arXiv subjects

Carlos F. Sopuerta

Publications and source records attributed to Carlos F. Sopuerta.

At least 73 records · Page 4Linked to original sources

arXiv2010

Testing Modified Gravity with Gravitational Wave Astronomy

The emergent area of gravitational wave astronomy promises to provide revolutionary discoveries in the areas of astrophysics, cosmology, and fundamental physics. One of the most exciting possibilities is to use gravitational-wave observations to test alternative theories of gravity. In this contribution we describe how to use observations of extreme-mass-ratio inspirals by the future Laser Interferometer Space Antenna to test a particular class of theories: Chern-Simons modified gravity.

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arXiv2010

An Efficient Time-Domain Method to Model Extreme-Mass-Ratio Inspirals

The gravitational-wave signals emitted by Extreme-Mass-Ratio Inspirals will be hidden in the instrumental LISA noise and the foreground noise produced by galactic binaries in the LISA band. Then, we need accurate gravitational-wave templates to extract these signals from the noise and obtain the relevant physical parameters. This means that in the modeling of these systems we have to take into account how the orbit of the stellar-mass compact object is modified by the action of its own gravitational field. This effect can be described as the action of a local force, the self-force. We present a time-domain technique to compute the self-force for geodesic eccentric orbits around a non-rotating massive black hole. To illustrate the method we have applied it to a testbed model consisting of scalar charged particle orbiting a non-dynamical black hole. A key feature of our method is that it does not introduce a small scale associated with the stellar-mass compact object. This is achieved by using a multidomain framework where the particle is located at the interface between two subdomains. In this way, we just have to evolve homogeneous wave-like equations with smooth solutions that have to be communicated across the subdomain boundaries using appropriate junction conditions. The numerical technique that we use to implement this scheme is the pseudospectral collocation method. We show the suitability of this technique for the modeling of Extreme-Mass-Ratio Inspirals and show that it can provide accurate results for the self-force.

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arXiv2010

Gravitational Waves Notes, Issue #4 : "A Roadmap to Fundamental Physics from LISA EMRI Observations"

GW Notes was born from the need for a journal where the distinct communities involved in gravitation wave research might gather. While these three communities - Astrophysics, General Relativity and Data Analysis - have made significant collaborative progress over recent years, we believe that it is indispensable to future advancement that they draw closer, and that they speak a common idiom. For this GW Notes issue we have approached Carlos F. Sopuerta to write the highlight article of this issue on his thoughts on fundamental physics with LISA.

astro-ph.CO↗

arXiv2010

Towards Tests of Alternative Theories of Gravity with LISA

The inspiral of stellar compact objects into massive black holes, usually known as extreme-mass-ratio inspirals (EMRIs), is one of the most important sources of gravitational-waves for the future Laser Interferometer Space Antenna (LISA). Intermediate-mass-ratio inspirals (IMRIs are also of interest to advance ground-based gravitational-wave observatories. We discuss here how modifications to the gravitational interaction can affect the signals emitted by these systems and their detectability by LISA. We concentrate in particular on Chern-Simons modified gravity, a theory that emerges in different quantum gravitational approaches.

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arXiv2010

Modelling Extreme-Mass-Ratio Inspirals using Pseudospectral Methods

We introduce a new time-domain method for computing the self-force acting on a scalar particle in a Schwarzschild geometry. The principal feature of our method consists in the division of the spatial domain into several subdomains and locating the particle at the interface betweem two them. In this way, we avoid the need of resolving a small length scale associated with the presence of a particle in the computational domain and, at the same time, we avoid numerical problems due to the low differentiability of solutions of equations with point-like singular behaviour.

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arXiv2009

Extreme- and Intermediate-Mass Ratio Inspirals in Dynamical Chern-Simons Modified Gravity

