Luciano Rezzolla | Goethe-Universität Frankfurt am Main (original) (raw)
Papers by Luciano Rezzolla
Physical Review D, 2014
We probe the gravitational interaction of two black holes in the strong-field regime by computing... more We probe the gravitational interaction of two black holes in the strong-field regime by computing the scattering angle χ of hyperbolic-like, close binary-black-hole encounters as a function of the impact parameter. The fully general-relativistic result from numerical relativity is compared to two analytic approximations: post-Newtonian theory and the effective-one-body formalism. As the impact parameter decreases, so that black holes pass within a few times their Schwarzschild radii, we find that the post-Newtonian prediction becomes quite inaccurate, while the effective-one-body one keeps showing a good agreement with numerical results. Because we have explored a regime which is very different from the one considered so far with binaries in quasi-circular orbits, our results open a new avenue to improve analytic representations of the general-relativistic two-body Hamiltonian.
Physical Review D, 2015
Extending previous work by a number of authors, we have recently presented a new approach in whic... more Extending previous work by a number of authors, we have recently presented a new approach in which the detection of gravitational waves from merging neutron star binaries can be used to determine the equation of state of matter at nuclear density and hence the structure of neutron stars. In particular, after performing a large number of numerical-relativity simulations of binaries with nuclear equations of state, we have found that the post-merger emission is characterized by two distinct and robust spectral features. While the high-frequency peak was already shown to be associated with the oscillations of the hypermassive neutron star produced by the merger and to depend on the equation of state, we have highlighted that the low-frequency peak is related to the merger process and to the total compactness of the stars in the binary. This relation is essentially universal and provides a powerful tool to set tight constraints on the equation of state. We here provide additional information on the extensive analysis performed, illustrating the methods used, the tests considered, and the robustness of the results. We also discuss additional relations that can be deduced when exploring the data and how these correlate with various properties of the binary. Finally, we present a simple mechanical toy model that explains the main spectral features of the post-merger signal and can even reproduce analytically the complex waveforms emitted right after the merger. PACS numbers: 04.25.Dm, 04.25.dk, 04.30.Db, 04.40.Dg, 95.30.Lz, 95.30.Sf, 97.60.Jd
Physical Review X, 2014
commitID: 01ffd337f9a75416522dfe67ead791f8117ce229) (LIGO-P1300211-v1)
Physical Review Letters, 2014
Determining the equation of state of matter at nuclear density and hence the structure of neutron... more Determining the equation of state of matter at nuclear density and hence the structure of neutron stars has been a riddle for decades. We show how the imminent detection of gravitational waves from merging neutron star binaries can be used to solve this riddle. Using a large number of accurate numerical-relativity simulations of binaries with nuclear equations of state, we have found that the postmerger emission is characterized by two distinct and robust spectral features. While the high-frequency peak has already been associated with the oscillations of the hypermassive neutron star produced by the merger and depends on the equation of state, a new correlation emerges between the low-frequency peak, related to the merger process, and the compactness of the progenitor stars. More importantly, such a correlation is essentially universal, thus providing a powerful tool to set tight constraints on the equation of state. If the mass of the binary is known from the inspiral signal, the combined use of the two frequency peaks sets four simultaneous constraints to be satisfied. Ideally, even a single detection would be sufficient to select one equation of state over the others. We have tested our approach with simulated data and verified it works well for all the equations of state considered.
Physical Review D, 2014
ABSTRACT We extend the Wald solution to a black hole that is also boosted. More specifically, we ... more ABSTRACT We extend the Wald solution to a black hole that is also boosted. More specifically, we derive analytic solutions for the Maxwell equations for a rotating black hole moving at constant speed in an asymptotically uniform magnetic test field. By adopting Kerr-Schild coordinates we avoid singular behaviours at the horizon and obtain a complete description of the charge and current distributions in terms of the black-hole spin and boost. Using this solution, we compute the energy losses expected when charged particles are accelerated along the magnetic field lines, improving previous estimates that had to cope with singular electromagnetic fields on the horizon. When used to approximate the emission from binary black holes in a uniform magnetic field, our estimates match reasonably well those from numerical-relativity calculations in the force-free approximation.
