arXiv subjects

David A. Nichols

Publications and source records attributed to David A. Nichols.

At least 37 records · Page 2Linked to original sources

arXiv2021

Detecting dark matter around black holes with gravitational waves: Effects of dark-matter dynamics on the gravitational waveform

A dark matter overdensity around a black hole may significantly alter the dynamics of the black hole's merger with another compact object. We consider here intermediate mass-ratio inspirals of stellar-mass compact objects with intermediate-mass black holes "dressed" with dark matter. We first demonstrate that previous estimates based on a fixed dark-matter dress are unphysical for a range of binaries and dark-matter distributions by showing that the total energy dissipated by the compact object through dynamical friction, as it inspirals through the dense dark matter environment towards the black hole, is larger than the gravitational binding energy of the dark-matter dress itself. We then introduce a new formalism that allows us to self-consistently follow the evolution of the dark-matter dress due to its gravitational interaction with the binary. We show that the dephasing of the gravitational waveform induced by dark matter is smaller than previously thought, but is still potentially detectable with the LISA space interferometer. The gravitational waves from such binaries could provide powerful diagnostics of the particle nature of dark matter.

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arXiv2021

Definitions of (super) angular momentum in asymptotically flat spacetimes: Properties and applications to compact-binary mergers

The symmetries of asymptotically flat spacetimes in general relativity are given by the Bondi-Metzner-Sachs (BMS) group, though there are proposed generalizations of its symmetry algebra. Associated with each symmetry is a charge and a flux, and the values of these charges and their changes can characterize a spacetime. The charges of the BMS group are relativistic angular momentum and supermomentum (which includes 4-momentum); the extensions of the BMS algebra also include generalizations of angular momentum called "super angular momentum." Several different formalisms have been used to define angular momentum, and they produce nonequivalent expressions for the charge. It was shown recently that these definitions can be summarized in a two-parameter family of angular momenta, which we investigate in this paper. We find that requiring that the angular momentum vanishes in flat spacetime restricts the two parameters to be equal. If we do not require that the angular momentum agrees with a common Hamiltonian definition, then we are left with a one-parameter family of angular momenta that includes the definitions from the several different formalisms. We then also propose a similar two-parameter family of super angular momentum. We examine the effect of the free parameters on the values of the angular momentum and super angular momentum from nonprecessing binary-black-hole mergers. The definitions of angular momentum differ at a high post-Newtonian order for these systems, but only when the system is radiating gravitational waves. The different super-angular-momentum definitions occur at lower orders, and there is a difference in the change of super angular momentum even after the gravitational waves pass, which arises because of the gravitational-wave memory effect. We estimate the size of these effects using numerical-relativity surrogate waveforms and find they are small but resolvable.

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arXiv2021

Brans-Dicke theory in Bondi-Sachs form: Asymptotically flat solutions, asymptotic symmetries and gravitational-wave memory effects

Gravitational-wave memory effects are identified by their distinctive effects on families of freely falling observers: after a burst of waves pass by their locations, memory effects can cause lasting relative displacements of the observers. These effects are closely related to the infrared properties of gravity and other massless field theories, including their asymptotic symmetries and conserved quantities. In this paper, we investigate the connection between memory effects, symmetries, and conserved quantities in Brans-Dicke theory. We compute the field equations in Bondi coordinates, and we define a set of boundary conditions that represent asymptotically flat solutions in this context. Next, we derive the asymptotic symmetry group of these spacetimes, and we find that it is the same as the Bondi-Metzner-Sachs group in general relativity. Because there is an additional polarization of gravitational waves in Brans-Dicke theory, we compute the memory effects associated with this extra polarization (the so-called "breathing" mode). This breathing mode produces a uniform expansion (or contraction) of a ring of freely falling observers. After these breathing gravitational waves pass by the observers' locations, there are two additional memory effects that depend on their initial displacements and relative velocities. Neither of these additional memory effects seems to be related to asymptotic symmetries or conserved quantities; rather, they are determined by the properties of the nonradiative region before and after the bursts of the scalar field and the gravitational waves. We discuss the properties of these regions necessary to support nontrivial breathing-mode-type memory effects.

