arXiv subjects

Luciano Rezzolla

Publications and source records attributed to Luciano Rezzolla.

At least 271 records · Page 15Linked to original sources

arXiv2006

Challenging the paradigm of singularity excision in gravitational collapse

A paradigm deeply rooted in modern numerical relativity calculations prescribes the removal of those regions of the computational domain where a physical singularity may develop. We here challenge this paradigm by performing three-dimensional simulations of the collapse of uniformly rotating stars to black holes without excision. We show that this choice, combined with suitable gauge conditions and the use of minute numerical dissipation, improves dramatically the long-term stability of the evolutions. In turn, this allows for the calculation of the waveforms well beyond what previously possible, providing information on the black-hole ringing and setting a new mark on the present knowledge of the gravitational-wave emission from the stellar collapse to a rotating black hole.

gr-qc↗

arXiv2006

A hybrid approach to black hole perturbations from extended matter sources

We present a new method for the calculation of black hole perturbations induced by extended sources in which the solution of the nonlinear hydrodynamics equations is coupled to a perturbative method based on Regge-Wheeler/Zerilli and Bardeen-Press-Teukolsky equations when these are solved in the frequency domain. In contrast to alternative methods in the time domain which may be unstable for rotating black-hole spacetimes, this approach is expected to be stable as long as an accurate evolution of the matter sources is possible. Hence, it could be used under generic conditions and also with sources coming from three-dimensional numerical relativity codes. As an application of this method we compute the gravitational radiation from an oscillating high-density torus orbiting around a Schwarzschild black hole and show that our method is remarkably accurate, capturing both the basic quadrupolar emission of the torus and the excited emission of the black hole.

gr-qc↗

arXiv2006

A powerful hydrodynamic booster for relativistic jets

Velocities close to the speed of light are a robust observational property of the jets observed in microquasars and AGNs, and are expected to be behind much of the phenomenology of GRBs. Yet, the mechanism boosting relativistic jets to such large Lorentz factors is still essentially unknown. Building on recent general-relativistic, multidimensional simulations of progenitors of short GRBs, we discuss a new effect in relativistic hydrodynamics which can act as an efficient booster in jets. This effect is purely hydrodynamical and occurs when large velocities tangential to a discontinuity are present in the flow, yielding Lorentz factors $Γ\sim 10^2-10^3$ or larger in flows with moderate initial Lorentz factors. Although without a Newtonian counterpart, this effect can be explained easily through the most elementary hydrodynamical flow: i.e., a relativistic Riemann problem.

astro-ph↗

arXiv2006

On the iterated Crank-Nicolson for hyperbolic and parabolic equations in numerical relativity

The iterated Crank-Nicolson is a predictor-corrector algorithm commonly used in numerical relativity for the solution of both hyperbolic and parabolic partial differential equations. We here extend the recent work on the stability of this scheme for hyperbolic equations by investigating the properties when the average between the predicted and corrected values is made with unequal weights and when the scheme is applied to a parabolic equation. We also propose a variant of the scheme in which the coefficients in the averages are swapped between two corrections leading to systematically larger amplification factors and to a smaller numerical dispersion.

gr-qc↗

arXiv2005

Quasi-periodic Oscillations in the X-ray Light Curves from Relativistic Tori

We use a relativistic ray-tracing code to analyze the X-ray emission from a pressure-supported oscillating relativistic torus around a black hole. We show that a strong correlation exists between the {\it intrinsic} frequencies of the torus normal modes and the {\it extrinsic} frequencies seen in the observed light curve power spectrum. This correlation demonstrates the feasibility of the oscillating-torus model to explain the multiple peaks seen in black hole high-frequency quasi-periodic oscillations. Using an optically thin, monochromatic emission model, we also determine how a relativistically broadened emission line and the amplitude of the X-ray modulations are dependent on the observer's inclination angle and on the torus oscillation amplitudes. Observations of these features can provide important information about the torus as well as the black hole.

