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# Approximately stealth black hole in higher-order scalar-tensor theories

Dec 2022

We investigate a generic quadratic higher-order scalar-tensor theory with ascordatura term, which is expected to provide a consistent perturbativedescription of stealth solutions with a timelike scalar field profile. In theDHOST subclass, exactly stealth solutions are known to yield perturbationsinfinitely strongly coupled and thus cannot be trusted. Beyond DHOST theorieswith the scordatura term, such as in ghost condensation and U-DHOST, we showthat stealth configurations cannot be realized as exact solutions but thosetheories instead admit approximately stealth solutions where the deviation fromthe exactly stealth configuration is controlled by the mass scale $M$ ofderivative expansion. The approximately stealth solution is time-dependent,which can be interpreted as the black hole mass growth due to the accretion ofthe scalar field. From observed astrophysical black holes, we put an upperbound on $M$ as $\hat{c}_{\rm D1}^{1/2} M\lesssim 2\times 10^{11}$ GeV, where$\hat{c}_{\rm D1}$ is a dimensionless parameter of order unity thatcharacterizes the scordatura term. As far as $M$ is sufficiently below theupper bound, the accretion is slow and the approximately stealth solutions canbe considered as stealth at astrophysical scales for all practical purposeswhile perturbations are weakly coupled all the way up to the cutoff $M$ and theapparent ghost is as heavy as or heavier than $M$.

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