Physical Review D, 2006
We present the first simulations in full General Relativity of the head-on collision between a ne... more We present the first simulations in full General Relativity of the head-on collision between a neutron star and a black hole of comparable mass. These simulations are performed through the solution of the Einstein equations combined with an accurate solution of the relativistic hydrodynamics equations via high-resolution shock-capturing techniques. The initial data is obtained by following the York-Lichnerowicz conformal decomposition with the assumption of time symmetry. Unlike other relativistic studies of such systems, no limitation is set for the mass ratio between the black hole and the neutron star, nor on the position of the black hole, whose apparent horizon is entirely contained within the computational domain. The latter extends over ∼ 400 M and is covered with six levels of fixed mesh refinement. Concentrating on a prototypical binary system with mass ratio ∼ 6, we find that although a tidal deformation is evident the neutron star is accreted promptly and entirely into the black hole. While the collision is completed before ∼ 300 M , the evolution is carried over up to ∼ 1700 M , thus providing time for the extraction of the gravitational-wave signal produced and allowing for a first estimate of the radiative efficiency of processes of this type.
Physical Review D, 2013
ABSTRACT We describe in detail the implementation of a simplified approach to radiative transfer ... more ABSTRACT We describe in detail the implementation of a simplified approach to radiative transfer in general relativity by means of the well-known neutrino leakage scheme (NLS). In particular, we carry out an extensive investigation of the properties and limitations of the NLS for isolated relativistic stars to a level of detail that has not been discussed before in a general-relativistic context. Although the numerous tests considered here are rather idealized, they provide a well-controlled environment in which to understand the relationship between the matter dynamics and the neutrino emission, which is important in order to model the neutrino signals from more complicated scenarios, such as binary neutron-star mergers. When considering nonrotating hot neutron stars we confirm earlier results of one-dimensional simulations, but also present novel results about the equilibrium properties and on how the cooling affects the stability of these configurations. In our idealized but controlled setup, we can then show that deviations from the thermal and weak-interaction equilibrium affect the stability of these models to radial perturbations, leading models that are stable in the absence of radiative losses, to a gravitational collapse to a black hole when neutrinos are instead radiated.
Physical Review D, 2006
The iterated Crank-Nicolson is a predictor-corrector algorithm commonly used in numerical relativ... more 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.
General Relativity, Cosmology and Astrophysics, 2014
The Astrophysical Journal, 2012
The Thirteenth Marcel Grossmann Meeting, 2014
The Astrophysical journal, Jan 10, 2000
We show that r-mode oscillations distort the magnetic fields of neutron stars and that their occu... more We show that r-mode oscillations distort the magnetic fields of neutron stars and that their occurrence is likely to be limited by this interaction. If the field is greater, similar1016(Omega/OmegaB) G, where Omega and OmegaB are the angular velocities of the star and at which mass shedding occurs, r-mode oscillations cannot occur. Much weaker fields will prevent gravitational radiation from exciting r-mode oscillations or will damp them on a relatively short timescale by extracting energy from the modes faster than gravitational-wave emission can pump energy into them. For example, a 1010 G poloidal magnetic field that threads the star's superconducting core is likely to prevent the l=2 mode from being excited unless Omega exceeds 0.35OmegaB. If Omega is larger than 0.35OmegaB initially, the l=2 mode may be excited but is likely to decay rapidly once Omega falls below 0.35OmegaB, which happens in less, similar15 days if the saturation amplitude is greater, similar0.1. The r-mod...