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arXiv2021

Classical and Quantized General-Relativistic Angular Momentum

Angular momentum at null infinity has a supertranslation ambiguity from the lack of a preferred Poincaré group and a similar ambiguity when the center-of-mass position changes as linear momentum is radiated. Recently, we noted there is an additional one-parameter ambiguity in the possible definitions of angular momentum and center-of-mass charge. We argue that this one-parameter ambiguity can be resolved by considering the generalized BMS charges that are constructed from local 2-sphere-covariant tensors near null infinity; these supertranslation-covariant charges differ from several expressions currently used. Quantizing angular momentum requires a supertranslation-invariant angular momentum in the center-of-mass frame. We propose one such definition of angular momentum involving nonlocal quantities on the 2-sphere, which could be used to define a quantum notion of general-relativistic angular momentum.

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arXiv2020

Persistent gravitational wave observables: Nonlinear plane wave spacetimes

In the first paper in this series, we introduced "persistent gravitational wave observables" as a framework for generalizing the gravitational wave memory effect. These observables are nonlocal in time and nonzero in the presence of gravitational radiation. We defined three specific examples of persistent observables: a generalization of geodesic deviation that allowed for arbitrary acceleration, a holonomy observable involving a closed curve, and an observable that can be measured using a spinning test particle. For linearized plane waves, we showed that our observables could be determined just from one, two, and three time integrals of the Riemann tensor along a central worldline, when the observers follow geodesics. In this paper, we compute these three persistent observables in nonlinear plane wave spacetimes, and we find that the fully nonlinear observables contain effects that differ qualitatively from the effects present in the observables at linear order. Many parts of these observables can be determined from two functions, the transverse Jacobi propagators, and their derivatives (for geodesic observers). These functions, at linear order in the spacetime curvature, reduce to the one, two, and three time integrals of the Riemann tensor mentioned above.

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arXiv2020

Forecasts for detecting the gravitational-wave memory effect with Advanced LIGO and Virgo

The detection of gravitational waves (GWs) from binary black holes (BBHs) has allowed the theory of general relativity to be tested in a previously unstudied regime: that of strong curvature and high GW luminosities. One distinctive and measurable effect associated with this aspect of the theory is the nonlinear GW memory effect. The GW memory effect is characterized by its effect on freely falling observers: the proper distance between their locations differs before and after a burst of GWs passes by their locations. Gravitational-wave interferometers, like the LIGO and Virgo detectors, can measure features of this effect from a single BBH merger, but previous work has shown that it will require an event that is significantly more massive and closer than any previously detected GW event. Finding evidence for the GW memory effect within the entire population of BBH mergers detected by LIGO and Virgo is more likely to occur sooner. A prior study has shown that the GW memory effect could be detected in a population of BBHs consisting of binaries like the first GW150914 event after roughly one-hundred events. In this paper, we compute forecasts of the time it will take the advanced LIGO and Virgo detectors (when the detectors are operating at their design sensitivities) to find evidence for the GW memory effect in a population of BBHs that is consistent with the measured population of events in the first two observing runs of the LIGO detectors. We find that after five years of data collected by the advanced LIGO and Virgo detectors the signal-to-noise ratio for the nonlinear GW memory effect in the population will be about three (near a previously used threshold for detection). We point out that the different approximation methods used to compute the GW memory effect can lead to notably different signal-to-noise ratios.

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arXiv2018

Center-of-mass angular momentum and memory effect in asymptotically flat spacetimes

Gravitational-wave (GW) memory effects are constant changes in the GW strain and its time integrals, which are closely connected to changes in the charges that characterize asymptotically flat spacetimes. The first GW memory effect discovered was a lasting change in the GW strain. It can occur when GWs or massless fields carry away 4-momentum from an isolated source. Subsequently, it was shown that fluxes of intrinsic angular momentum can generate a new type of memory effect called the spin memory, which is an enduring change in a portion of the time integral of the GW strain. In this paper, we note that there is another new type of memory effect. We call it the center-of-mass (CM) memory effect, because it is related to changes in the CM part of the angular momentum of a spacetime. We first examine a few properties of the CM angular momentum. Specifically, we describe how it transforms under the supertranslation symmetry transformations of the Bondi-Metzner-Sachs group, and we compute a new expression for the flux of CM angular momentum carried by GWs in terms of a set of radiative multipole moments of the GW strain. We then turn to the CM memory effect. The CM memory effect appears in a quantity which has units of the time integral of the GW strain. We define the effect in asymptotically flat spacetimes that start in a stationary state, radiate, and settle to a different stationary state. We show that it is invariant under infinitesimal supertranslation symmetries in this context. To determine the magnitude of the flux of CM angular momentum and the CM memory effect, we compute these quantities for nonspinning, quasicircular compact binaries in the post-Newtonian approximation. The CM memory effect arises from terms in the gravitational waveform for such binaries beginning at third and fourth post-Newtonian order for unequal- and equal-mass binaries, respectively. [Abstract abridged]

