Non Axisymmetric Relativistic Wind Accretion with Velocity Gradients onto a Rotating Black Hole

We model, for the first time, the Bondi-Hoyle accretion of a fluid with velocity gradients onto a Kerr black hole, by numerically solving the fully relativistic hydrodynamics equations. Specifically, we consider a supersonic ideal gas, which has velocity gradients perpendicular to the relative motion. We measure the mass and specific angular accretion rates to illustrate whether the fluid presents unstable patterns or not. The initial parameters, we consider in this work, are the velocity gradient $\epsilon_{v}$, the black hole spin $a$, the asymptotic Mach number ${\cal M}_{\infty}$ and adiabatic index $\Gamma$. We show that the flow accretion reaches a fairly stationary regime, unlike in the Newtonian case, where significant fluctuations of the mass and angular momentum accretion rates are found. On the other hand, we consider a special case where both density and velocity gradients of the fluid are taken into account. The spin of the black hole and the asymptotic Newtonian Mach number, for this case, are $a=0.98$ and ${\cal M}_{\infty}=1$, respectively. A kind of flip-flop behavior is found at the early times; nevertheless, the system also reaches a steady state.Comment: 11 pages, 20 figures, 1 table. Accepted for publication in MNRA

Relativistic Static Thin Disks of Polarized Matter

An infinite family of exact solutions of the electrovacuum Einstein-Maxwell equations is presented. The family is static, axially symmetric and describe thin disks composed by electrically polarized material in a conformastatic spacetime. The form of the conformastatic metric allows us to write down the metric functions and the electromagnetic potentials in terms of a solution of the Laplace equation. We find a general expression for the surface energy density of the disk, the pressure, the polarization vector, the electromagnetic fields and the velocity rotation for circular orbits. As an example, we present the first model of the family and show the behavior of the different physical variables.Comment: 7 pages, 4 figures, 70 and 70 Gravitation Fest, 28 September 2016, Cartagena, Colombi

On the conservation of the Jacobi integral in the post-Newtonian circular restricted three-body problem

In the present paper, using the first-order approximation of the $n$-body Lagrangian (derived on the basis of the post-Newtonian gravitational theory of Einstein, Infeld, and Hoffman), we explicitly write down the equations of motion for the planar circular restricted three-body problem. Additionally, with some simplified assumptions, we obtain two formulas for estimating the values of the mass/distance and velocity/speed of light ratios appropriate for a given post-Newtonian approximation. We show that the formulas derived in the present study, lead to a good numerical conservation of the Jacobi constant and allow for an approximate equivalence between the Lagrangian and Hamiltonian approaches at the same post-Newtonian order. Accordingly, the dynamics of the system is analyzed in terms of the Poincar\'e sections method and Lyapunov exponents, finding that for specific values of the Jacobi constant the dynamics can be either chaotic or regular. Our results suggest that the chaoticity of the post-Newtonian system is slightly in- creased in comparison with its Newtonian counterpart.Comment: 13 pages, 6 figures. This version has been substantially revised. Some new results were adde

Is the flip-flop behaviour of accretion shock cones on to black holes an effect of coordinates?

We study numerically the relativistic Bondi-Hoyle accretion of an ideal gas onto a Kerr fixed background space-time on the equatorial plane with s-lab symmetry. We use both Kerr-Schild (KS) and Boyer-Lindquist (BL) coordinates. We particularly focus on the study of the flip-flop motion of the shock cone formed when the gas is injected at supersonic speed. The development of the flip-flop instability of the shock cone in the relativistic regime was reported recently for the first time. We reproduce the flip-flop behaviour found in the past when BL coordinates are used, and perform similar numerical experiments using horizon penetrating KS coordinates. We find that when using KS coordinates the shock cone oscillates, however such oscillations are not of the flip-flop type and their amplitude decrease with resolution.Comment: 8 pages, 9 eps figures, accepted for publication in MNRA

Evolution of a mass-less test scalar field on Boson Stars space-times

We numerically solve the mass-less test scalar field equation on the space-time background of boson stars and black holes. In order to do so, we use a numerical domain that contains future null infinity. We achieve this construction using a scri-fixing conformal compactification technique based on hyperboloidal constant mean curvature foliations of the space-time and solve the conformally invariant wave equation. We present two results: the scalar field shows oscillations of the quasi- normal-mode type found for black holes only for boson star configurations that are compact, and no signs of tail decay is found in the parameter space we explored. Even though our results do not correspond to the master equation of perturbations of boson star solutions, they indicate that the parameter space of boson stars as black hole mimickers is restricted to compact configurations.Comment: 9 pages, 15 eps figures, revtex