Astronomische Nachrichten, 2014
ABSTRACT Magnetic fields represent a crucial aspect of the physics and astrophysics of neutron st... more ABSTRACT Magnetic fields represent a crucial aspect of the physics and astrophysics of neutron stars. Despite its great relevance, the internal magnetic field configuration of neutron stars is very poorly constrained by the observations, and understanding its properties is a long-standing theoretical challenge. The investigation on the subject is focused on the search for those magnetic field geometries which are stable on several Alfv\`en timescales, thus constituting a viable description of neutron star interiors. Assesing the stability of a given magnetic field geometry is therefore an important part of this research. So far only simple configurations, such as the purely poloidal or purely toroidal ones, have been studied in detail in perturbation theory and, most recently, by means of nonlinear magnetohydrodynamic simulations. Here we review the basic results of the state-of-the-art general relativistic nonlinear studies, discussing the present status of the field and its future directions.
Physical Review D, 2015
Extending previous work by a number of authors, we have recently presented a new approach in whic... more Extending previous work by a number of authors, we have recently presented a new approach in which the detection of gravitational waves from merging neutron star binaries can be used to determine the equation of state of matter at nuclear density and hence the structure of neutron stars. In particular, after performing a large number of numerical-relativity simulations of binaries with nuclear equations of state, we have found that the post-merger emission is characterized by two distinct and robust spectral features. While the high-frequency peak was already shown to be associated with the oscillations of the hypermassive neutron star produced by the merger and to depend on the equation of state, we have highlighted that the low-frequency peak is related to the merger process and to the total compactness of the stars in the binary. This relation is essentially universal and provides a powerful tool to set tight constraints on the equation of state. We here provide additional information on the extensive analysis performed, illustrating the methods used, the tests considered, and the robustness of the results. We also discuss additional relations that can be deduced when exploring the data and how these correlate with various properties of the binary. Finally, we present a simple mechanical toy model that explains the main spectral features of the post-merger signal and can even reproduce analytically the complex waveforms emitted right after the merger. PACS numbers: 04.25.Dm, 04.25.dk, 04.30.Db, 04.40.Dg, 95.30.Lz, 95.30.Sf, 97.60.Jd
Physical Review D, 2014
We probe the gravitational interaction of two black holes in the strong-field regime by computing... more We probe the gravitational interaction of two black holes in the strong-field regime by computing the scattering angle χ of hyperbolic-like, close binary-black-hole encounters as a function of the impact parameter. The fully general-relativistic result from numerical relativity is compared to two analytic approximations: post-Newtonian theory and the effective-one-body formalism. As the impact parameter decreases, so that black holes pass within a few times their Schwarzschild radii, we find that the post-Newtonian prediction becomes quite inaccurate, while the effective-one-body one keeps showing a good agreement with numerical results. Because we have explored a regime which is very different from the one considered so far with binaries in quasi-circular orbits, our results open a new avenue to improve analytic representations of the general-relativistic two-body Hamiltonian.