[abridged] Chern-Simons (CS) modified gravity is a 4D effective theory that descends both from string theory and loop quantum gravity, and that corrects the Einstein-Hilbert action by adding the product of a scalar field and the parity-violating, Pontryagin density. In this theory, the gravitational field of spinning black holes is described by a modified Kerr geometry whose multipole moments deviate from the Kerr ones only at the fourth multipole, l = 4. We investigate possible signatures of this theory in the gravitational wave emission produced in the inspiral of stellar compact objects into massive black holes, both for intermediate- and extreme-mass ratios. We use the semi-relativistic approximation, where the trajectories are geodesics of the massive black hole geometry and the gravitational waveforms are obtained from a multipolar decomposition of the radiative field. The main CS corrections to the waveforms arise from modifications to the geodesic trajectories, due to changes to the massive black hole geometry, and manifest themselves as an accumulating dephasing relative to the general relativistic case. We also explore the propagation and the stress-energy tensor of gravitational waves in this theory. We find that, although this tensor has the same form as in General Relativity, the energy and angular momentum balance laws are indeed modified through the stress-energy tensor of the CS scalar field. These balance laws could be used to describe the inspiral through adiabatic changes in the orbital parameters, which in turn would enhance the dephasing effect. Gravitational-wave observations of intermediate- or extreme-mass ratio inspirals with advanced ground detectors or with LISA could use such dephasing to test the dynamical theory to unprecedented levels.

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arXiv2009

An Efficient Pseudospectral Method for the Computation of the Self-force on a Charged Particle: Circular Geodesics around a Schwarzschild Black Hole

The description of the inspiral of a stellar-mass compact object into a massive black hole sitting at a galactic centre is a problem of major relevance for the future space-based gravitational-wave observatory LISA (Laser Interferometer Space Antenna), as the signals from these systems will be buried in the data stream and accurate gravitational-wave templates will be needed to extract them. The main difficulty in describing these systems lies in the estimation of the gravitational effects of the stellar-mass compact object on his own trajectory around the massive black hole, which can be modeled as the action of a local force, the self-force. In this paper, we present a new time-domain numerical method for the computation of the self-force in a simplified model consisting of a charged scalar particle orbiting a nonrotating black hole. We use a multi-domain framework in such a way that the particle is located at the interface between two domains so that the presence of the particle and its physical effects appear only through appropriate boundary conditions. In this way we eliminate completely the presence of a small length scale associated with the need of resolving the particle. This technique also avoids the problems associated with the impact of a low differentiability of the solution in the accuracy of the numerical computations. The spatial discretization of the field equations is done by using the pseudospectral collocation method and the time evolution, based on the method of lines, uses a Runge-Kutta solver. We show how this special framework can provide very efficient and accurate computations in the time domain, which makes the technique amenable for the intensive computations required in the astrophysically-relevant scenarios for LISA.

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arXiv2008

Simulations of Extreme-Mass-Ratio Inspirals Using Pseudospectral Methods

Extreme-mass-ratio inspirals (EMRIs), stellar-mass compact objects (SCOs) inspiralling into a massive black hole, are one of the main sources of gravitational waves expected for the Laser Interferometer Space Antenna (LISA). To extract the EMRI signals from the expected LISA data stream, which will also contain the instrumental noise as well as other signals, we need very accurate theoretical templates of the gravitational waves that they produce. In order to construct those templates we need to account for the gravitational backreaction, that is, how the gravitational field of the SCO affects its own trajectory. In general relativity, the backreaction can be described in terms of a local self-force, and the foundations to compute it have been laid recently. Due to its complexity, some parts of the calculation of the self-force have to be performed numerically. Here, we report on an ongoing effort towards the computation of the self-force based on time-domain multi-grid pseudospectral methods.

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arXiv2008

Gravitational Radiation from Neutron Stars and Black Holes

Gravitational Wave Astronomy is becoming a reality as Earth-based interferometric gravitational-wave detectors reach the design sensitivities and move towards advanced configurations that may lead to gravitational-wave detections in the immediate future. In this contribution, I briefly summarize the basic characteristics of this new area, the discovery prospects and the potential for fundamental physics. Then, I present results of some investigations of two different sources of gravitational waves that are potential targets for present and future planned observatories. First, I will discuss the generation of gravitational radiation by non-linear effects arising from the coupling between radial and non-radial oscillations of neutron stars, which may produce distinctive gravitational-wave signatures. The gravitational radiation emitted by these sources is in the frequency band of Earth-based detectors. And second, I will discuss the gravitational-wave emission during the inspiral of extreme-mass-ratio compact binaries. In this case, the gravitational waves have low frequencies, inside the frequency band of space observatories like LISA.