CAFE: A New Relativistic MHD Code

We introduce CAFE, a new independent code designed to solve the equations of Relativistic ideal Magnetohydrodynamics (RMHD) in 3D. We present the standard tests for a RMHD code and for the Relativistic Hydrodynamics (RHD) regime since we have not reported them before. The tests include the 1D Riemann problems related to blast waves, head-on collision of streams and states with transverse velocities, with and without magnetic field, which is aligned or transverse, constant or discontinuous across the initial discontinuity. Among the 2D and 3D tests, without magnetic field we include the 2D Riemann problem, a one dimensional shock tube along a diagonal, the high speed Emery wind tunnel, the Kelvin-Helmholtz instability, a set of jets and a 3D spherical blast wave, whereas in the presence of a magnetic field we show the magnetic rotor, the cylindrical explosion, a case of Kelvin-Helmholtz instability and a 3D magnetic field advection loop. The code uses High Resolution Shock Capturing methods and we present the error analysis for a combination that uses the HLLE flux formula combined with linear, PPM and fifth order WENO reconstructors. We use the flux-CT and the divergence cleaning methods to control the divergence free magnetic field constraint.Comment: 30 pages, 110 png figures, 4 tables. Accepted for publication in the Astrophysical Journal Supplement. More numerical details, tests and additional reference

Pseudo-Newtonian planar circular restricted 3-body problem

We study the dynamics of the planar circular restricted three-body problem in the context of a pseudo-Newtonian approximation. By using the Fodor-Hoenselaers-Perj\'es procedure, we perform an expansion in the mass potential of a static massive spherical source up to the first non-Newtonian term, giving place to a gravitational potential that includes first-order general relativistic effects. With this result, we model a system composed by two pseudo-Newtonian primaries describing circular orbits around their common center of mass, and a test particle orbiting the system in the equatorial plane. The dynamics of the new system of equations is studied in terms of the Poincar\'e section method and the Lyapunov exponents, where the introduction of a new parameter $\epsilon$, allows us to observe the transition from the Newtonian to the pseudo-Newtonian regime. We show that when the Jacobian constant is fixed, a chaotic orbit in the Newtonian regime can be either chaotic or regular in the pseudo-Newtonian approach. As a general result, we find that most of the pseudo-Newtonian configurations are less stable than their Newtonian equivalent.Comment: 11 pages, 2 figures. Accepted for publication in Physics Letters A, In Pres

Bondi-Hoyle-Lyttleton accretion in the presence of small rigid bodies around a black hole

We study the relativistic Bondi-Hoyle-Lyttleton accretion onto a Schwarzschild black hole (BH), which is surrounded by rigid and small, randomly distributed, bodies. These bodies are idealized representations of substructure like stars passing close to the BH, bubbles created by stellar winds or cold clumps.We explore cases where the filling factor of these bodies is small. The flow is assumed to be adiabatic and move supersonically towards the black hole. The interaction with these rigid obstacles transforms ram pressure of the flow into thermal pressure through bow shocks, slowing down the flow and making the accreting gas turbulent. As a consequence, although the flow reaches a statistically-steady state, the accretion rate presents some variability. For a flow Mach number at infinity of 4, a few of these objects (5 - 10) are enough to increase the accretion rate about 50% over the accretion rate without bodies, even though the gas is adiabatic and the filling factor of the obstacles is small.Comment: 8 pages, 13 figures, 1 table. Accepted for publication in Monthly Notices of the Royal Astronomical Societ

PBH mass growth through radial accretion during the radiation dominated era

We model the radial accretion of radiation on Primordial Black Holes (PBH) by numerically solving Einstein's equations coupled to an ultrarelativistic ideal gas with equation of state $p=\rho/3$. We calculate the final mass of a black hole by the integration of the accreted radiation energy density during the leptonic era between $t\sim10^{-4}s$ to $t\sim 10^2s$ after the Big Bang. Our results indicate that small PBHs with initial masses between $10^{-4}$ to $1M_{\odot}$ may grow up to hundreds of solar masses, and thus can be SMBH seeds. On the other hand, PBHs formed at $t\sim 1s$ with initial mass between 900 and $\sim 980M_{\odot}$, by the time $t\sim 100s$ show masses of $10^4$ to $10^6M_{\odot}$ which are masses of seeds or already formed SMBHs. The fact that we consider only radial flow implies that our results work well as limiting cases, and it is expected that under more general scenarios the accretion rates may change significantly. Nevertheless we show that it is possible that SMBHs can be PBHs that grew due to the accretion of radiation.Comment: 15 pages, 6 eps figures. Accepted for publication in JCA

General Relativistic Razor-Thin Disks with Magnetically Polarized Matter

The origin of magnetic fields in the universe still remains unknown and constitutes one of the most intriguing questions in astronomy and astrophysics. Their significance is enormous since they have a strong influence on many astrophysical phenomena. In regards of this motivation, theoretical models of galactic disks with sources of magnetic field may contribute to understand the physics behind them. Inspired by this, we present a new family of analytical models for thin disks composed by magnetized material. The solutions are axially symmetric, conformastatic and are obtained by solving the Einstein-Maxwell Field Equations for continuum media without the test field approximation, and assuming that the sources are razor-thin disk of magnetically polarized matter. We find analytical expressions for the surface energy density, the pressure, the polarization vector, the electromagnetic fields, the mass and the rotational velocity for circular orbits, for two particular solutions. In each case, the energy-momentum tensor agrees with the energy conditions and also the convergence of the mass for all the solutions is proved. Since the solutions are well-behaved, they may be used to model astrophysical thin disks, and also may contribute as initial data in numerical simulations. In addition, the process to obtain the solutions is described in detail, which may be used as a guide to find solutions with magnetized material in General Relativity.Comment: 18 pages, 11 .pdf figures, Accepted for publication in General Relativity and Gravitatio