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

Abstract

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.

arXiv comment25 pages, 3 figures. V3 includes additional changes to match the published version

References in corpus (35)

• GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs
• GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Aspects of the BMS/CFT correspondence
• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• Total recoil: the maximum kick from nonspinning black-hole binary inspiral
• The SXS Collaboration catalog of binary black hole simulations
• BMS charge algebra
• Asymptotic symmetries and subleading soft graviton theorem
• Superrotation Charge and Supertranslation Hair on Black Holes
• New Gravitational Memories
• Surrogate model of hybridized numerical relativity binary black hole waveforms
• Conserved charges of the extended Bondi-Metzner-Sachs algebra
• New symmetries for the Gravitational S-matrix
• Binary-black-hole initial data with nearly-extremal spins
• Superboost transitions, refraction memory and super-Lorentz charge algebra
• Post-Newtonian corrections to the gravitational-wave memory for quasicircular, inspiralling compact binaries
• Bondi-Sachs Formalism
• High-accuracy mass, spin, and recoil predictions of generic black-hole merger remnants
• The $\Lambda$-BMS${}_4$ Charge Algebra
• Spin memory effect for compact binaries in the post-Newtonian approximation
• The Poincaré and BMS flux-balance laws with application to binary systems
• Computation of Displacement and Spin Gravitational Memory in Numerical Relativity
• Vacua of the gravitational field
• Gravitational memory in binary black hole mergers
• Center-of-mass angular momentum and memory effect in asymptotically flat spacetimes
• Adding Gravitational Memory to Waveform Catalogs using BMS Balance Laws
• Approximate Killing Vectors on S^2
• Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation
• Classical static final state of collapse with supertranslation memory
• Extensions of the asymptotic symmetry algebra of general relativity
• Flux-balance equations for linear momentum and center-of-mass position of self-gravitating post-Newtonian systems
• Compact binary coalescences: The subtle issue of angular momentum
• Spectral Cauchy Characteristic Extraction of strain, news and gravitational radiation flux
• Coulombic contribution to the flux of angular momentum in general relativity

Cited by in corpus (7)

• The Weyl BMS group and Einstein's equations
• BMS Flux Algebra in Celestial Holography
• Persistent gravitational wave observables: Curve deviation in asymptotically flat spacetimes
• Null Infinity and Horizons: A New Approach to Fluxes and Charges
• Higher memory effects and the post-Newtonian calculation of their gravitational-wave signals
• Higher Memory Effects in Numerical Simulations of Binary Black Hole Mergers
• On the Definition of the Spin Charge in Asymptotically-Flat Spacetimes