Chad Galley | California Institute of Technology (original) (raw)

Papers by Chad Galley

Research paper thumbnail of Radiation reaction and gravitational waves in the eective eld theory approach

eld theory (EFT) approach of Goldberger and Rothstein. We use an initial value for- mulation of t... more eld theory (EFT) approach of Goldberger and Rothstein. We use an initial value for- mulation of the underlying (quantum) framework to implement retarded boundary conditions and describe these real-time dissipative processes. We also demonstrate why the usual scattering formal- ism of quantum eld theory inadequately accounts for these. The methods discussed here should be useful for deriving real-time quantities (including

Research paper thumbnail of Reduced basis for spinning, non precessing binaries

We extend our Reduced Basis results of Phys.Rev.Lett. 106, 221102 (2011) to the case in which spi... more We extend our Reduced Basis results of Phys.Rev.Lett. 106, 221102 (2011) to the case in which spin in the absence of precession is included. We find that the number of bases needed to represent the full spectrum of such waveforms is marginally larger than the one needed for the non-spinning case. The method, in particular, gives a set of nearly optimal points in parameter space, in a precise mathematical sense, for purposes such as calibration of phenomenological or EOB models. On a broader perspective, these results suggest that Reduced Basis with further enhancements can beat the curse of dimensionality in the two body problem in GR.

Research paper thumbnail of Sparse Representations of Gravitational Waves from Precessing Compact Binaries

Physical Review Letters, 2014

Many relevant applications in gravitational wave physics share a significant common problem: the ... more Many relevant applications in gravitational wave physics share a significant common problem: the seven-dimensional parameter space of gravitational waveforms from precessing compact binary inspirals and coalescences is large enough to prohibit covering the space of waveforms with sufficient density. We find that by using the reduced basis method together with a parametrization of waveforms based on their phase and precession, we can construct ultra-compact yet high-accuracy representations of this large space. As a demonstration, we show that less than 100 judiciously chosen precessing inspiral waveforms are needed for 200 cycles, mass ratios from 1 to 10 and spin magnitudes ≤ 0.9. In fact, using only the first 10 reduced basis waveforms yields a maximum mismatch of 0.016 over the whole range of considered parameters. We test whether the parameters selected from the inspiral regime result in an accurate reduced basis when including merger and ringdown; we find that this is indeed the case in the context of a non-precessing effective-one-body model. This evidence suggests that as few as ∼ 100 numerical simulations of binary black hole coalescences may accurately represent the seven-dimensional parameter space of precession waveforms for the considered ranges.

Research paper thumbnail of Relaxation effects in the charge-ordered state of La $ _ {0.5} $ Ca $ _ {0.5} $ MnO $ _ {3} $

Relaxation effects in the charge-ordered state of La 0.5 Ca 0.5 MnO 3

Research paper thumbnail of Properties of Reduced Basis catalogs for gravitational wave templates

We discuss properties of gravitational waveform template banks constructed using the Reduced Basi... more We discuss properties of gravitational waveform template banks constructed using the Reduced Basis (RB) method. We find that the continuum of gravitational waveforms can be represented by a finite and comparatively compact basis, which implies that the space of inspiral waveforms is effectively finite dimensional. Furthermore, the RB catalogs are robust under variations in the power spectral density of ground-based

Research paper thumbnail of Reduced Basis for Gravitational Waves

We introduce Reduced Basis (RB) as a method for gravitational wave representation and analysis. W... more We introduce Reduced Basis (RB) as a method for gravitational wave representation and analysis. We comment on computational aspects and compare template catalogs for different detectors to other methods. In particular, we point out exponential convergence on the error of the resulting RB catalogs with the number of templates.

