Ricardo Becerril

Numerical studies of Φ2-oscillatons

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.

Exact solutions of SL(N,R)-invariant chiral equations one- and two-dimensional subspaces

A methodology for integrating the chiral equation (ρg,zg−1),z+ (ρg,zg−1),z=0 is developed, when g is a matrix of the SL(N,R) group. In this work the ansatze g=g(λ) where λ satisfy the Laplace equation and g=g(λ,τ) are made, where λ and τ are geodesic parameters of an arbitrary Riemannian space. This reduces the chiral equation to an algebraic problem and g can be obtained by integrating a homogeneous linear system of differential equations. As an example of the first ansatz, all the matrices for N=3 and one example for N=8, which corresponds to exact solutions of the d=5 and d=10 Kaluza–Klein theory, respectively are given. For the second ansatz the chiral equations are integrated for the subgroups SL(2,R), SO(2,1R), Sp(2,R), and the Abelian subgroups.

Numerical studies of Phi^2-Oscillatons

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.

Numerical studies of ?2-oscillatons

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.

Obtaining mass parameters of compact objects from redshifts and blueshifts emitted by geodesic particles around them

The mass parameters of compact objects such as Boson Stars, Schwarzschild, Reissner Nordstrom and Kerr black holes are computed in terms of the measurable redshift-blueshift (zred, zblue) of photons emitted by particles moving along circular geodesics around these objects and the radius of their orbits. We found bounds for the values of (zred, zblue) that may be observed. For the case of Kerr black hole, recent observational estimates of SrgA\* mass and rotation parameter are employed to determine the corresponding values of these red-blue shifts.

Evolution and stability ?4 oscillatons

We solve numerically the Einstein–Klein–Gordon (EKG) system, assuming spherical symmetry, for a real scalar field endowed with a quartic self-interaction potential, and obtain the so-called oscillatons: oscillating soliton stars. We obtain the equilibrium configurations for Φ4oscillatons. Also, we analyze numerically the evolution of the EKG equations to study the stability of such oscillatons. We present the influence of the quartic potential on the behavior of both the stable (S-oscillatons) and unstable (U-oscillatons) branches, under the influence of small and large radial perturbations.

An axially symmetric scalar field as a gravitational lens

The gravitational lensing due to an axially symmetric lens with a minimally coupled scalar field is considered. Comparison is made with the case of a spherically symmetric lens analysed previously in the literature, and a different dependence of the image positions on the ‘scalar charge’ is found. In particular, while the formation of four images, two Einstein rings and one radial critical curve (RCC) is possible for different configurations with both types of lenses, their positions are different from one metric to the other. Nevertheless, these differences are very small and, even if such configurations are ever observed, it seems to be very difficult to distinguish between the spacetimes studied here. PACS number: 0420

Evolution of boson-fermion stars

The boson-fermion stars can be modeled with a complex scalar field coupled minimally to a perfect fluid (i.e., without viscosity and non-dissipative). We present a study of these solutions and their dynamical evolution by solving numerically the Einstein-Klein-Gordon-Hydrodynamic (EKGHD) system. It is shown that stable configurations exist, but stability of general configurations depends finely upon the number of bosons and fermions.

Evolution and stability Φ4oscillatons

We solve numerically the Einstein–Klein–Gordon (EKG) system, assuming spherical symmetry, for a real scalar field endowed with a quartic self-interaction potential, and obtain the so-called oscillatons: oscillating soliton stars. We obtain the equilibrium configurations for Φ4oscillatons. Also, we analyze numerically the evolution of the EKG equations to study the stability of such oscillatons. We present the influence of the quartic potential on the behavior of both the stable (S-oscillatons) and unstable (U-oscillatons) branches, under the influence of small and large radial perturbations.

Evolution and stability Φ4 oscillatons

We solve numerically the Einstein–Klein–Gordon (EKG) system, assuming spherical symmetry, for a real scalar field endowed with a quartic self-interaction potential, and obtain the so-called oscillatons: oscillating soliton stars. We obtain the equilibrium configurations for Φ4oscillatons. Also, we analyze numerically the evolution of the EKG equations to study the stability of such oscillatons. We present the influence of the quartic potential on the behavior of both the stable (S-oscillatons) and unstable (U-oscillatons) branches, under the influence of small and large radial perturbations.