astro-ph↗

arXiv2007

Perturbations of Schwarzschild Black Holes in Chern-Simons Modified Gravity

We study perturbations of a Schwarzschild black hole in Chern-Simons modified gravity. We begin by showing that Birkhoff's theorem holds for a wide family of Chern-Simons coupling functions, a scalar field present in the theory that controls the strength of the Chern-Simons correction to the Einstein-Hilbert action. After decomposing the perturbations in spherical harmonics, we study the linearized modified field equations and find that axial and polar modes are coupled, in contrast to general relativity. The divergence of the modified equations leads to the Pontryagin constraint, which forces the vanishing of the Cunningham-Price-Moncrief master function associated with axial modes. We analyze the structure of these equations and find that the appearance of the Pontryagin constraint yields an overconstrained system that does not allow for generic black hole oscillations. We illustrate this situation by studying the case characterized by a canonical choice of the coupling function and pure-parity perturbative modes. We end with a discussion of how to extend Chern-Simons modified gravity to bypass the Pontryagin constraint and the suppression of perturbations.

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arXiv2007

Relativistic Effects in Extreme Mass Ratio Gravitational Wave Bursts

Extreme mass ratio bursts (EMRBs) have been proposed as a possible source for future space-borne gravitational wave detectors, such as the Laser Interferometer Space Antenna (LISA). These events are characterized by long-period, nearly-radial orbits of compact objects around a central massive black hole. The gravitational radiation emitted during such events consists of a short burst, corresponding to periapse passage, followed by a longer, silent interval. In this paper we investigate the impact of including relativistic corrections to the description of the compact object's trajectory via a geodesic treatment, as well as including higher-order multipole corrections in the waveform calculation. The degree to which the relativistic corrections are important depends on the EMRB's orbital parameters. We find that relativistic EMRBs (v_{max}}/c > 0.25) are not rare and actually account for approximately half of the events in our astrophysical model. The relativistic corrections tend to significantly change the waveform amplitude and phase relative to a Newtonian description, although some of this dephasing could be mimicked by parameter errors. The dephasing over several bursts could be of particular importance not only to gravitational wave detection, but also to parameter estimation, since it is highly correlated to the spin of the massive black hole. Consequently, we postulate that if a relativistic EMRB is detected, such dephasing might be used to probe the relativistic character of the massive black hole and obtain information about its spin.

astro-ph↗

arXiv2007

Gravitational Recoil from Binary Black Hole Mergers: the Close-Limit Approximation

[abridged] The coalescence of a binary black hole system is one of the main sources of gravitational waves that present and future detectors will study. Apart from the energy and angular momentum that these waves carry, for unequal-mass binaries there is also a net flux of linear momentum that implies a recoil velocity of the resulting final black hole in the opposite direction. We present a computation of the recoil velocity based on the close-limit approximation scheme, which gives excellent results for head-on and grazing collisions of black holes when compared to full numerical relativistic calculations. We obtain a maximum recoil velocity of ~ 64 km/s for a symmetric mass ratio eta = M_1 M_2/(M_1+M_2)^2 ~ 0.19 and an initial proper separation of 4 M, where M is the total ADM mass of the system. This separation is the maximum at which the close-limit approximation is expected to provide accurate results. If we supplement this estimate with PN calculations up to the innermost stable circular orbit, we obtain a lower bound for the recoil velocity, with a maximum around 84 km/s. This is a lower bound because it neglects the initial merger phase. We can however obtain a rough estimate by using PN methods or the close-limit approximation. Since both methods are known to overestimate the amount of radiation, we obtain in this way an upper bound for the recoil with maxima in the range of 220-265 km/s. We also provide non-linear fits to these estimated upper and lower bounds. These estimates are subject to uncertainties related to issues such as the choice of initial data and higher effects in perturbation theory. Nonetheless, our estimates are consistent with previous results in the literature and suggest a narrower range of possible recoil velocities.

astro-ph↗

arXiv2006

Gravitational recoil velocities from eccentric binary black hole mergers

The formation and growth of supermassive black holes is a key issue to unveil the secrets of galaxy formation. In particular, the gravitational recoil produced in the merger of unequal mass black hole binaries could have a number of astrophysical implications, such as the ejection of black holes from the host galaxy or globular cluster. We present estimates of the recoil velocity that include the effect of small eccentricities. The approach is specially suited for the last stage of the merger, where most of the emission of linear momentum in gravitational waves takes place. Supplementing our estimates with post-Newtonian approximations, we obtain lower and upper bounds that constrain previous recoil velocities estimates as well as a best estimate that agrees with numerical simulations in the quasi-circular case. For eccentricities e <= 0.1, the maximum recoil is found for mass ratios of M_1/M_2 ~ 0.38 with a best estimate of ~ 167 (1 + e) km/s and upper and lower bounds of 79 (1 + e) km/s and 216 (1 + e) km/s respectively.

