Rotating stealth black holes with a cohomogeneity-1 metric
arXiv:2104.13834 · doi:10.1140/epjc/s10052-021-09449-2
Abstract
In five dimensions we consider a general shift symmetric and parity preserving scalar tensor action that contains up to second order covariant derivatives of the scalar field. A rotating stealth black hole solution is constructed where the metric is given by the Myers-Perry spacetime with equal momenta and the scalar field is identified with the Hamilton-Jacobi potential. This nontrivial scalar field has an extra hair associated with the rest mass of the test particle, and the solution does not require any fine tuning of the coupling functions of the theory. Interestingly enough, we show that the disformal transformation, generated by this scalar field, and with a constant degree of disformality, leaves invariant (up to diffeomorphisms) the Myers-Perry metric with equal momenta. This means that the hair of the scalar field, along with the constant disformality parameter, can be consistently absorbed into further redefinitions of the mass and of the single angular parameter of the disformed metric. These results are extended in higher odd dimensions with a Myers-Perry metric for which all the momenta are equal. The key of the invariance under disformal transformation of the metric is mainly the cohomogeneity-1 character of the Myers-Perry metric with equal momenta. Starting from this observation, we consider a general class of cohomogeneity-1 metrics in arbitrary dimension, and we list the conditions ensuring that this class of metrics remain invariant (up to diffeomorphisms) under a disformal transformation with a constant degree of disformality and with a scalar field with constant kinetic term. The extension to the Kerr-(A)dS case is also considered where it is shown that rotating stealth solutions may exist provided some fine tuning of the coupling functions of the scalar tensor theory.
arXiv comment19 pages (added new references)
References in corpus (37)
- Observation of Gravitational Waves from a Binary Black Hole Merger
- The Large N Limit of Superconformal Field Theories and Supergravity
- Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
- Black Holes in Higher Dimensions
- Rotation and the AdS/CFT correspondence
- Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
- Horndeski theory and beyond: a review
- Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian
- Dressing a black hole with a time-dependent Galileon
- Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
- Extended Scalar-Tensor Theories of Gravity
- General Kerr-NUT-AdS Metrics in All Dimensions
- Asymptotically flat black holes in Horndeski theory and beyond
- Quantum Radiation from a 5-Dimensional Rotating Black Hole
- Hamiltonian analysis of higher derivative scalar-tensor theories
- Healthy degenerate theories with higher derivatives
- An instability of higher-dimensional rotating black holes
- Exact black hole solutions in shift symmetric scalar-tensor theories
- Horndeski: beyond, or not beyond?
- Rotating Black Holes in Higher Order Gravity
- Stealth Scalar Field Overflying a 2+1 Black Hole
- Stability of a black hole and the speed of gravity waves within self-tuning cosmological models
- Gravitational Cheshire effect: Nonminimally coupled scalar fields may not curve spacetime
- Cosmological self-tuning and local solutions in generalized Horndeski theories
- Hairy black holes in DHOST theories: Exploring disformal transformation as a solution-generating method
- Lifshitz black holes with a time-dependent scalar field in Horndeski theory
- Hamiltonian vs stability and application to Horndeski theory
- On Rotating Black Holes in DHOST Theories
- General Relativity solutions with stealth scalar hair in quadratic higher-order scalar-tensor theories
- Disforming the Kerr metric
- Regular black holes via the Kerr-Schild construction in DHOST theories
- Black hole solutions in shift-symmetric degenerate higher-order scalar-tensor theories
- Relativistic stars in degenerate higher-order scalar-tensor theories after GW170817
- Compact objects in scalar-tensor theories after GW170817
- Black holes with a nonconstant kinetic term in degenerate higher-order scalar tensor theories
- Regular black holes and gravitational particle-like solutions in generic DHOST theories
- The sound of DHOST