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Register a new userCosmological black holes from self-gravitating fields
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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 Hov{r}ava-Lifshitz gravity with anisotropic Weyl symmetry.
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We present a self-gravitating, analytic and globally regular Skyrmion solution of the Einstein-Skyrme system with winding number w = 1, in presence of a cosmological constant. The static spacetime metric is the direct product RxS3 and the Skyrmion is the self-gravitating generalization of the static hedgehog solution of Manton and Ruback with unit topological charge. This solution can be promoted to a dynamical one in which the spacetime is a cosmology of the Bianchi type-IX with time-dependent scale and squashing coefficients. Remarkably, the Skyrme equations are still identically satisfied for all values of these parameters. Thus, the complete set of field equations for the Einstein-Skyrme-Lambda system in the topological sector reduces to a pair of coupled, autonomous, nonlinear differential equations for the scale factor and a squashing coefficient. These equations admit analytic bouncing cosmological solutions in which the universe contracts to a minimum non-vanishing size, and then expands. A non-trivial byproduct of this solution is that a minor modification of the construction gives rise to a family of stationary, regular configurations in General Relativity with negative cosmological constant supported by an SU(2) nonlinear sigma model. These solutions represent traversable AdS wormholes with NUT parameter in which the only exotic matter required for their construction is a negative cosmological constant.
We address the question whether a medium featuring $p + rho = 0$, dubbed $Lambda$- medium, has to be necessarily a cosmological constant. By using effective field theory, we show that this is not the case for a class of media comprising perfect fluids, solids and special super solids, providing an explicit construction. The low energy excitations are non trivial and lensing, the growth of large scale structures can be used to clearly distinguish $Lambda$-media from a cosmological constant.
It has been well known since the 1970s that stationary black holes do not generically support scalar hair. Most of the no-hair theorems which support this depend crucially upon the assumption that the scalar field has no time dependence. Here we fill in this omission by ruling out the existence of stationary black hole solutions even when the scalar field may have time dependence. Our proof is fairly general, and in particular applies to non-canonical scalar fields and certain non-asymptotically flat spacetimes. It also does not rely upon the spacetime being a black hole.
We discuss the possibility of producing a significant fraction of dark matter in the form of primordial black holes in the context of the pre-big bang inflationary scenario. We take into account, to this purpose, the enhancement of curvature perturbations possibly induced by a variation of the sound-speed parameter $c_s$ during the string phase of high-curvature inflation. After imposing all relevant observational constraints, we find that the considered class of models is compatible with the production of a large amount of primordial black holes in the mass range relevant to dark matter, provided the sound-speed parameter is confined in a rather narrow range of values, $0.003 < c_s < 0.01$.
We investigate stationary, self-gravitating, magnetised disks (or tori) around black holes. The models are obtained by numerically solving the coupled system of the Einstein equations and the equations of ideal general-relativistic magnetohydrodynamics. The mathematical formulation and numerical aspects of our approach are similar to those reported in previous works modeling stationary self-gravitating perfect-fluid tori, but the inclusion of magnetic fields represents a new ingredient. Following previous studies of purely hydrodynamical configurations, we construct our models assuming Keplerian rotation in the disks and both spinning and spinless black holes. We focus on the case of a toroidal distribution of the magnetic field and build a large set of models corresponding to a wide range of values of the magnetisation parameter, starting with weakly magnetised disks and ending at configurations in which the magnetic pressure dominates over the thermal one. In all our models, the magnetic field affects the equilibrium structure of the torus mainly due to the magnetic pressure. In particular, an increasing contribution of the magnetic field shifts the location of the maximum of the rest-mass density towards inner regions of the disk. The total mass of the system and the angular momentum are affected by the magnetic field in a complex way, that depends on the black hole spin and the location of the inner radius of the disk. The non-linear dynamical stability of the solutions presented in this paper will be reported elsewhere.
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