arXiv subjects
Publications and source records attributed to Pablo Laguna.
We summarize the results of an investigation into the late time behavior of massless scalar fields propagating on spherically symmetric black hole spacetimes with a non-zero cosmological constant. The compatibility of these results with the `minimal requirement' of Brady and Poisson is commented upon.
We present results of numerical studies of the Landau-Ginzburg dynamics of the order parameter in one-dimensional models inspired by the condensed matter analogues of cosmological phase transitions. The main goal of our work is to show that, as proposed by one of us \cite{Zurek85b}, the density of the frozen-out topological defects is set by the competition between the quench rate --- the rate at which the phase transition is taking place --- and the relaxation rate of the order parameter. In other words, the characteristic domain size, which determines the typical separation of topological defects in the new broken symmetry phase, is of the order of the correlation length at the instant at which the relaxation timescale of the order parameter equals the time remaining to the phase transition. In estimating the size of topological domains, this scenario shares with the original Kibble mechanism the idea that topological defects will form along the boundaries of independently selected regions of the new broken symmetry vacuum. However, it derives the size of such domains from non-equilibrium aspects of the transition (quench rate), as opposed to Kibble's original proposal in which their size was estimated from the Ginzburg temperature above which thermally activated symmetry restoration can occur.
We present a study of the gravitational time delay of arrival of signals from binary pulsar systems with rotating black hole companions. In particular, we investigate the strength of this effect (Shapiro delay) as a function of the inclination, eccentricity and period of the orbit, as well as the mass and angular momentum of the black hole. This study is based on direct numerical integration of null geodesics in a Kerr background geometry. We find that, for binaries with sufficiently high orbital inclinations ($> 89^o$) and compact companion masses $> 10 M_\odot$, the effect arising from the rotation of the black hole in the system amounts to a microsecond-level variation of the arrival times of the pulsar pulses. If measurable, this variation could provide a unique signature for the presence of a rotating black hole in a binary pulsar system.
We perform the numerical field evolution for the collision of two Abelian type I cosmic strings. We present evidence that, for collisions at small but characteristic relative velocities and angles, these cosmic strings do not exchange ends and separate. Rather, local higher winding number bound states are formed close to the collision point, which promote multiple local scatterings at right angles and prevent intercommutation from happening. This constitutes the simplest example of the breakdown of the intercommutation rule, usually assumed in the construction of effective models for cosmic string network evolution.
We study the evolution of massless scalar waves propagating on spherically symmetric spacetimes with a non-zero cosmological constant. Considering test fields on both Schwarzschild-de Sitter and Reissner-Nordstrom-de Sitter backgrounds, we demonstrate the existence of exponentially decaying tails at late times. Interestingly the l=0 mode asymptotes to a non-zero value, contrasting the asymptotically flat situation. We also compare these results, for l=0, with a numerical integration of the Einstein-Scalar field equations, finding good agreement between the two. Finally, the significance of these results to the study of the Cauchy horizon stability in black hole-de Sitter spacetimes is discussed.
The Cauchy+characteristic matching (CCM) problem for the scalar wave equation is investigated in the background geometry of a Schwarzschild black hole. Previously reported work developed the CCM framework for the coupled Einstein-Klein-Gordon system of equations, assuming a regular center of symmetry. Here, the time evolution after the formation of a black hole is pursued, using a CCM formulation of the governing equations perturbed around the Schwarzschild background. An extension of the matching scheme allows for arbitrary matching boundary motion across the coordinate grid. As a proof of concept, the late time behavior of the dynamics of the scalar field is explored. The power-law tails in both the time-like and null infinity limits are verified.
Numerical study of order parameter dynamics in the course of second order (Landau-Ginzburg) symmetry breaking transitions shows that the density of topological defects, kinks, is proportional to the fourth root of the rate of the quench. This confirms the more general theory of domain-size evolution in the course of symmetry breaking transformations proposed by one of us \cite{Zurek85}. Using these ideas, it is possible to compute the density of topological defects from the quench timescale and from the equilibrium scaling of the correlation length and relaxation time near the critical point.
A Cauchy-characteristic initial value problem for the Einstein-Klein-Gordon system with spherical symmetry is presented. Initial data are specified on the union of a space-like and null hypersurface. The development of the data is obtained with the combination of a constrained Cauchy evolution in the interior domain and a characteristic evolution in the exterior, asymptotically flat region. The matching interface between the space-like and characteristic foliations is constructed by imposing continuity conditions on metric, extrinsic curvature and scalar field variables, ensuring smoothness across the matching surface. The accuracy of the method is established for all ranges of $M/R$, most notably, with a detailed comparison of invariant observables against reference solutions obtained with a calibrated, global, null algorithm.