Physical Review D, 2015
Extending previous work by a number of authors, we have recently presented a new approach in whic... more Extending previous work by a number of authors, we have recently presented a new approach in which the detection of gravitational waves from merging neutron star binaries can be used to determine the equation of state of matter at nuclear density and hence the structure of neutron stars. In particular, after performing a large number of numerical-relativity simulations of binaries with nuclear equations of state, we have found that the post-merger emission is characterized by two distinct and robust spectral features. While the high-frequency peak was already shown to be associated with the oscillations of the hypermassive neutron star produced by the merger and to depend on the equation of state, we have highlighted that the low-frequency peak is related to the merger process and to the total compactness of the stars in the binary. This relation is essentially universal and provides a powerful tool to set tight constraints on the equation of state. We here provide additional information on the extensive analysis performed, illustrating the methods used, the tests considered, and the robustness of the results. We also discuss additional relations that can be deduced when exploring the data and how these correlate with various properties of the binary. Finally, we present a simple mechanical toy model that explains the main spectral features of the post-merger signal and can even reproduce analytically the complex waveforms emitted right after the merger. PACS numbers: 04.25.Dm, 04.25.dk, 04.30.Db, 04.40.Dg, 95.30.Lz, 95.30.Sf, 97.60.Jd
Physical Review X, 2014
commitID: 01ffd337f9a75416522dfe67ead791f8117ce229) (LIGO-P1300211-v1)
Physical Review Letters, 2014
Determining the equation of state of matter at nuclear density and hence the structure of neutron... more Determining the equation of state of matter at nuclear density and hence the structure of neutron stars has been a riddle for decades. We show how the imminent detection of gravitational waves from merging neutron star binaries can be used to solve this riddle. Using a large number of accurate numerical-relativity simulations of binaries with nuclear equations of state, we have found that the postmerger emission is characterized by two distinct and robust spectral features. While the high-frequency peak has already been associated with the oscillations of the hypermassive neutron star produced by the merger and depends on the equation of state, a new correlation emerges between the low-frequency peak, related to the merger process, and the compactness of the progenitor stars. More importantly, such a correlation is essentially universal, thus providing a powerful tool to set tight constraints on the equation of state. If the mass of the binary is known from the inspiral signal, the combined use of the two frequency peaks sets four simultaneous constraints to be satisfied. Ideally, even a single detection would be sufficient to select one equation of state over the others. We have tested our approach with simulated data and verified it works well for all the equations of state considered.
Physical Review D, 2014
ABSTRACT We extend the Wald solution to a black hole that is also boosted. More specifically, we ... more ABSTRACT We extend the Wald solution to a black hole that is also boosted. More specifically, we derive analytic solutions for the Maxwell equations for a rotating black hole moving at constant speed in an asymptotically uniform magnetic test field. By adopting Kerr-Schild coordinates we avoid singular behaviours at the horizon and obtain a complete description of the charge and current distributions in terms of the black-hole spin and boost. Using this solution, we compute the energy losses expected when charged particles are accelerated along the magnetic field lines, improving previous estimates that had to cope with singular electromagnetic fields on the horizon. When used to approximate the emission from binary black holes in a uniform magnetic field, our estimates match reasonably well those from numerical-relativity calculations in the force-free approximation.
Physical Review D, 2006
We present the first simulations in full General Relativity of the head-on collision between a ne... more We present the first simulations in full General Relativity of the head-on collision between a neutron star and a black hole of comparable mass. These simulations are performed through the solution of the Einstein equations combined with an accurate solution of the relativistic hydrodynamics equations via high-resolution shock-capturing techniques. The initial data is obtained by following the York-Lichnerowicz conformal decomposition with the assumption of time symmetry. Unlike other relativistic studies of such systems, no limitation is set for the mass ratio between the black hole and the neutron star, nor on the position of the black hole, whose apparent horizon is entirely contained within the computational domain. The latter extends over ∼ 400 M and is covered with six levels of fixed mesh refinement. Concentrating on a prototypical binary system with mass ratio ∼ 6, we find that although a tidal deformation is evident the neutron star is accreted promptly and entirely into the black hole. While the collision is completed before ∼ 300 M , the evolution is carried over up to ∼ 1700 M , thus providing time for the extraction of the gravitational-wave signal produced and allowing for a first estimate of the radiative efficiency of processes of this type.
Physical Review D, 2013
ABSTRACT We describe in detail the implementation of a simplified approach to radiative transfer ... more ABSTRACT We describe in detail the implementation of a simplified approach to radiative transfer in general relativity by means of the well-known neutrino leakage scheme (NLS). In particular, we carry out an extensive investigation of the properties and limitations of the NLS for isolated relativistic stars to a level of detail that has not been discussed before in a general-relativistic context. Although the numerous tests considered here are rather idealized, they provide a well-controlled environment in which to understand the relationship between the matter dynamics and the neutrino emission, which is important in order to model the neutrino signals from more complicated scenarios, such as binary neutron-star mergers. When considering nonrotating hot neutron stars we confirm earlier results of one-dimensional simulations, but also present novel results about the equilibrium properties and on how the cooling affects the stability of these configurations. In our idealized but controlled setup, we can then show that deviations from the thermal and weak-interaction equilibrium affect the stability of these models to radial perturbations, leading models that are stable in the absence of radiative losses, to a gravitational collapse to a black hole when neutrinos are instead radiated.
