We present a theorem which allows one to recognize and classify the asymptotic behavior and causal structure of McVittie metrics for different choices of scale factor, establishing whether a black hole or a pair black-white hole appears in the appropriate limit. Incidentally, the theorem also solves an apparent contradiction present in the literature over the causal structure analysis of the McVittie solution. Although the classification we present is not fully complete, we argue that this result covers most if not all physically relevant scenarios.
The cuscuton was introduced in the context of cosmology as a field with
infinite speed of propagation. It has been claimed to resemble Ho\v{r}ava
gravity in a certain limit, and it is a good candidate for an ether theory in
which a time-dependent cosmological constant appears naturally. The analysis of
its properties is usually performed in the Lagrangian framework, which makes
issues like the counting of its dynamical degrees of freedom less clear-cut.
Here we perform a Hamiltonian analysis of the theory. We show that the
homogeneous limit with local degrees of freedom has singular behavior in the
Hamiltonian framework. In other frames, it has an extra scalar degree of
freedom. The homogeneous field has regular behavior only if defined a priori as
a spatially constant field in a CMC foliation and contributing with a single
global degree of freedom. Lastly, we find conditions on the cuscuton potential
for the resulting lapse function to be non-zero throughout evolution.Comment: 10 page
We show that a single imperfect fluid can be used as a source to obtain a mass-varying black hole in an expanding universe. This approach generalizes the well-known McVittie spacetime, by allowing the mass to vary thanks to a novel mechanism based on the presence of a temperature gradient. This fully dynamical solution, which does not require phantom fields or fine-tuning, is a step forward in a new direction in the study of systems whose local gravitational attraction is coupled to the expansion of the universe. We present a simple but instructive example for the mass function and briefly discuss the structure of the apparent horizons and the past singularity.
We show that the generalized McVittie spacetime, which represents a black hole with timedependent mass in an expanding universe, is an exact solution of a subclass of the Horndeski family of actions. The heat-flow term responsible for the energy transfer between the black hole and the cosmological background is generated by the higher-order kinetic gravity braiding term, which generalizes the cuscuton action that yields McVittie with constant mass as a solution. Finally, we show that this generalization can be understood in terms of a duality realized by a disformal transformation, connecting the cuscuton field theory to an extension of the Horndeski action which does not propagate any scalar degrees of freedom. Our finding opens a novel window into studies of non-trivial interactions between dark energy/modified gravity theories and astrophysical black holes.
Both cosmological expansion and black holes are ubiquitous features of our observable Universe, yet exact solutions connecting the two have remained elusive. To this end, we study self-gravitating classical fields within dynamical spherically symmetric solutions that can describe black holes in an expanding universe. After attempting a perturbative approach of a known black-hole solution with scalar hair, we show by exact methods that the unique scalar field action with first-order derivatives that can source shear-free expansion around a black hole requires noncanonical kinetic terms. The resulting action is an incompressible limit of k-essence, otherwise known as the cuscuton theory, and the spacetime it describes is the McVittie metric. We further show that this solution is an exact solution to the vacuum Hořava-Lifshitz gravity with anisotropic Weyl symmetry.
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