2,115 research outputs found
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]Comment: v2: 26 pages; updated to match version published in Phys. Rev.
Hybrid method for understanding black-hole mergers: Inspiralling case
We adapt a method of matching post-Newtonian and black-hole-perturbation theories on a timelike surface (which proved useful for understanding head-on black-hole-binary collisions) to treat equal-mass, inspiralling black-hole binaries. We first introduce a radiation-reaction potential into this method, and we show that it leads to a self-consistent set of equations that describe the simultaneous evolution of the waveform and of the timelike matching surface. This allows us to produce a full inspiral-merger-ringdown waveform of the l=2, m=±2 modes of the gravitational waveform of an equal-mass black-hole-binary inspiral. These modes match those of numerical-relativity simulations well in phase, though less well in amplitude for the inspiral. As a second application of this method, we study a merger of black holes with spins antialigned in the orbital plane (the superkick configuration). During the ringdown of the superkick, the phases of the mass- and current-quadrupole radiation become locked together, because they evolve at the same quasinormal-mode frequencies. We argue that this locking begins during the merger, and we show that if the spins of the black holes evolve via geodetic precession in the perturbed black-hole spacetime of our model, then the spins precess at the orbital frequency during the merger. In turn, this gives rise to the correct behavior of the radiation, and produces a kick similar to that observed in numerical simulations
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 ( Riemann area), and we derive
the leading-order inhomogeneous part of the generalized holonomy (
Riemann area). 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.Comment: 18 pages, 4 figures, new short section (Sec. 5) in v3; updated to
match article published in GR
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.Comment: 18 pages, 1 table, no figures; some corrections and generalizations
in v2; additional clarifications, corrections, and generalizations in v3; new
table and subsection in v
The Relentless Business of Treaties: How Indigenous Land Became U.S. Property
Review of: "The Relentless Business of Treaties: How Indigenous Land Became U.S. Property," by Martin Case
The Relentless Business of Treaties: How Indigenous Land Became U.S. Property
Review of: The Relentless Business of Treaties: How Indigenous Land Became U.S. Property, by Martin Case
Momentum flow in black-hole binaries. I. Post-Newtonian analysis of the inspiral and spin-induced bobbing
A brief overview is presented of a new Caltech/Cornell research program that is exploring the nonlinear dynamics of curved spacetime in binary black-hole collisions and mergers, and of an initial project in this program aimed at elucidating the flow of linear momentum in binary black holes (BBHs). The “gauge-dependence” (arbitrariness) in the localization of linear momentum in BBHs is discussed, along with the hope that the qualitative behavior of linear momentum will be gauge-independent. Harmonic coordinates are suggested as a possibly preferred foundation for fixing the gauge associated with linear momentum. For a BBH or other compact binary, the Landau-Lifshitz formalism is used to define the momenta of the binary’s individual bodies in terms of integrals over the bodies’ surfaces or interiors, and define the momentum of the gravitational field (spacetime curvature) outside the bodies as a volume integral over the field’s momentum density. These definitions will be used in subsequent papers that explore the internal nonlinear dynamics of BBHs via numerical relativity. This formalism is then used, in the 1.5 post-Newtonian approximation, to explore momentum flow between a binary’s bodies and its gravitational field during the binary’s orbital inspiral. Special attention is paid to momentum flow and conservation associated with synchronous spin-induced bobbing of the black holes, in the so-called “extreme-kick configuration” (where two identical black holes have their spins lying in their orbital plane and antialigned)
Boundary changing operators in the O(n) matrix model
We continue the study of boundary operators in the dense O(n) model on the
random lattice. The conformal dimension of boundary operators inserted between
two JS boundaries of different weight is derived from the matrix model
description. Our results are in agreement with the regular lattice findings. A
connection is made between the loop equations in the continuum limit and the
shift relations of boundary Liouville 3-points functions obtained from Boundary
Ground Ring approach.Comment: 31 pages, 4 figures, Introduction and Conclusion improve
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