Research paper thumbnail of Caustic Echoes as X-ray follow-ups from Sagittarius A*

ABSTRACT The supermassive black hole Sgr A* at the center of our Galaxy is a source of bright X-r... more ABSTRACT The supermassive black hole Sgr A* at the center of our Galaxy is a source of bright X-ray flares. In certain cases, the bright flares are followed up by weaker ones, also referred to as X-ray hiccups. A recent X-ray Visionary Project (XVP) using the High Energy Transmission Grating Spectrometer (HETGS) of the Chandra X-ray Observatory is expected to observe about three dozen X-ray flares within 2012, thereby providing a unique opportunity to understand the mechanism behind X-ray flares in accretion disks around supermassive black holes and their follow-ups. Such follow-ups may also appear due to caustic echoes. A bright flare near the event horizon of a black hole leads to the formation of a caustic on the other side of the horizon. The echoes generated by these caustics may, in principle, be detected as X-ray follow-ups with sufficiently accurate instruments. Their detection would allow us to measure the mass and the angular momentum of the supermassive black hole. We discuss astrophysical properties of caustic echoes and investigate their detectability as X-ray follow-ups with Chandra--HETGS.

Research paper thumbnail of Caustic echoes and their astrophysical applications

We present the first numerical approximation of the scalar Schwarzschild Green function in the ti... more We present the first numerical approximation of the scalar Schwarzschild Green function in the time domain, which reveals several universal features of wave propagation in black hole spacetimes. We demonstrate the trapping of energy near the photon sphere and confirm its exponential decay. The trapped wavefront passes through caustics resulting in echoes that propagate to infinity. The arrival times and the decay rate of these caustic echoes are consistent with propagation along null geodesics and the large ' limit of quasinormal modes. We show that the fourfold singularity structure of the retarded Green function is due to the well-known action of a Hilbert transform on the trapped wavefront at caustics. A twofold cycle is obtained for degenerate source-observer configurations along the caustic line, where the energy amplification increases with an inverse power of the scale of the source. Finally, we discuss the tail piece of the solution due to propagation within the light cone, up to and including null infinity, and argue that, even with ideal instruments, only a finite number of echoes can be observed. Putting these pieces together, we provide a heuristic expression that approximates the Green function with a few free parameters. Accurate calculations and approximations of the Green function are the most general way of solving for wave propagation in curved spacetimes and should be useful in a variety of studies such as the computation of the self-force on a particle.

Research paper thumbnail of Surrogate models for numerical relativity waveforms

Research paper thumbnail of Surrogate models for EOB gravitational waveforms

Research paper thumbnail of Surrogate waveform models

Research paper thumbnail of Nonspinning numerical relativity waveform surrogates: assessing the model

Research paper thumbnail of Theory of optomechanics: Oscillator-field model of moving mirrors

Research paper thumbnail of Self-force via Green functions and worldline integration

A compact object moving in curved spacetime interacts with its own gravitational field. This lead... more A compact object moving in curved spacetime interacts with its own gravitational field. This leads to both dissipative and conservative corrections to the motion, which can be interpreted as a self-force acting on the object. The original formalism describing this self-force relied heavily on the Green function of the linear differential operator that governs gravitational perturbations. However, because the global calculation of Green functions in non-trivial black hole spacetimes has been an open problem until recently, alternative methods were established to calculate self-force effects using sophisticated regularization techniques that avoid the computation of the global Green function. We present a method for calculating the self-force that employs the global Green function and is therefore closely modeled after the original self-force expressions. Our quantitative method involves two stages: (i) numerical approximation of the retarded Green function in the background spacetime; (ii) evaluation of convolution integrals along the worldline of the object. This novel approach can be used along arbitrary worldlines, including those currently inaccessible to more established computational techniques. Furthermore, it yields geometrical insight into the contributions to selfinteraction from curved geometry (back-scattering) and trapping of null geodesics. We demonstrate the method on the motion of a scalar charge in Schwarzschild spacetime. This toy model retains the physical history-dependence of the self-force but avoids gauge issues and allows us to focus on basic principles. We compute the self-field and self-force for many worldlines including accelerated circular orbits, eccentric orbits at the separatrix, and radial infall. This method, closely modeled after the original formalism, provides a promising complementary approach to the self-force problem.