Physical Review D, 2006
The iterated Crank-Nicolson is a predictor-corrector algorithm commonly used in numerical relativ... more 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.
General Relativity, Cosmology and Astrophysics, 2014
The Astrophysical Journal, 2012
The Thirteenth Marcel Grossmann Meeting, 2014
The Astrophysical journal, Jan 10, 2000
We show that r-mode oscillations distort the magnetic fields of neutron stars and that their occu... more We show that r-mode oscillations distort the magnetic fields of neutron stars and that their occurrence is likely to be limited by this interaction. If the field is greater, similar1016(Omega/OmegaB) G, where Omega and OmegaB are the angular velocities of the star and at which mass shedding occurs, r-mode oscillations cannot occur. Much weaker fields will prevent gravitational radiation from exciting r-mode oscillations or will damp them on a relatively short timescale by extracting energy from the modes faster than gravitational-wave emission can pump energy into them. For example, a 1010 G poloidal magnetic field that threads the star's superconducting core is likely to prevent the l=2 mode from being excited unless Omega exceeds 0.35OmegaB. If Omega is larger than 0.35OmegaB initially, the l=2 mode may be excited but is likely to decay rapidly once Omega falls below 0.35OmegaB, which happens in less, similar15 days if the saturation amplitude is greater, similar0.1. The r-mod...
Astronomische Nachrichten, 2014
ABSTRACT Magnetic fields represent a crucial aspect of the physics and astrophysics of neutron st... more ABSTRACT Magnetic fields represent a crucial aspect of the physics and astrophysics of neutron stars. Despite its great relevance, the internal magnetic field configuration of neutron stars is very poorly constrained by the observations, and understanding its properties is a long-standing theoretical challenge. The investigation on the subject is focused on the search for those magnetic field geometries which are stable on several Alfv\`en timescales, thus constituting a viable description of neutron star interiors. Assesing the stability of a given magnetic field geometry is therefore an important part of this research. So far only simple configurations, such as the purely poloidal or purely toroidal ones, have been studied in detail in perturbation theory and, most recently, by means of nonlinear magnetohydrodynamic simulations. Here we review the basic results of the state-of-the-art general relativistic nonlinear studies, discussing the present status of the field and its future directions.
Physical Review D, 2015
Extending previous work by a number of authors, we have recently presented a new approach in whic... more Extending previous work by a number of authors, we have recently presented a new approach in which the detection of gravitational waves from merging neutron star binaries can be used to determine the equation of state of matter at nuclear density and hence the structure of neutron stars. In particular, after performing a large number of numerical-relativity simulations of binaries with nuclear equations of state, we have found that the post-merger emission is characterized by two distinct and robust spectral features. While the high-frequency peak was already shown to be associated with the oscillations of the hypermassive neutron star produced by the merger and to depend on the equation of state, we have highlighted that the low-frequency peak is related to the merger process and to the total compactness of the stars in the binary. This relation is essentially universal and provides a powerful tool to set tight constraints on the equation of state. We here provide additional information on the extensive analysis performed, illustrating the methods used, the tests considered, and the robustness of the results. We also discuss additional relations that can be deduced when exploring the data and how these correlate with various properties of the binary. Finally, we present a simple mechanical toy model that explains the main spectral features of the post-merger signal and can even reproduce analytically the complex waveforms emitted right after the merger. PACS numbers: 04.25.Dm, 04.25.dk, 04.30.Db, 04.40.Dg, 95.30.Lz, 95.30.Sf, 97.60.Jd