arXiv subjects

Éanna É. Flanagan

Publications and source records attributed to Éanna É. Flanagan.

At least 19 recordsLinked to original sources

arXiv2026

Subleading Asymptotic Charges in Massless Scalar QED

We study subleading asymptotic charges of a U(1) gauge field coupled to a charged massless scalar field in Minkowski spacetime. We consider a phase space for which the scalar-field initial data on null infinity have compact support, while the gauge-field initial data admit an asymptotic expansion with inverse-power tails in retarded (advanced) time, which we refer to as initial-data tails. We identify three finite charges at the null infinities which are conserved under scattering. One is a renormalized version of the standard subleading soft charge. The second is a logarithmic charge which is the difference of the coefficients of the leading order tails at the future and past ends of null infinity. The third is a new charge that probes the average of the tail coefficients. We conjecture that the third charge is associated with a new class of large gauge transformations which diverge linearly in retarded time.

hep-th↗

arXiv2026

Subregion algebras in classical and quantum gravity

We study the kinematics and dynamics of subregion algebras in classical and perturbative quantum gravity associated with portions of null surfaces such as event horizons and finite causal diamonds. We construct half-sided supertranslation generators by extending subregion phase spaces of the event horizon to include doubled pairs of corner edge modes obtained from splitting the horizon, namely relative boosts and null translations of the respective corners. These edge modes carry a corner symplectic form and give rise to canonical charges generating half-sided boosts and translations. We show that the null translation generator is necessarily two-sided in the complementary translation edge modes. The charges act nontrivially on gravitationally dressed local observables on the horizon, such that the horizon subalgebra naturally takes the form of a crossed product by the associated automorphism group. Quantizing the extended phase space after linearizing around a black hole background, we obtain for each horizon cut a Type II$_{\infty}$ von Neumann algebra equipped with a trace, whose von Neumann entropy coincides with the generalized entropy of that cut. The integrability of the half-sided null translation generator lifts to the existence of a self-adjoint operator that implements null time evolution on the Type II$_\infty$ horizon subalgebras. The area operator is identified as the bulk implementation of the Connes cocycle flow for one-sided observables in excited states. The nesting property of the resulting one-parameter family of horizon subalgebras implies a generalized second law for non-stationary linearized perturbations of Killing horizons. Lastly, we use gravitational half-sided modular inclusion algebras to prove the quantum focusing conjecture in the perturbative quantum gravity regime.

hep-th↗

arXiv2023

Conserved charges of the extended Bondi-Metzner-Sachs algebra

Isolated objects in asymptotically flat spacetimes in general relativity are characterized by their conserved charges associated with the Bondi-Metzner-Sachs (BMS) group. These charges include total energy, linear momentum, intrinsic angular momentum and center-of-mass location, and, in addition, an infinite number of supermomentum charges associated with supertranslations. Recently, it has been suggested that the BMS symmetry algebra should be enlarged to include an infinite number of additional symmetries known as superrotations. We show that the corresponding charges are finite and well defined, and can be divided into electric parity "super center-of-mass" charges and magnetic parity "superspin" charges. The supermomentum charges are associated with ordinary gravitational-wave memory, and the super center-of-mass charges are associated with total (ordinary plus null) gravitational-wave memory, in the terminology of Bieri and Garfinkle. Superspin charges are associated with the ordinary piece of spin memory. Some of these charges can give rise to black-hole hair, as described by Strominger and Zhiboedov. We clarify how this hair evades the no-hair theorems.

hep-th↗

arXiv2023

Motion of a spinning particle under the conservative piece of the self-force is Hamiltonian to first order in mass and spin

We consider the motion of a point particle with spin in a stationary spacetime. We define, following Witzany (2019) and later Ramond (2022), a twelve dimensional Hamiltonian dynamical system whose orbits coincide with the solutions of the Mathisson-Papapetrou-Dixon equations of motion with the Tulczyjew-Dixon spin supplementary condition, to linear order in spin. We then perturb this system by adding the conservative pieces of the leading order gravitational self-force and self-torque sourced by the particle's mass and spin. We show that this perturbed system is Hamiltonian and derive expressions for the Hamiltonian function and symplectic form. This result extends our previous result for spinless point particles.