Research paper thumbnail of The principle of stationary nonconservative action for classical mechanics and field theories

We further develop a recently introduced variational principle of stationary action for problems ... more We further develop a recently introduced variational principle of stationary action for problems in nonconservative classical mechanics and extend it to classical field theories. The variational calculus used is consistent with an initial value formulation of physical problems and allows for time-irreversible processes, such as dissipation, to be included at the level of the action. In this formalism, the equations of motion are generated by extremizing a nonconservative action S, which is a functional of a doubled set of degrees of freedom. The corresponding nonconservative Lagrangian contains a "potential" K which generates nonconservative forces and interactions. Such a nonconservative potential can arise in several ways, including from an open system interacting with inaccessible degrees of freedom or from integrating out or coarse-graining a subset of variables in closed systems. We generalize Noether's theorem to show how Noether currents are modified and no longer conserved when K is non-vanishing. Consequently, the nonconservative aspects of a physical system are derived solely from K. We show how to use the formalism with several examples of nonconservative actions for discrete systems including forced damped harmonic oscillators, radiation reaction on an accelerated charge, and RLC circuits. We also present several examples for nonconservative classical field theories. We demonstrate how our approach naturally allows for irreversible thermodynamic processes to be included in an unconstrained variational principle for problems in fluid dynamics. We present the nonconservative action for a Navier-Stokes fluid including the effects of viscous dissipation and heat diffusion, as well as an action that generates the Maxwell model for viscoelastic materials, which can be easily generalized to more realistic rheological models. We also show that the nonconservative action has a fundamental origin and can be derived as the classical limit of a more complete quantum theory. ; Einstein fellow 1 By "level of the action" we mean the action, Lagrangian, and Hamiltonian and manipulations performed on them directly as opposed to the "level of the equations of motion."

Research paper thumbnail of Fast prediction and evaluation of gravitational waveforms using surrogate models

We propose a solution to the problem of quickly and accurately predicting gravitational waveforms... more We propose a solution to the problem of quickly and accurately predicting gravitational waveforms within any given physical model. The method is relevant for both real-time applications and in more traditional scenarios where the generation of waveforms using standard methods can be prohibitively expensive. Our approach is based on three offline steps resulting in an accurate reduced-order model in both parameter and physical dimensions that can be used as a surrogate for the true/fiducial waveform family. First, a set of m parameter values is determined using a greedy algorithm from which a reduced basis representation is constructed. Second, these m parameters induce the selection of m time values for interpolating a waveform time series using an empirical interpolant that is built for the fiducial waveform family. Third, a fit in the parameter dimension is performed for the waveform's value at each of these m times. The cost of predicting L waveform time samples for a generic parameter choice is of order O (mL + mc fit ) online operations where c fit denotes the fitting function operation count and, typically, m L. The result is a compact, computationally efficient, and accurate surrogate model that retains the original physics of the fiducial waveform family while also being fast to evaluate. We generate accurate surrogate models for Effective One Body (EOB) waveforms of non-spinning binary black hole coalescences with durations as long as 10 5 M , mass ratios from 1 to 10, and for multiple spherical harmonic modes. We find that these surrogates are more than three orders of magnitude faster to evaluate as compared to the cost of generating EOB waveforms in standard ways. Surrogate model building for other waveform families and models follow the same steps and have the same low computational online scaling cost. For expensive numerical simulations of binary black hole coalescences we thus anticipate extremely large speedups in generating new waveforms with a surrogate. As waveform generation is one of the dominant costs in parameter estimation algorithms and parameter space exploration, surrogate models offer a new and practical way to dramatically accelerate such studies without impacting accuracy.

Research paper thumbnail of Reduced Basis Catalogs for Gravitational Wave Templates

Physical Review Letters, 2011

We introduce a reduced basis approach as a new paradigm for modeling, representing and searching ... more We introduce a reduced basis approach as a new paradigm for modeling, representing and searching for gravitational waves. We construct waveform catalogs for non-spinning compact binary coalescences, and we find that for accuracies of 99% and 99.999% the method generates a factor of about 10 − 10 5 fewer templates than standard placement methods. The continuum of gravitational waves can be represented by a finite and comparatively compact basis. The method is robust under variations in the noise of detectors, implying that only a single catalog needs to be generated.