We investigate the imprint of nonlinear matter condensations on the Cosmic Microwave Background (CMB) in $Ω_{0}<1$ cold dark matter (CDM) model universes. We consider simulation domains ranging from $120h^{-1}$ Mpc to $360h^{-1}$ Mpc in size. We concentrate on the secondary temperature anisotropies induced by time varying gravitational potentials occurring after decoupling. Specifically, we investigate the importance of the Rees-Sciama effect due to: (1) intrinsic changes in the gravitational potential of forming, nonlinear structures, (2) proper motion of nonlinear structures, and (3) late time decay of gravitational potential perturbations in open universes. CMB temperature anisotropies are obtained by numerically evolving matter inhomogeneities and CMB photons from an early, linear epoch ($z=100$) to the present, nonlinear epoch $(z=0)$. We test the dependence and relative importance of these secondary temperature anisotropies as a function of the scale of the underlying matter (voids, superclusters) and as a function of $Ω_{0}$. The results of the $Ω_{0}<1$ models are compared to a similarly executed $Ω_{0}=1.0$ simulation. We find that in low density models all three sources of anisotropy could be relevant and reach levels of $ΔT/T \sim 10^{-6}$. In particular, we find that for $Ω_{0}<1$ at large scales, secondary temperature anisotropies are dominated by the decaying potential.
We investigate the imprint of nonlinear matter condensations on the Cosmic Microwave Background (CMB) in an $Ω=1$, Cold Dark Matter (CDM) model universe. Temperature anisotropies are obtained by numerically evolving matter inhomogeneities and CMB photons from the beginning of decoupling until the present epoch. The underlying density field produced by the inhomogeneities is followed from the linear, through the weakly clustered, into the fully nonlinear regime. We concentrate on CMB temperature distortions arising from variations in the gravitational potentials of nonlinear structures. We find two sources of temperature fluctuations produced by time-varying potentials: (1) anisotropies due to intrinsic changes in the gravitational potentials of the inhomogeneities and (2) anisotropies generated by the peculiar, bulk motion of the structures across the microwave sky. Both effects generate CMB anisotropies in the range of $10^{-7} \siml ΔT/T \siml 10^{-6}$ on scales of $ \sim 1^{\circ}$. For isolated structures, anisotropies due to proper motion exhibit a dipole-like signature in the CMB sky that in principle could yield information on the transverse velocity of the structures.
The globular clusters that we observe in galaxies may be only a fraction of the initial population. Among the evolutionary influences on the population is the destruction of globular clusters by tidal forces as the cluster moves through the field of influence of a disk, a bulge, and/or a putative nuclear component (black hole). We have conducted a series of N-body simulations of globular clusters on bound and marginally bound orbits through potentials that include black hole and spheroidal components. The degree of concentration of the spheroidal component can have a considerable impact on the extent to which a globular cluster is disrupted. If half the mass of a $10^{10} \msun$ spheroid is concentrated within 800pc, then only black holes with masses $>10^9 \msun$ can have a significant tidal influence over that already exerted by the bulge. However, if the matter in the spheroidal component is not so strongly concentrated toward the center of the galaxy, a more modest central black hole (down to $10^8 \msun$) could have a dominant influence on the globular cluster distribution, particularly if many of the clusters were initially on highly radial orbits. Our simulations show that the stars that are stripped from a globular cluster follow orbits with roughly the same eccentricity as the initial cluster orbit, spreading out along the orbit like a ``string of pearls''. Since only clusters on close to radial orbits will suffer substantial disruption, the population of stripped stars will be on orbits of high eccentricity.
Smoothed particle hydrodynamics (SPH) discretization techniques are generalized to develop a method, smoothed particle interpolation (SPI), for solving initial value problems of systems of non-hydrodynamical nature. Under this approach, SPH is viewed as strictly an interpolation scheme and, as such, suitable for solving general hyperbolic and parabolic equations. The SPI method is tested on (1) the wave equation with inhomogeneous sound speed and (2) Burgers equation. The efficiency of SPI is studied by comparing SPI solutions to those obtained with standard finite difference methods. It is shown that the power of SPI arises when the smoothing particles are free to move.
We describe our 3-dimensional numerical relativity code for the evolution of inhomogeneous cosmologies. During the evolution the constraint equations are monitored but not solved. The code has been tested against perturbation theory with good results. We present some runs of inhomogeneous inflation with strongly inhomogeneous initial data.