gr-qc↗

arXiv2022

Particle motion under the conservative piece of the self-force is Hamiltonian

We consider the motion of a point particle in a stationary spacetime under the influence of a scalar, electromagnetic or gravitational self-force. We show that the conservative piece of the first-order self-force gives rise to Hamiltonian dynamics, and we derive an explicit expression for the Hamiltonian on phase space. Specialized to the Kerr spacetime, our result generalizes the Hamiltonian function previously obtained by Fujita et. al., which is valid only for non-resonant orbits. We discuss implications for the first law of binary black hole mechanics.

gr-qc↗

arXiv2022

Persistent gravitational wave observables: general framework

The gravitational wave memory effect is characterized by the permanent relative displacement of a pair of initially comoving test particles that is caused by the passage of a burst of gravitational waves. Recent research on this effect has clarified the physical origin and the interpretation of this gravitational phenomenon in terms of conserved charges at null infinity and "soft theorems." In this paper, we describe a more general class of effects than the gravitational wave memory that are not necessarily associated with these charges and soft theorems, but that are, in principle, measurable. We shall refer to these effects as persistent gravitational wave observables. These observables vanish in non-radiative regions of a spacetime, and their effects "persist" after a region of spacetime which is radiating. We give three examples of such persistent observables, as well as general techniques to calculate them. These examples, for simplicity, restrict the class of non-radiative regions to those which are exactly flat. Our first example is a generalization of geodesic deviation that allows for arbitrary acceleration. The second example is a holonomy observable, which is defined in terms of a closed loop. It contains the usual "displacement" gravitational wave memory; three previously identified, though less well known memory effects (the proper time, velocity, and rotation memories); and additional new observables. Finally, the third example we give is an explicit procedure by which an observer could measure a persistent effect using a spinning test particle. We briefly discuss the ability of gravitational wave detectors (such as LIGO and Virgo) to measure these observables.

gr-qc↗

arXiv2021

A class of conserved currents for linearized gravity in the Kerr spacetime

We construct a class of conserved currents for linearized gravity on a Kerr background. Our procedure, motivated by the current for scalar fields discovered by Carter (1977), is given by taking the symplectic product of solutions to the linearized Einstein equations that are defined by symmetry operators. We consider symmetry operators that are associated with separation of variables in the Teukolsky equation, as well as those arising due the self-adjoint nature of the Einstein equations. In the geometric optics limit, the charges associated with these currents reduce to sums over gravitons of positive powers of their Carter constants, much like the conserved current for scalar fields. We furthermore compute the fluxes of these conserved currents through null infinity and the horizon and identify which are finite.

gr-qc↗

arXiv2020

Conserved currents for electromagnetic fields in the Kerr spacetime

We construct a variety of conserved currents for test electromagnetic fields on a Kerr background. Our procedure, which involves the symplectic product for electromagnetism and symmetry operators, generates the conserved currents given by Andersson, Bäckdahl, and Blue (2015), as well as a new conserved current. These currents reduce to the sum of (positive powers of) the Carter constants of photons in the geometric optics limit, and generalize the current for scalar fields discovered by Carter (1977) involving the Killing tensor. We furthermore show that the fluxes of our new current through null infinity and the horizon are finite.

gr-qc↗

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.