Research paper thumbnail of Electromagnetic and gravitational self-force on a relativistic particle from quantum fields in curved space

Physical Review D, 2006

We provide a quantum field theoretical derivation of the Abraham-Lorentz-Dirac (ALD) equation, de... more We provide a quantum field theoretical derivation of the Abraham-Lorentz-Dirac (ALD) equation, describing the motion of an electric point charge sourcing an electromagnetic field, which back-reacts on the charge as a self-force, and the Mino-Sasaki-Tanaka-Quinn-Wald (MSTQW) equation describing the motion of a point mass with self-force interacting with the linearized metric perturbations caused by the mass off an otherwise vacuous curved background spacetime. We regularize the formally divergent self-force by smearing the direct part of the retarded Green's function and using a quasilocal expansion. We also derive the ALD-Langevin and the MSTQW-Langevin equations with a classical stochastic force accounting for the effect of the quantum fluctuations in the field, which causes small fluctuations on the particle trajectory. These equations will be useful for studying the stochastic motion of charges and small masses under the influence of both quantum and classical noise sources, derived either self-consistently or put in by hand phenomenologically. We also show that history-dependent noise-induced drift motions could arise from such stochastic sources on the trajectory that could be a hidden feature of gravitational wave forms hitherto unknown.

Research paper thumbnail of Radiation reaction and gravitational waves in the effective field theory approach

Physical Review D, 2009

We compute the contribution to the Lagrangian from the leading order (2.5 post-Newtonian) radiati... more We compute the contribution to the Lagrangian from the leading order (2.5 post-Newtonian) radiation reaction and the quadrupolar gravitational waves emitted from a binary system using the effective field theory (EFT) approach of Goldberger and Rothstein. We use an initial value formulation of the underlying (quantum) framework to implement retarded boundary conditions and describe these real-time dissipative processes. We also demonstrate why the usual scattering formalism of quantum field theory inadequately accounts for these. The methods discussed here should be useful for deriving real-time quantities (including radiation reaction forces and gravitational wave emission) and hereditary terms in the post-Newtonian approximation (including memory, tail and other causal, history-dependent integrals) within the EFT approach. We also provide a consistent and correct formulation of the radiation sector in the equivalent effective field theory approach of Kol and Smolkin.

Research paper thumbnail of Self-force on extreme mass ratio inspirals via curved spacetime effective field theory

Physical Review D, 2009

In this series we construct an effective field theory (EFT) in curved spacetime to study gravitat... more In this series we construct an effective field theory (EFT) in curved spacetime to study gravitational radiation and backreaction effects. We begin in this paper with a derivation of the selfforce on a compact object moving in the background spacetime of a supermassive black hole. The EFT approach utilizes the disparity between two length scales, which in this problem are the size of the compact object rm and the radius of curvature of the background spacetime R such that ε ≡ rm/R 1, to treat the orbital dynamics of the compact object, described as an effective point particle, separately from its tidal deformations. The equation of motion of an effective relativistic point particle coupled to the gravitational waves generated by its motion in a curved background spacetime can be derived without making a slow motion or weak field approximation, as was assumed in earlier EFT treatment of post-Newtonian binaries. Ultraviolet divergences are regularized using Hadamard's partie finie to isolate the non-local finite part from the quasi-local divergent part. The latter is constructed from a momentum space representation for the graviton retarded propagator and is evaluated using dimensional regularization in which only logarithmic divergences are relevant for renormalizing the parameters of the theory. As a first important application of this framework we explicitly derive the first order self-force given by Mino, Sasaki, Tanaka, Quinn and Wald. Going beyond the point particle approximation, to account for the finite size of the object, we demonstrate that for extreme mass ratio inspirals the motion of a compact object is affected by tidally induced moments at O(ε 4 ), in the form of an Effacement Principle. The relatively large radius-to-mass ratio of a white dwarf star allows for these effects to be enhanced until the white dwarf becomes tidally disrupted, a potentially O(ε 2 ) process, or plunges into the supermassive black hole. This work provides a new foundation for further exploration of higher order self force corrections, gravitational radiation and spinning compact objects.