astro-ph↗

arXiv2005

Computations of primordial black hole formation

Results are presented from general relativistic numerical computations of primordial black-hole formation during the radiation-dominated era of the universe. Growing-mode perturbations are specified within the linear regime and their subsequent evolution is followed as they become nonlinear. We use a spherically symmetric Lagrangian code and study both super-critical perturbations, which go on to produce black holes, and sub-critical perturbations, for which the overdensity eventually disperses into the background medium. For super-critical perturbations, we confirm the results of previous work concerning scaling-laws but note that the threshold amplitude for a perturbation to lead to black-hole formation is substantially reduced when the initial conditions are taken to represent purely growing modes. For sub-critical cases, where an initial collapse is followed by a subsequent re-expansion, strong compressions and rarefactions are seen for perturbation amplitudes near to the threshold. We have also investigated the effect of including a significant component of vacuum energy and have calculated the resulting changes in the threshold and in the slope of the scaling law.

gr-qc↗

arXiv2004

Oscillations of vertically integrated relativistic tori -II. Axisymmetric modes in a Kerr spacetime

This is the second of a series of papers investigating the oscillation properties of relativistic, non-selfgravitating tori orbiting around black holes. Extending the work done in a Schwarzschild background, we here consider the axisymmetric oscillations of vertically integrated tori in a Kerr spacetime. The tori are modeled with a number of different non-Keplerian distributions of specific angular momentum and we discuss how the oscillation properties depend on these and on the rotation of the central black hole. We first consider a local analysis to highlight the relations between acoustic and epicyclic oscillations in a Kerr spacetime and subsequently perform a global eigenmode analysis to compute the axisymmetric p modes. In analogy with what found in a Schwarzschild background, these modes behave as sound waves that are modified by rotation and are globally trapped in the torus. For constant distributions of specific angular momentum, the eigenfrequencies appear in a sequence 2:3:4:... which is essentially independent of the size of the disc and of the black hole rotation. For non-constant distributions of angular momentum, on the other hand, the sequence depends on the properties of the disc and on the spin of the black hole, becoming harmonic for sufficiently large tori. We also comment on how p modes could explain the high frequency quasi-periodic oscillations observed in low-mass X-ray binaries with a black hole candidate and the properties of an equivalent model in Newtonian physics.

astro-ph↗

arXiv2004

Electromagnetic Fields in the Exterior of an Oscillating Relativistic Star -- I. General Expressions and application to a rotating magnetic dipole

Relativistic stars are endowed with intense electromagnetic fields but are also subject to oscillations of various types. We here investigate the impact that oscillations have on the electric and magnetic fields external to a relativistic star in vacuum. In particular, modelling the star as a relativistic polytrope with infinite conductivity, we consider the solution of the general relativistic Maxwell equations both in the vicinity of the stellar surface and far from it, once a perturbative velocity field is specified. In this first paper we present general analytic expressions that are not specialized to a particular magnetic field topology or velocity field. However, as a validating example and an astrophysically important application, we consider a dipolar magnetic field and the velocity field corresponding to the rotation of the misaligned dipole. Besides providing analytic expressions for the electromagnetic fields produced by this configuration, we calculate, for the first time, the general relativistic energy loss through dipolar electromagnetic radiation. We find that the widely used Newtonian expression under-estimates this loss by a factor of 2-6 depending on the stellar compactness. This correction could have important consequences in the study of the spin evolution of pulsars.

gr-qc↗

arXiv2003

Dynamics of thick discs around Schwarzschild-de Sitter black holes

We consider the effects of a cosmological constant on the dynamics of constant angular momentum discs orbiting Schwarzschild-de Sitter black holes. The motivation behind this study is to investigate whether the presence of a radial force contrasting the black hole's gravitational attraction can influence the occurrence of the runaway instability, a robust feature of the dynamics of constant angular momentum tori in Schwarzschild and Kerr spacetimes. In addition to the inner cusp near the black hole horizon through which matter can accrete onto the black hole, in fact, a positive cosmological constant introduces also an outer cusp through which matter can leave the torus without accreting onto the black hole. To assess the impact of this outflow on the development of the instability we have performed time-dependent and axisymmetric hydrodynamical simulations of equilibrium initial configurations in a sequence of background spacetimes of Schwarzschild-de Sitter black holes with increasing masses. The simulations have been performed with an unrealistic value for the cosmological constant which, however, yields sufficiently small discs to be resolved accurately on numerical grids and thus provides a first qualitative picture of the dynamics. The calculations, carried out for a wide range of initial conditions, show that the mass-loss from the outer cusp can have a considerable impact on the instability, with the latter being rapidly suppressed if the outflow is large enough.