gr-qc↗

arXiv2020

Extensions of the asymptotic symmetry algebra of general relativity

We consider a recently proposed extension of the Bondi-Metzner-Sachs algebra to include arbitrary infinitesimal diffeomorphisms on a (2)-sphere. To realize this extended algebra as asymptotic symmetries, we work with an extended class of spacetimes in which the unphysical metric at null infinity is not universal. We show that the symplectic current evaluated on these extended symmetries is divergent in the limit to null infinity. We also show that this divergence cannot be removed by a local and covariant redefinition of the symplectic current. This suggests that such an extended symmetry algebra cannot be realized as symmetries on the phase space of vacuum general relativity at null infinity, and that the corresponding asymptotic charges are ill-defined. However, a possible loophole in the argument is the possibility that symplectic current may not need to be covariant in order to have a covariant symplectic form. We also show that the extended algebra does not have a preferred subalgebra of translations and therefore does not admit a universal definition of Bondi 4-momentum.

gr-qc↗

arXiv2018

Gravitational backreaction on a cosmic string: Formalism

We develop a method for computing the linearized gravitational backreaction for Nambu-Goto strings using a fully covariant formalism. We work with equations of motion expressed in terms of a higher dimensional analog of the geodesic equation subject to self-generated forcing terms. The approach allows arbitrary spacetime and worldsheet gauge choices for the background and perturbation. The perturbed spacetime metric may be expressed as an integral over a distributional stress-energy tensor supported on the string worldsheet. By formally integrating out the distribution, this quantity may be re-expressed in terms of an integral over the retarded image of the string. In doing so, one must pay particular attention to contributions that arise from the field point and from non-smooth regions of the string. Then, the gradient of the perturbed metric decomposes into a sum of boundary and bulk terms. The decomposition depends upon the worldsheet coordinates used to describe the string, but the total is independent of those considerations. We illustrate the method with numerical calculations of the self-force at every point on the worldsheet for loops with kinks, cusps and self-intersections using a variety of different coordinate choices. For field points on smooth parts of the worldsheet the self-force is finite. As the field point approaches a kink or cusp the self-force diverges, but is integrable in the sense that the displacement of the worldsheet remains finite. As a consistency check, we verify that the period-averaged flux of energy-momentum at infinity matches the direct work the self-force performs on the string. The methodology can be applied to address many fundamental questions for string loop evolution.

gr-qc↗

arXiv2017

Self-forces in arbitrary dimensions

Bodies coupled to electromagnetic or other long-range fields are subject to radiation reaction and other effects in which their own fields can influence their motion. Self-force phenomena such as these have been poorly understood for spacetime dimensions not equal to four, despite the relevance of differing dimensionalities for holographic duals, effectively two-dimensional condensed matter and fluid systems, and so on. We remedy this by showing that forces and torques acting on extended electromagnetic charges in all dimensions $d \geq 3$ have the same functional form as the usual test body expressions, except that the electromagnetic field appearing in those expressions is not the physical one; it is an effective surrogate. For arbitrary even $d \geq 4$, our surrogate field locally satisfies the source-free field equations, and is conceptually very similar to what arises in the Detweiler-Whiting prescription previously established when $d=4$. The odd-dimensional case is different, involving effective fields which are not necessarily source-free. Moreover, we find a 1-parameter family of natural effective fields for each odd $d$, where the free parameter--a lengthscale--is degenerate with (finite) renormalizations of a body's stress-energy tensor. While different parameter choices can result in different forces, they do so without affecting physical observables. Having established these general results, explicit point-particle self-forces are derived in odd-dimensional Minkowski spacetimes. Simple examples are discussed for $d=3$ and $d=5$, one of which illustrates that the particularly slow decay of fields in three spacetime dimensions results in particles creating their own "preferred rest frames:" Initially-static charges which are later perturbed have a strong tendency to return to rest. Our results easily extend also to the scalar and gravitational self-force problems.