astro-ph↗

arXiv2006

Time Domain Simulations of EMRIs using Finite Element Methods

This is a brief report on time-domain numerical simulations of extreme-mass-ratio binaries based on finite element methods. We discuss a new technique for solving the perturbative equations describing a point-like object orbiting a non-rotating massive black hole and the prospects of using it for the evaluation of the gravitational self-force responsible of the inspiral of these binary systems. We also discuss the perspectives of transferring this technology to the more astrophysically relevant case of a central rotating massive black hole.

astro-ph↗

arXiv2006

Hydro-without-Hydro Framework for Simulations of Black Hole-Neutron Star Binaries

We introduce a computational framework which avoids solving explicitly hydrodynamic equations and is suitable to study the pre-merger evolution of black hole-neutron star binary systems. The essence of the method consists of constructing a neutron star model with a black hole companion and freezing the internal degrees of freedom of the neutron star during the course of the evolution of the space-time geometry. We present the main ingredients of the framework, from the formulation of the problem to the appropriate computational techniques to study these binary systems. In addition, we present numerical results of the construction of initial data sets and evolutions that demonstrate the feasibility of this approach.

gr-qc↗

arXiv2006

A Toy Model for Testing Finite Element Methods to Simulate Extreme-Mass-Ratio Binary Systems

Extreme mass ratio binary systems, binaries involving stellar mass objects orbiting massive black holes, are considered to be a primary source of gravitational radiation to be detected by the space-based interferometer LISA. The numerical modelling of these binary systems is extremely challenging because the scales involved expand over several orders of magnitude. One needs to handle large wavelength scales comparable to the size of the massive black hole and, at the same time, to resolve the scales in the vicinity of the small companion where radiation reaction effects play a crucial role. Adaptive finite element methods, in which quantitative control of errors is achieved automatically by finite element mesh adaptivity based on posteriori error estimation, are a natural choice that has great potential for achieving the high level of adaptivity required in these simulations. To demonstrate this, we present the results of simulations of a toy model, consisting of a point-like source orbiting a black hole under the action of a scalar gravitational field.

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arXiv2005

A Finite Element Computation of the Gravitational Radiation emitted by a Point-like object orbiting a Non-rotating Black Hole

The description of extreme-mass-ratio binary systems in the inspiral phase is a challenging problem in gravitational wave physics with significant relevance for the space interferometer LISA. The main difficulty lies in the evaluation of the effects of the small body's gravitational field on itself. To that end, an accurate computation of the perturbations produced by the small body with respect the background geometry of the large object, a massive black hole, is required. In this paper we present a new computational approach based on Finite Element Methods to solve the master equations describing perturbations of non-rotating black holes due to an orbiting point-like object. The numerical computations are carried out in the time domain by using evolution algorithms for wave-type equations. We show the accuracy of the method by comparing our calculations with previous results in the literature. Finally, we discuss the relevance of this method for achieving accurate descriptions of extreme-mass-ratio binaries.

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arXiv2005

Coupling of radial and non-radial oscillations of relativistic stars: gauge-invariant formalism

Linear perturbation theory is appropriate to describe small oscillations of stars, while a mild non-linearity is still tractable perturbatively but requires to consider mode coupling. It is natural to start to look at this problem by considering the coupling between linear radial and non-radial modes. Radial pulsations of a spherical compact objects do not per se emit gravitational waves but, if the coupling is efficient in driving and possibly amplifying the non-radial modes, gravitational radiation could then be produced to a significant level. In this paper we develop the relativistic formalism to study the coupling of radial and non-radial first order perturbations of a compact spherical star. From a mathematical point of view, it is convenient to treat the two sets of perturbations as separately parametrized, using a 2-parameter perturbative expansion of the metric, the energy-momentum tensor and Einstein equations in which $λ$ is associated with the radial modes, $ε$ with the non-radial perturbations, and the $λε$ terms describe the coupling. This approach provides a well-defined framework to consider the gauge dependence of perturbations, allowing us to use $ε$ order gauge-invariant non-radial variables on the static background and to define new second order $λε$ gauge-invariant variables describing the non-linear coupling. We present the evolution and constraint equations for our variables outlining the setup for numerical computations, and briefly discuss the surface boundary conditions in terms of the second order $λε$ Lagrangian pressure perturbation.

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