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arXiv2017

Spin memory effect for compact binaries in the post-Newtonian approximation

The spin memory effect is a recently predicted relativistic phenomenon in asymptotically flat spacetimes that become nonradiative infinitely far in the past and future. Between these early and late times, the magnetic-parity part of the time integral of the gravitational-wave strain can undergo a nonzero change; this difference is the spin memory effect. Families of freely falling observers around an isolated source can measure this effect, in principle, and fluxes of angular momentum per unit solid angle (or changes in superspin charges) generate the effect. The spin memory effect had not been computed explicitly for astrophysical sources of gravitational waves, such as compact binaries. In this paper, we compute the spin memory in terms of a set of radiative multipole moments of the gravitational-wave strain. The result of this calculation allows us to establish the following results about the spin memory: (i) We find that the accumulation of the spin memory behaves in a qualitatively different way from that of the displacement memory effect for nonspinning, quasicircular compact binaries in the post-Newtonian approximation: the spin memory undergoes a large secular growth over the duration of the inspiral, whereas for the displacement effect this increase is small. (ii) The rate at which the spin memory grows is equivalent to a nonlinear, but nonoscillatory and nonhereditary effect in the gravitational waveform that had been previously calculated for nonspinning, quasicircular compact binaries. (iii) This rate of build-up of the spin memory could potentially be detected by future gravitational-wave detectors by carefully combining the measured waveforms from hundreds of gravitational-wave detections of compact binaries.

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arXiv2016

Properties of an affine transport equation and its holonomy

An affine transport equation was used recently to study properties of angular momentum and gravitational-wave memory effects in general relativity. In this paper, we investigate local properties of this transport equation in greater detail. Associated with this transport equation is a map between the tangent spaces at two points on a curve. This map consists of a homogeneous (linear) part given by the parallel transport map along the curve plus an inhomogeneous part, which is related to the development of a curve in a manifold into an affine tangent space. For closed curves, the affine transport equation defines a "generalized holonomy" that takes the form of an affine map on the tangent space. We explore the local properties of this generalized holonomy by using covariant bitensor methods to compute the generalized holonomy around geodesic polygon loops. We focus on triangles and "parallelogramoids" with sides formed from geodesic segments. For small loops, we recover the well-known result for the leading-order linear holonomy ($\sim$ Riemann $\times$ area), and we derive the leading-order inhomogeneous part of the generalized holonomy ($\sim$ Riemann $\times$ area$^{3/2}$). Our bitensor methods let us naturally compute higher-order corrections to these leading results. These corrections reveal the form of the finite-size effects that enter into the holonomy for larger loops; they could also provide quantitative errors on the leading-order results for finite loops.

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arXiv2016

Testing general relativity using golden black-hole binaries

The coalescences of stellar-mass black-hole binaries through their inspiral, merger, and ringdown are among the most promising sources for ground-based gravitational-wave (GW) detectors. If a GW signal is observed with sufficient signal-to-noise ratio, the masses and spins of the black holes can be estimated from just the inspiral part of the signal. Using these estimates of the initial parameters of the binary, the mass and spin of the final black hole can be uniquely predicted making use of general-relativistic numerical simulations. In addition, the mass and spin of the final black hole can be independently estimated from the merger--ringdown part of the signal. If the binary black hole dynamics is correctly described by general relativity (GR), these independent estimates have to be consistent with each other. We present a Bayesian implementation of such a test of general relativity, which allows us to combine the constraints from multiple observations. Using kludge modified GR waveforms, we demonstrate that this test can detect sufficiently large deviations from GR, and outline the expected constraints from upcoming GW observations using the second-generation of ground-based GW detectors.