gr-qc↗

arXiv2016

Self-forces on static bodies in arbitrary dimensions

We derive exact expressions for the scalar and electromagnetic self-forces and self-torques acting on arbitrary static extended bodies in arbitrary static spacetimes with any number of dimensions. Non-perturbatively, our results are identical in all dimensions. Meaningful point particle limits are quite different in different dimensions, however. These limits are defined and evaluated, resulting in simple "regularization algorithms" which can be used in concrete calculations. In these limits, self-interaction is shown to be progressively less important in higher numbers of dimensions; it generically competes in magnitude with increasingly high-order extended-body effects. Conversely, we show that self-interaction effects can be relatively large in $1+1$ and $2+1$ dimensions. Our motivations for this work are twofold: First, no previous derivation of the self-force has been provided in arbitrary dimensions, and heuristic arguments presented by different authors have resulted in conflicting conclusions. Second, the static self-force problem in arbitrary dimensions provides a valuable testbed with which to continue the development of general, non-perturbative methods in the theory of motion. Several new insights are obtained in this direction, including a significantly improved understanding of the renormalization process. We also show that there is considerable freedom to use different "effective fields" in the laws of motion---a freedom which can be exploited to optimally simplify specific problems. Different choices give rise to different inertias, gravitational forces, and electromagnetic or scalar self-forces, but there is a sense in which none of these quantities are individually accessible to experiment. Certain combinations are observable, however, and these remain invariant under all possible field redefinitions.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗

arXiv2015

Static Self-Forces in a Five-Dimensional Black Hole Spacetime

We obtain the electric field and scalar field for a static point charge in closed form in the 5D Schwarzschild-Tangherlini black hole spacetime. We then compute the static self-force in each of these cases by assuming that the appropriate singular field is a 4D Hadamard Green's function on the constant time Riemannian slice. It is well known that the Hadamard Green's function involves an arbitrary regular biscalar $W_{0}(x,x')$, whose coincidence limit $w(x)$ appears in the expression for the self-force. We develop an axiomatic approach to reduce this arbitrary function to a single arbitrary dimensionless coefficient. We show that in the context of this approach to regularization, the self-force does not depend on any undetermined length-scale and need not depend on the internal structure of the charge.

gr-qc↗

arXiv2015

Is motion under the conservative self-force in black hole spacetimes an integrable Hamiltonian system?

A point-like object moving in a background black hole spacetime experiences a gravitational self-force which can be expressed as a local function of the object's instantaneous position and velocity, to linear order in the mass ratio. We consider the worldline dynamics defined by the conservative part of the local self-force, turning off the dissipative part, and we ask: Is that dynamical system a Hamiltonian system, and if so, is it integrable? In the Schwarzschild spacetime, we show that the system is Hamiltonian and integrable, to linear order in the mass ratio, for generic (but not necessarily all) stable bound orbits. There exist an energy and an angular momentum, being perturbed versions of their counterparts for geodesic motion, which are conserved under the forced motion. We also discuss difficulties associated with establishing analogous results in the Kerr spacetime. This result may be useful for future computational schemes, based on a local Hamiltonian description, for calculating the conservative self-force and its observable effects. It is also relevant to the assumption of the existence of a Hamiltonian for the conservative dynamics for generic orbits in the effective-one-body formalism, to linear order in the mass ratio, but to all orders in the post-Newtonian expansion.

gr-qc↗

arXiv2014

First-post-Newtonian quadrupole tidal interactions in binary systems

We consider tidal coupling in a binary stellar system to first-post-Newtonian order. We derive the orbital equations of motion for bodies with spins and mass quadrupole moments and show that they conserve the total linear momentum of the binary. We note that spin-orbit coupling must be included in a 1PN treatment of tidal interactions in order to maintain consistency (except in the special case of adiabatically induced quadrupoles); inclusion of 1PN quadrupolar tidal effects while omitting spin effects would lead to a failure of momentum conservation for generic evolution of the quadrupoles. We use momentum conservation to specialize our analysis to the system's center-of-mass-energy frame; we find the binary's relative equation of motion in this frame and also present a generalized Lagrangian from which it can be derived. We then specialize to the case in which the quadrupole moment is adiabatically induced by the tidal field (in which case it is consistent to ignore spin effects). We show how the adiabatic dynamics for the quadrupole can be incorporated into our action principle and present the simplified orbital equations of motion and conserved energy for the adiabatic case. These results are relevant to gravitational wave signals from inspiralling binary neutron stars.

gr-qc↗