Research paper thumbnail of Radiation reaction and gravitational waves in the eective eld theory approach

eld theory (EFT) approach of Goldberger and Rothstein. We use an initial value for- mulation of t... more eld theory (EFT) approach of Goldberger and Rothstein. We use an initial value for- mulation of the underlying (quantum) framework to implement retarded boundary conditions and describe these real-time dissipative processes. We also demonstrate why the usual scattering formal- ism of quantum eld theory inadequately accounts for these. The methods discussed here should be useful for deriving real-time quantities (including

Research paper thumbnail of Reduced basis for spinning, non precessing binaries

We extend our Reduced Basis results of Phys.Rev.Lett. 106, 221102 (2011) to the case in which spi... more We extend our Reduced Basis results of Phys.Rev.Lett. 106, 221102 (2011) to the case in which spin in the absence of precession is included. We find that the number of bases needed to represent the full spectrum of such waveforms is marginally larger than the one needed for the non-spinning case. The method, in particular, gives a set of nearly optimal points in parameter space, in a precise mathematical sense, for purposes such as calibration of phenomenological or EOB models. On a broader perspective, these results suggest that Reduced Basis with further enhancements can beat the curse of dimensionality in the two body problem in GR.

Research paper thumbnail of Sparse Representations of Gravitational Waves from Precessing Compact Binaries

Physical Review Letters, 2014

Many relevant applications in gravitational wave physics share a significant common problem: the ... more Many relevant applications in gravitational wave physics share a significant common problem: the seven-dimensional parameter space of gravitational waveforms from precessing compact binary inspirals and coalescences is large enough to prohibit covering the space of waveforms with sufficient density. We find that by using the reduced basis method together with a parametrization of waveforms based on their phase and precession, we can construct ultra-compact yet high-accuracy representations of this large space. As a demonstration, we show that less than 100 judiciously chosen precessing inspiral waveforms are needed for 200 cycles, mass ratios from 1 to 10 and spin magnitudes ≤ 0.9. In fact, using only the first 10 reduced basis waveforms yields a maximum mismatch of 0.016 over the whole range of considered parameters. We test whether the parameters selected from the inspiral regime result in an accurate reduced basis when including merger and ringdown; we find that this is indeed the case in the context of a non-precessing effective-one-body model. This evidence suggests that as few as ∼ 100 numerical simulations of binary black hole coalescences may accurately represent the seven-dimensional parameter space of precession waveforms for the considered ranges.

Research paper thumbnail of Relaxation effects in the charge-ordered state of La $ _ {0.5} $ Ca $ _ {0.5} $ MnO $ _ {3} $

Relaxation effects in the charge-ordered state of La 0.5 Ca 0.5 MnO 3

Research paper thumbnail of Properties of Reduced Basis catalogs for gravitational wave templates

We discuss properties of gravitational waveform template banks constructed using the Reduced Basi... more We discuss properties of gravitational waveform template banks constructed using the Reduced Basis (RB) method. We find that the continuum of gravitational waveforms can be represented by a finite and comparatively compact basis, which implies that the space of inspiral waveforms is effectively finite dimensional. Furthermore, the RB catalogs are robust under variations in the power spectral density of ground-based

Research paper thumbnail of Reduced Basis for Gravitational Waves

We introduce Reduced Basis (RB) as a method for gravitational wave representation and analysis. W... more We introduce Reduced Basis (RB) as a method for gravitational wave representation and analysis. We comment on computational aspects and compare template catalogs for different detectors to other methods. In particular, we point out exponential convergence on the error of the resulting RB catalogs with the number of templates.

