K-essence sources of Kerr-Schild spacetimes
arXiv:2504.14229 · doi:10.3390/universe11030100
Abstract
We extend a result by one of the authors, established for nonvacuum Einstein gravity, to minimally coupled k-essence scalar-tensor theories. First we prove that in order to source a Kerr-Schild type spacetime, the k-essence Lagrangian should be at most quadratic in the kinetic term. This is reduced to linear dependence when the Kerr-Schild null congruence is autoparallel. Finally, we show that requiring the solutions of the Einstein equations linearized in Kerr-Schild type perturbations to also solve the full nonlinear system of Einstein equations, selects once again k-essence scalar fields with Lagrangians linear in the kinetic term. The only other k-essence sharing the property of sourcing perturbative Kerr-Schild spacetimes which are also exact, is the scalar field constant along the integral curves of the Kerr-Schild congruence, with otherwise unrestricted Lagrangian.
20 pages
References in corpus (34)
- Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
- A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration
- Essentials of k-essence
- Testing General Relativity with Present and Future Astrophysical Observations
- From k-essence to generalised Galileons
- Dark Energy after GW170817: dead ends and the road ahead
- Strong constraints on cosmological gravity from GW170817 and GRB 170817A
- Dark Energy after GW170817 and GRB170817A
- Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
- Imperfect Dark Energy from Kinetic Gravity Braiding
- Purely kinetic k-essence as unified dark matter
- Dilatonic ghost condensate as dark energy
- Dark energy in Horndeski theories after GW170817: A review
- Dust of Dark Energy
- Primordial black hole evolution in tensor-scalar cosmology
- Black Holes and Scalar Fields
- Speeding up the universe using dust with pressure
- Cosmic Black-Hole Hair Growth and Quasar OJ287
- Healing the cosmological constant problem during inflation through a unified quasi-quintessence matter field
- The correspondence between a scalar field and an effective perfect fluid
- Speed of gravitational waves and black hole hair
- Non-Existence of Black Holes with Non-Canonical Scalar Fields
- Gravitational collapse of k-essence
- Note on the thermodynamics and the speed of sound of a scalar field
- Gravitational Collapse for the K-essence Emergent Vaidya Spacetime
- K-essence Emergent Spacetime as Generalized Vaidya Geometry
- Evaporation of dynamical horizon with the Hawking temparature in the {\bf K-}essence emergent Vaidya spacetime
- Linear Einstein equations and Kerr-Schild maps
- Kerr-Schild metrics revisited I. The ground state
- Kerr-Schild metrics revisited II. The complete vacuum solution
- Kerr-Schild-Kundt Metrics in Generic Gravity Theories with Modified Horndeski Couplings
- Vacuum Kerr-Schild metrics generated by nontwisting congruences
- Minimally coupled scalar fields as imperfect fluids
- Lanczos equation on light-like hypersurfaces in a cosmologically viable class of kinetic gravity braiding theories