbations in odd- and even-parity sectors are derived without choosing particular gauge conditions, so they can be used for any convenient gauges at hand.
• The odd-parity sector contains one dynamical gravitational degree of freedom coupled to a time-independent four velocity of the fluid.