Research paper thumbnail of Caustic Echoes as X-ray follow-ups from Sagittarius A*

ABSTRACT The supermassive black hole Sgr A* at the center of our Galaxy is a source of bright X-r... more ABSTRACT The supermassive black hole Sgr A* at the center of our Galaxy is a source of bright X-ray flares. In certain cases, the bright flares are followed up by weaker ones, also referred to as X-ray hiccups. A recent X-ray Visionary Project (XVP) using the High Energy Transmission Grating Spectrometer (HETGS) of the Chandra X-ray Observatory is expected to observe about three dozen X-ray flares within 2012, thereby providing a unique opportunity to understand the mechanism behind X-ray flares in accretion disks around supermassive black holes and their follow-ups. Such follow-ups may also appear due to caustic echoes. A bright flare near the event horizon of a black hole leads to the formation of a caustic on the other side of the horizon. The echoes generated by these caustics may, in principle, be detected as X-ray follow-ups with sufficiently accurate instruments. Their detection would allow us to measure the mass and the angular momentum of the supermassive black hole. We discuss astrophysical properties of caustic echoes and investigate their detectability as X-ray follow-ups with Chandra--HETGS.

Research paper thumbnail of Caustic echoes and their astrophysical applications

We present the first numerical approximation of the scalar Schwarzschild Green function in the ti... more We present the first numerical approximation of the scalar Schwarzschild Green function in the time domain, which reveals several universal features of wave propagation in black hole spacetimes. We demonstrate the trapping of energy near the photon sphere and confirm its exponential decay. The trapped wavefront passes through caustics resulting in echoes that propagate to infinity. The arrival times and the decay rate of these caustic echoes are consistent with propagation along null geodesics and the large ' limit of quasinormal modes. We show that the fourfold singularity structure of the retarded Green function is due to the well-known action of a Hilbert transform on the trapped wavefront at caustics. A twofold cycle is obtained for degenerate source-observer configurations along the caustic line, where the energy amplification increases with an inverse power of the scale of the source. Finally, we discuss the tail piece of the solution due to propagation within the light cone, up to and including null infinity, and argue that, even with ideal instruments, only a finite number of echoes can be observed. Putting these pieces together, we provide a heuristic expression that approximates the Green function with a few free parameters. Accurate calculations and approximations of the Green function are the most general way of solving for wave propagation in curved spacetimes and should be useful in a variety of studies such as the computation of the self-force on a particle.

Research paper thumbnail of Surrogate models for numerical relativity waveforms

Research paper thumbnail of Surrogate models for EOB gravitational waveforms

Research paper thumbnail of Surrogate waveform models

Research paper thumbnail of Nonspinning numerical relativity waveform surrogates: assessing the model

Research paper thumbnail of Theory of optomechanics: Oscillator-field model of moving mirrors

Research paper thumbnail of Self-force via Green functions and worldline integration

A compact object moving in curved spacetime interacts with its own gravitational field. This lead... more A compact object moving in curved spacetime interacts with its own gravitational field. This leads to both dissipative and conservative corrections to the motion, which can be interpreted as a self-force acting on the object. The original formalism describing this self-force relied heavily on the Green function of the linear differential operator that governs gravitational perturbations. However, because the global calculation of Green functions in non-trivial black hole spacetimes has been an open problem until recently, alternative methods were established to calculate self-force effects using sophisticated regularization techniques that avoid the computation of the global Green function. We present a method for calculating the self-force that employs the global Green function and is therefore closely modeled after the original self-force expressions. Our quantitative method involves two stages: (i) numerical approximation of the retarded Green function in the background spacetime; (ii) evaluation of convolution integrals along the worldline of the object. This novel approach can be used along arbitrary worldlines, including those currently inaccessible to more established computational techniques. Furthermore, it yields geometrical insight into the contributions to selfinteraction from curved geometry (back-scattering) and trapping of null geodesics. We demonstrate the method on the motion of a scalar charge in Schwarzschild spacetime. This toy model retains the physical history-dependence of the self-force but avoids gauge issues and allows us to focus on basic principles. We compute the self-field and self-force for many worldlines including accelerated circular orbits, eccentric orbits at the separatrix, and radial infall. This method, closely modeled after the original formalism, provides a promising complementary approach to the self-force problem.