gr-qc↗

arXiv2003

Mean-field dynamo action in protoneutron stars

We have investigated the turbulent mean-field dynamo action in protoneutron stars that are subject to convective and neutron finger instabilities. While the first one develops mostly in the inner regions of the star, the second one is favoured in the outer regions, where the Rossby number is much smaller and a mean-field dynamo action is more efficient. By solving the mean-field induction equation we have computed the critical spin period below which no dynamo action is possible and found it to be ~1 s for a wide range of stellar models. Because this critical period is substantially longer than the characteristic spin period of very young pulsars, we expect that a mean-field dynamo will be effective for most protoneutron stars.

astro-ph↗

arXiv2003

A New Simple Model for High Frequency Quasi Periodic Oscillations in Black Hole Candidates

Observations of X-ray emissions from binary systems have long since been considered important tools to test General Relativity in strong-field regimes. The high frequency quasi-periodic oscillations (HFQPOs) observed in binaries containing a black hole candidate, in particular, have been proposed as a means to measure more directly the black hole properties such as its mass and spin. Numerous models have been suggested to explain the HFQPOs and the rich phenomenology accompanying them. Many of these models rest on a number of assumptions and are at times in conflict with the most recent observations. We here propose a new, simple model in which the HFQPOs result from basic $p$-mode oscillations of a small accretion torus orbiting close to the black hole. We show that within this model the key properties of the HFQPOs can be explained simply, given a single reasonable assumption. We also discuss observational tests that can falsify the model.

astro-ph↗

arXiv2003

Oscillations of vertically integrated relativistic tori -- I. Axisymmetric modes in a Schwarzschild spacetime

This is the first of a series of papers investigating the oscillation properties of relativistic, non-selfgravitating tori orbiting around a black hole. In this initial paper we consider the axisymmetric oscillation modes of a torus constructed in a Schwarzschild spacetime. To simplify the treatment and make it as analytical as possible, we build our tori with vertically integrated and vertically averaged quantities. Our investigation progresses by steps. We first consider a local analysis in Newtonian gravity and determine the properties of acoustic wave propagation within these objects, as well as the relations between acoustic and epicyclic oscillations. Next, we extend the local analysis to a general relativistic framework. Finally, we perform a global analysis and determine both the eigenfunctions and the eigenfrequencies of the axisymmetric oscillations corresponding to the p modes of relativistic tori. These behave as sound waves globally trapped in the torus and possess eigenfrequencies appearing in the simple sequence 2:3:4:..., independently of the distribution of angular momentum considered. The properties of the modes investigated here are in good agreement with those observed in recent numerical simulations and could have a number of different applications. In X-ray binary systems containing a black hole candidate, for instance, p-mode oscillations could be used to explain the harmonic relations in the high frequency quasi-periodic oscillations observed. In systems comprising a massive torus orbiting a black hole, on the other hand, p-mode oscillations could be used to explain the development or the suppression of the runaway instability.

astro-ph↗

arXiv2003

Linear and Nonlinear Dynamics of Relativistic Tori

I present results of two-dimensional general relativistic hydrodynamical simulations of constant specific angular momentum tori orbiting around a Schwarzschild black hole. After introducing axisymmetric perturbations, these objects either become unstable to the runaway instability or respond with regular oscillations. The latter, in particular, are responsible for quasi-periodic bursts of accretion onto the black hole as well as for the emission of intense gravitational radiation, with signal-to-noise ratios at the detector which are comparable or even larger than the typical ones expected in stellar-core collapse.