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arXiv2016

Prescriptions for measuring and transporting local angular momenta in general relativity

For observers in curved spacetimes, elements of the dual space of the set of linearized Poincaré transformations from an observer's tangent space to itself can be naturally interpreted as local linear and angular momenta. We present an operational procedure by which observers can measure such quantities using only information about the spacetime curvature at their location. When applied by observers near spacelike or null infinity in stationary, vacuum, asymptotically flat spacetimes, there is a sense in which the procedure yields the well-defined linear and angular momenta of the spacetime. We also describe a general method by which observers can transport local linear and angular momenta from one point to another, which improves previous prescriptions. This transport is not path independent in general, but becomes path independent for the measured momenta in the same limiting regime. The transport prescription is defined in terms of differential equations, but it can also be interpreted as parallel transport in a particular direct-sum vector bundle. Using the curvature of the connection on this bundle, we compute and discuss the holonomy of the transport law. We anticipate that these measurement and transport definitions may ultimately prove useful for clarifying the physical interpretation of the Bondi-Metzner-Sachs charges of asymptotically flat spacetimes.

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arXiv2016

Observer dependence of angular momentum in general relativity and its relationship to the gravitational-wave memory effect

We define a procedure by which observers can measure a type of special-relativistic linear and angular momentum $(P^a, J^{ab})$ at a point in a curved spacetime using only the spacetime geometry in a neighborhood of that point. The method is chosen to yield the conventional results in stationary spacetimes near future null infinity. We also explore the extent to which spatially separated observers can compare the values of angular momentum that they measure and find consistent results. We define a generalization of parallel transport along curves which gives a prescription for transporting values of angular momentum along curves that yields the correct result in special relativity. If observers use this prescription, then they will find that the angular momenta they measure are observer dependent, because of the effects of spacetime curvature. The observer dependence can be quantified by a kind of generalized holonomy. We show that bursts of gravitational waves with memory generically give rise to a nontrivial generalized holonomy: there is, in this context, a close relation between the observer dependence of angular momentum and the gravitational-wave memory effect.

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arXiv2015

Reply to "On the branching of quasinormal resonances of near-extremal Kerr black holes" by Shahar Hod

In a study of the quasinormal mode frequencies of nearly extremal black holes, we pointed out a bifurcation of the mode spectrum into modes with finite decay and modes with vanishing decay in the extremal limit. We provided analytic and semi-analytic results identifying which families of modes bifurcated, and when modes with finite decay rates exist when approaching the extremal limit. In a recent note (arXiv:1510.05604), Hod suggests that additional modes asymptote to finite decay at extremely high spin parameter, based on past work by Detweiler. We search for these suggested modes and find no evidence of their existence. In addition, we point out an inconsistency in the derivation of the proposed modes, which further indicates that these damped modes do not exist.

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arXiv2013

Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes II. Stationary Black Holes

When one splits spacetime into space plus time, the Weyl curvature tensor (which equals the Riemann tensor in vacuum) splits into two spatial, symmetric, traceless tensors: the tidal field $E$, which produces tidal forces, and the frame-drag field $B$, which produces differential frame dragging. In recent papers, we and colleagues have introduced ways to visualize these two fields: tidal tendex lines (integral curves of the three eigenvector fields of $E$) and their tendicities (eigenvalues of these eigenvector fields); and the corresponding entities for the frame-drag field: frame-drag vortex lines and their vorticities. These entities fully characterize the vacuum Riemann tensor. In this paper, we compute and depict the tendex and vortex lines, and their tendicities and vorticities, outside the horizons of stationary (Schwarzschild and Kerr) black holes; and we introduce and depict the black holes' horizon tendicity and vorticity (the normal-normal components of $E$ and $B$ on the horizon). For Schwarzschild and Kerr black holes, the horizon tendicity is proportional to the horizon's intrinsic scalar curvature, and the horizon vorticity is proportional to an extrinsic scalar curvature. We show that, for horizon-penetrating time slices, all these entities ($E$, $B$, the tendex lines and vortex lines, the lines' tendicities and vorticities, and the horizon tendicities and vorticities) are affected only weakly by changes of slicing and changes of spatial coordinates, within those slicing and coordinate choices that are commonly used for black holes. [Abstract is abbreviated.]