Research paper thumbnail of The principle of stationary nonconservative action for classical mechanics and field theories

We further develop a recently introduced variational principle of stationary action for problems ... more We further develop a recently introduced variational principle of stationary action for problems in nonconservative classical mechanics and extend it to classical field theories. The variational calculus used is consistent with an initial value formulation of physical problems and allows for time-irreversible processes, such as dissipation, to be included at the level of the action. In this formalism, the equations of motion are generated by extremizing a nonconservative action S, which is a functional of a doubled set of degrees of freedom. The corresponding nonconservative Lagrangian contains a "potential" K which generates nonconservative forces and interactions. Such a nonconservative potential can arise in several ways, including from an open system interacting with inaccessible degrees of freedom or from integrating out or coarse-graining a subset of variables in closed systems. We generalize Noether's theorem to show how Noether currents are modified and no longer conserved when K is non-vanishing. Consequently, the nonconservative aspects of a physical system are derived solely from K. We show how to use the formalism with several examples of nonconservative actions for discrete systems including forced damped harmonic oscillators, radiation reaction on an accelerated charge, and RLC circuits. We also present several examples for nonconservative classical field theories. We demonstrate how our approach naturally allows for irreversible thermodynamic processes to be included in an unconstrained variational principle for problems in fluid dynamics. We present the nonconservative action for a Navier-Stokes fluid including the effects of viscous dissipation and heat diffusion, as well as an action that generates the Maxwell model for viscoelastic materials, which can be easily generalized to more realistic rheological models. We also show that the nonconservative action has a fundamental origin and can be derived as the classical limit of a more complete quantum theory. ; Einstein fellow 1 By "level of the action" we mean the action, Lagrangian, and Hamiltonian and manipulations performed on them directly as opposed to the "level of the equations of motion."

Research paper thumbnail of Fast prediction and evaluation of gravitational waveforms using surrogate models

We propose a solution to the problem of quickly and accurately predicting gravitational waveforms... more We propose a solution to the problem of quickly and accurately predicting gravitational waveforms within any given physical model. The method is relevant for both real-time applications and in more traditional scenarios where the generation of waveforms using standard methods can be prohibitively expensive. Our approach is based on three offline steps resulting in an accurate reduced-order model in both parameter and physical dimensions that can be used as a surrogate for the true/fiducial waveform family. First, a set of m parameter values is determined using a greedy algorithm from which a reduced basis representation is constructed. Second, these m parameters induce the selection of m time values for interpolating a waveform time series using an empirical interpolant that is built for the fiducial waveform family. Third, a fit in the parameter dimension is performed for the waveform's value at each of these m times. The cost of predicting L waveform time samples for a generic parameter choice is of order O (mL + mc fit ) online operations where c fit denotes the fitting function operation count and, typically, m L. The result is a compact, computationally efficient, and accurate surrogate model that retains the original physics of the fiducial waveform family while also being fast to evaluate. We generate accurate surrogate models for Effective One Body (EOB) waveforms of non-spinning binary black hole coalescences with durations as long as 10 5 M , mass ratios from 1 to 10, and for multiple spherical harmonic modes. We find that these surrogates are more than three orders of magnitude faster to evaluate as compared to the cost of generating EOB waveforms in standard ways. Surrogate model building for other waveform families and models follow the same steps and have the same low computational online scaling cost. For expensive numerical simulations of binary black hole coalescences we thus anticipate extremely large speedups in generating new waveforms with a surrogate. As waveform generation is one of the dominant costs in parameter estimation algorithms and parameter space exploration, surrogate models offer a new and practical way to dramatically accelerate such studies without impacting accuracy.

Research paper thumbnail of Reduced Basis Catalogs for Gravitational Wave Templates

Physical Review Letters, 2011

We introduce a reduced basis approach as a new paradigm for modeling, representing and searching ... more We introduce a reduced basis approach as a new paradigm for modeling, representing and searching for gravitational waves. We construct waveform catalogs for non-spinning compact binary coalescences, and we find that for accuracies of 99% and 99.999% the method generates a factor of about 10 − 10 5 fewer templates than standard placement methods. The continuum of gravitational waves can be represented by a finite and comparatively compact basis. The method is robust under variations in the noise of detectors, implying that only a single catalog needs to be generated.

