We study a spherically symmetric fluctuation of scalar dark matter in the cosmos and show that it could be the dark matter in galaxies, provided that the scalar field has an exponential potential whose overall sign is negative and whose exponent is constrained observationally by the rotation velocities of galaxies. The local space-time of the fluctuation contains a three dimensional space-like hypersurface with surplus of angle.PACS numbers: 95.35.+d, 95.35.G.The existence of dark matter in the Universe has been firmly established by astronomical observations at very different length-scales, ranging from single galaxies, to clusters of galaxies, up to cosmological scale (see for example [1]). A large fraction of the mass needed to produce the observed dynamical effects in all these very different systems is not seen. At the galactic scale, the problem is clearly posed: The measurements of rotation curves (tangential velocities of objects) in spiral galaxies show that the coplanar orbital motion of gas in the outer parts of these galaxies keeps a more or less constant velocity up to several luminous radii [2], forming a radii independent curve in the outer parts of the rotational curves profile; a motion which does not correspond to the one due to the observed matter distribution, hence there must be present some type of dark matter causing the observed motion. The flat profile of the rotational curves is maybe the main feature observed in many galaxies. It is believed that the dark matter in galaxies has an almost spherical distribution which decays like 1/r 2 . With this distribution of some kind of matter it is possible to fit the rotational curves of galaxies quite well [3]. Nevertheless, the main question of the dark matter problem remains; which is the nature of the dark matter in galaxies? The problem is not easy to solve, it is not sufficient to find out an exotic particle which could exist in galaxies in the low energy regime of some theory. It is necessary to show as well, that this particle (baryonic or exotic) distributes in a very similar manner in all these galaxies, and finally, to give some reason for its existence in galaxies.In previous works it has been explored, with considerable success, the possibility that scalar fields could be the dark matter in spiral galaxies by assuming that the scalar dark matter distributes as an axially symmetric halo [4,5]. The idea of these works is to explore whether a scalar field can fluctuate along the history of the Universe and thus forming concentrations of scalar field density. If, for example, the scalar field evolves with a scalar field potential V (Φ) ∼ Φ 2 , the evolution of this scalar field will be similar to the evolution of a perfect fluid with equation of state p = 0, i.e., it would evolve as cold dark matter [6]. However, it is not clear whether a spherical scalar field fluctuation can serve as dark matter in galaxies. In this letter we show that this could be the case. We assume that the halo of a galaxy is a spherical fluctuation of cosmologica...

We show that in all theories in which black hole hair has been discovered the region with nontrivial structure of the nonlinear matter fields must extend beyond 3͞2 the horizon radius, independently of all other parameters present in the theory. We argue that this is a universal lower bound that applies in every theory where hair is present. This no short hair conjecture is then put forward as a more modest alternative to the original no hair conjecture, the validity of which now seems doubtful.

We present an exhaustive analysis of the numerical evolution of the Einstein-Klein-Gordon equations for the case of a real scalar field endowed with a quadratic self-interaction potential. The self-gravitating equilibrium configurations are called oscillatons and are close relatives of boson stars, their complex counterparts. Unlike boson stars, for which the oscillations of the two components of the complex scalar field are such that the spacetime geometry remains static, oscillatons give rise to a geometry that is time-dependent and oscillatory in nature. However, they can still be classified into stable (S-branch) and unstable (U-branch) cases. We have found that S-oscillatons are indeed stable configurations under small perturbations and typically migrate to other S-profiles when perturbed strongly. On the other hand, U-oscillatons are intrinsically unstable: they migrate to the S-branch if their mass is decreased and collapse to black holes if their mass is increased even by a small amount. The S-oscillatons can also be made to collapse to black holes if enough mass is added to them, but such collapse can be efficiently prevented by the gravitational cooling mechanism in the case of diluted oscillatons.PACS numbers: 04.25. Dm, 95.30.Sf, 95.35.+d, 98.62.Ai,

We give an exact spherically symmetric solution for the Einstein-scalar field system. The solution may be interpreted as an inhomogeneous dynamical scalar field cosmology. The spacetime has a timelike conformal Killing vector field and is asymptotically conformally flat. It also has black or white holelike regions containing trapped surfaces. We describe the properties of the apparent horizon and comment on the relevance of the solution to the recently discovered critical behaviour in scalar field collapse.

We study the evolution of a massive scalar field surrounding a Schwarzschild black hole and find configurations that can survive for arbitrarily long times, provided the black hole or the scalar field mass is small enough. In particular, both ultralight scalar field dark matter around supermassive black holes and axionlike scalar fields around primordial black holes can survive for cosmological times. Moreover, these results are quite generic in the sense that fairly arbitrary initial data evolve, at late times, as a combination of those long-lived configurations.