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arXiv2013

Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes III. Quasinormal Pulsations of Schwarzschild and Kerr Black Holes

In recent papers, we and colleagues have introduced a way to visualize the full vacuum Riemann curvature tensor using frame-drag vortex lines and their vorticities, and tidal tendex lines and their tendicities. We have also introduced the concepts of horizon vortexes and tendexes and 3-D vortexes and tendexes (regions where vorticities or tendicities are large). Using these concepts, we discover a number of previously unknown features of quasinormal modes of Schwarzschild and Kerr black holes. These modes can be classified by mode indexes (n,l,m), and parity, which can be electric [(-1)^l] or magnetic [(-1)^(l+1)]. Among our discoveries are these: (i) There is a near duality between modes of the same (n,l,m): a duality in which the tendex and vortex structures of electric-parity modes are interchanged with the vortex and tendex structures (respectively) of magnetic-parity modes. (ii) This near duality is perfect for the modes' complex eigenfrequencies (which are well known to be identical) and perfect on the horizon; it is slightly broken in the equatorial plane of a non-spinning hole, and the breaking becomes greater out of the equatorial plane, and greater as the hole is spun up; but even out of the plane for fast-spinning holes, the duality is surprisingly good. (iii) Electric-parity modes can be regarded as generated by 3-D tendexes that stick radially out of the horizon. As these "longitudinal," near-zone tendexes rotate or oscillate, they generate longitudinal-transverse near-zone vortexes and tendexes, and outgoing and ingoing gravitational waves. The ingoing waves act back on the longitudinal tendexes, driving them to slide off the horizon, which results in decay of the mode's strength. (iv) By duality, magnetic-parity modes are driven in this same manner by longitudinal, near-zone vortexes that stick out of the horizon. [Abstract abridged.]

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arXiv2012

Comparison of electromagnetic and gravitational radiation; what we can learn about each from the other

We compare the nature of electromagnetic fields and of gravitational fields in linearized general relativity. We carry out this comparison both mathematically and visually. In particular the "lines of force" visualizations of electromagnetism are contrasted with the recently introduced tendex/vortex eigenline technique for visualizing gravitational fields. Specific solutions, visualizations, and comparisons are given for an oscillating point quadrupole source. Among the similarities illustrated are the quasistatic nature of the near fields, the transverse 1/r nature of the far fields, and the interesting intermediate field structures connecting these two limiting forms. Among the differences illustrated are the meaning of field line motion, and of the flow of energy.

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arXiv2012

Branching of quasinormal modes for nearly extremal Kerr black holes

We show that nearly extremal Kerr black holes have two distinct sets of quasinormal modes, which we call zero-damping modes (ZDMs) and damped modes (DMs). The ZDMs exist for all harmonic indices $l$ and $m \ge 0$, and their frequencies cluster onto the real axis in the extremal limit. The DMs have nonzero damping for all black hole spins; they exist for all counterrotating modes ($m<0$) and for corotating modes with $0\leq μ\lesssim μ_c=0.74$ (in the eikonal limit), where $μ\equiv m/(l+1/2)$. When the two families coexist, ZDMs and DMs merge to form a single set of quasinormal modes as the black hole spin decreases. Using the effective potential for perturbations of the Kerr spacetime, we give intuitive explanations for the absence of DMs in certain areas of the spectrum and for the branching of the spectrum into ZDMs and DMs at large spins.

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arXiv2012

Quasinormal-mode spectrum of Kerr black holes and its geometric interpretation

There is a well-known, intuitive geometric correspondence between high-frequency QNMs of Schwarzschild black holes and null geodesics that reside on the light-ring : the real part of the mode's frequency relates to the geodesic's orbital frequency, and the imaginary part of the frequency corresponds to the Lyapunov exponent of the orbit. For slowly rotating black holes, the QNM real frequency is a linear combination of a the orbit's precessional and orbital frequencies, but the correspondence is otherwise unchanged. In this paper, we find a relationship between the QNM frequencies of Kerr black holes of arbitrary (astrophysical) spins and general spherical photon orbits, which is analogous to the relationship for slowly rotating holes. To derive this result, we first use the WKB approximation to compute accurate algebraic expressions for large-l QNM frequencies. Comparing our WKB calculation to the leading-order, geometric-optics approximation to scalar-wave propagation in the Kerr spacetime, we then draw a correspondence between the real parts of the parameters of a QNM and the conserved quantities of spherical photon orbits. At next-to-leading order in this comparison, we relate the imaginary parts of the QNM parameters to coefficients that modify the amplitude of the scalar wave. With this correspondence, we find a geometric interpretation to two features of the QNM spectrum of Kerr black holes: First, for Kerr holes rotating near the maximal rate, a large number of modes have nearly zero damping; we connect this characteristic to the fact that a large number of spherical photon orbits approach the horizon in this limit. Second, for black holes of any spins, the frequencies of specific sets of modes are degenerate; we find that this feature arises when the spherical photon orbits corresponding to these modes form closed (as opposed to ergodically winding) curves.

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