Research paper thumbnail of Electromagnetic and gravitational self-force on a relativistic particle from quantum fields in curved space

Physical Review D, 2006

We provide a quantum field theoretical derivation of the Abraham-Lorentz-Dirac (ALD) equation, de... more We provide a quantum field theoretical derivation of the Abraham-Lorentz-Dirac (ALD) equation, describing the motion of an electric point charge sourcing an electromagnetic field, which back-reacts on the charge as a self-force, and the Mino-Sasaki-Tanaka-Quinn-Wald (MSTQW) equation describing the motion of a point mass with self-force interacting with the linearized metric perturbations caused by the mass off an otherwise vacuous curved background spacetime. We regularize the formally divergent self-force by smearing the direct part of the retarded Green's function and using a quasilocal expansion. We also derive the ALD-Langevin and the MSTQW-Langevin equations with a classical stochastic force accounting for the effect of the quantum fluctuations in the field, which causes small fluctuations on the particle trajectory. These equations will be useful for studying the stochastic motion of charges and small masses under the influence of both quantum and classical noise sources, derived either self-consistently or put in by hand phenomenologically. We also show that history-dependent noise-induced drift motions could arise from such stochastic sources on the trajectory that could be a hidden feature of gravitational wave forms hitherto unknown.

Research paper thumbnail of Radiation reaction and gravitational waves in the effective field theory approach

Physical Review D, 2009

We compute the contribution to the Lagrangian from the leading order (2.5 post-Newtonian) radiati... more We compute the contribution to the Lagrangian from the leading order (2.5 post-Newtonian) radiation reaction and the quadrupolar gravitational waves emitted from a binary system using the effective field theory (EFT) approach of Goldberger and Rothstein. We use an initial value formulation of the underlying (quantum) framework to implement retarded boundary conditions and describe these real-time dissipative processes. We also demonstrate why the usual scattering formalism of quantum field theory inadequately accounts for these. The methods discussed here should be useful for deriving real-time quantities (including radiation reaction forces and gravitational wave emission) and hereditary terms in the post-Newtonian approximation (including memory, tail and other causal, history-dependent integrals) within the EFT approach. We also provide a consistent and correct formulation of the radiation sector in the equivalent effective field theory approach of Kol and Smolkin.

Research paper thumbnail of Self-force on extreme mass ratio inspirals via curved spacetime effective field theory

Physical Review D, 2009

In this series we construct an effective field theory (EFT) in curved spacetime to study gravitat... more In this series we construct an effective field theory (EFT) in curved spacetime to study gravitational radiation and backreaction effects. We begin in this paper with a derivation of the selfforce on a compact object moving in the background spacetime of a supermassive black hole. The EFT approach utilizes the disparity between two length scales, which in this problem are the size of the compact object rm and the radius of curvature of the background spacetime R such that ε ≡ rm/R 1, to treat the orbital dynamics of the compact object, described as an effective point particle, separately from its tidal deformations. The equation of motion of an effective relativistic point particle coupled to the gravitational waves generated by its motion in a curved background spacetime can be derived without making a slow motion or weak field approximation, as was assumed in earlier EFT treatment of post-Newtonian binaries. Ultraviolet divergences are regularized using Hadamard's partie finie to isolate the non-local finite part from the quasi-local divergent part. The latter is constructed from a momentum space representation for the graviton retarded propagator and is evaluated using dimensional regularization in which only logarithmic divergences are relevant for renormalizing the parameters of the theory. As a first important application of this framework we explicitly derive the first order self-force given by Mino, Sasaki, Tanaka, Quinn and Wald. Going beyond the point particle approximation, to account for the finite size of the object, we demonstrate that for extreme mass ratio inspirals the motion of a compact object is affected by tidally induced moments at O(ε 4 ), in the form of an Effacement Principle. The relatively large radius-to-mass ratio of a white dwarf star allows for these effects to be enhanced until the white dwarf becomes tidally disrupted, a potentially O(ε 2 ) process, or plunges into the supermassive black hole. This work provides a new foundation for further exploration of higher order self force corrections, gravitational radiation and spinning compact objects.