gr-qc↗

arXiv2003

Gravitational Waves from Perturbed Black Holes and Relativistic Stars

These lectures aim at providing an introduction to the properties of gravitational waves and in particular to those gravitational waves that are expected as a consequence of perturbations of black holes and neutron stars. Imprinted in the gravitational radiation emitted by these objects is, in fact, a wealth of physical information. In the case of black holes, a detailed knowledge of the gravitational radiation emitted as a response to perturbations will reveal us important details about their mass and spin, but also about the fundamental properties of the event horizon. In the case of neutron stars, on the other hand, this information can provide a detailed map of their internal structure and tell us about the equation of state of matter at very high density, thus filling-in a gap in energies and densities that cannot be investigated by experiments in terrestrial laboratories.

gr-qc↗

arXiv2002

Frequencies of f-modes in differentially rotating relativistic stars and secular stability limits

We have computed the eigenfrequencies of f-modes for a constant-rest-mass sequences of rapidly rotating relativistic inviscid stars in differential rotation. The frequencies have been calculated neglecting the metric perturbations (the relativistic Cowling approximation) and expressed as a function of the ratio between the rotational kinetic energy and the absolute value of the gravitational energy of the stellar model beta=T/|W|. The zeros and the end-points of these sequences mark respectively the onset of the secular instability driven by gravitational radiation-reaction and the maximum value of beta at which an equilibrium model exists. In differentially rotating stars the secular stability limits appear at a beta larger than those found for uniformly rotating stars. Differential rotation, on the other hand, also allows for the existence of equilibrium models at values of beta larger than those for uniformly rotating stars, moving the end-point of the sequences to larger beta. As a result, for some degrees of differential rotation, the onset of the secular instability for f-modes is generally favoured by the presence of differential rotation.

gr-qc↗

arXiv2001

General Relativistic Rossby-Haurwitz waves of a slowly and differentially rotating fluid shell

We show that, at first order in the angular velocity, the general relativistic description of Rossby-Haurwitz waves (the analogues of r-waves on a thin shell) can be obtained from the corresponding Newtonian one after a coordinate transformation. As an application, we show that the results recently obtained by Rezzolla and Yoshida (2001) in the analysis of Newtonian Rossby-Haurwitz waves of a slowly and differentially rotating, fluid shell apply also in General Relativity, at first order in the angular velocity.

gr-qc↗

arXiv2001

Properties of r modes in rotating magnetic neutron stars. I. Kinematic Secular Effects and Magnetic Evolution Equations

The instability of r-mode oscillations in rapidly rotating neutron stars has attracted attention as a potential mechanism for producing high frequency, almost periodic gravitational waves. The analyses carried so far have shown the existence of these modes and have considered damping by shear and bulk viscosity. However, the magnetohydrodynamic coupling of the modes with a stellar magnetic field and its role in the damping of the instability has not been fully investigated yet. Following our introductory paper (Rezzolla, Lamb and Shapiro 2000), we here discuss in more detail the existence of secular higher-order kinematical effects which will produce toroidal fluid drifts. We also define the sets of equations that account for the time evolution of the magnetic fields produced by these secular velocity fields and show that the magnetic fields produced can reach equipartition in less than a year. The full numerical calculations as well as the evaluation of the impact of strong magnetic fields on the onset and evolution of the r-mode instability will be presented in a companion paper.

gr-qc↗

arXiv2001

Properties of r modes in rotating magnetic neutron stars. II. Evolution of the r modes and stellar magnetic field

The evolution of the r-mode instability is likely to be accompanied by secular kinematic effects which will produce differential rotation with large scale drifts of fluid elements, mostly in the azimuthal direction. As first discussed by Rezzolla, Lamb and Shapiro 2000, the interaction of these secular velocity fields with a pre-existing neutron star magnetic field could result in the generation of intense and large scale toroidal fields. Following their derivation in the companion paper, we here discuss the numerical solution of the evolution equations for the magnetic field. The values of the magnetic fields obtained in this way are used to estimate the conditions under which the r-mode instability might be prevented or suppressed. We also assess the impact of the generation of large magnetic fields on the gravitational wave detectability of r-mode unstable neutron stars. Our results indicate that the signal to noise ratio in the detection of gravitational waves from the r-mode instability might be considerably decreased if the latter develops in neutron stars with initial magnetic fields larger than 10^10 G.

gr-qc↗