Classical soft graviton theorem rewritten

Classical soft graviton theorem gives the gravitational wave-form at future null infinity at late retarded time u for a general classical scattering. The large u expansion has three known universal terms: the constant term, the term proportional to 1/u and the term proportional to ln u/u2, whose coefficients are determined solely in terms of the momenta of incoming and the outgoing hard particles, including the momenta carried by outgoing gravitational and electromagnetic radiation produced during scattering. For the constant term, also known as the memory effect, the dependence on the momenta carried away by the final state radiation / massless particles is known as non-linear memory or null memory. It was shown earlier that for the coefficient of the 1/u term the dependence on the momenta of the final state massless particles / radiation cancels and the result can be written solely in terms of the momenta of the incoming particles / radiation and the final state massive particles. In this note we show that the same result holds for the coefficient of the ln u/u2 term. Our result implies that for scattering of massless particles the coefficients of the 1/u and ln u/u2 terms are determined solely by the incoming momenta, even if the particles coalesce to form a black hole and massless radiation. We use our result to compute the low frequency flux of gravitational radiation from the collision of massless particles at large impact parameter.

Note on the asymptotic structure of Kerr-Schild form

The Kerr-Schild form provides a natural way of realizing the classical double copy that relates exact solutions in general relativity to exact solutions in gauge theory. In this paper, we examine the asymptotic structure of Kerr-Schild form. In Newman-Unti gauge, we find a generic solution space satisfying the Kerr-Schild form in series expansion around null infinity. The news function in the solution space is chiral and can not lead to a mass loss formula. A class of asymptotically flat complex pp-wave solutions in closed form is obtained from the solution space.

Post-Newtonian waveforms from spinning scattering amplitudes

We derive the classical gravitational radiation from an aligned spin binary black hole on closed orbits, using a dictionary built from the 5-point QFT scattering amplitude of two massive particles exchanging and emitting a graviton. We show explicitly the agreement of the transverse-traceless components of the radiative linear metric perturbations — and the corresponding gravitational wave energy flux — at future null infinity, derived from the scattering amplitude and those derived utilizing an effective worldline action in conjunction with multipolar post-Minkowskian matching. At the tree-level, this result holds at leading orders in the black holes’ velocities and up to quadratic order in their spins. At sub-leading order in black holes’ velocities, we demonstrate a matching of the radiation field for quasi-circular orbits in the no-spin limit. At the level of the radiation field, and to leading order in the velocities, there exists a one-to-one correspondence between the binary black hole mass and current quadrupole moments, and the scalar and linear-in-spin scattering amplitudes, respectively. Therefore, we show explicitly that waveforms, needed to detect gravitational waves from inspiraling binary black holes, can be derived consistently, to the orders considered, from the classical limit of quantum scattering amplitudes.

Asymptotic symmetries at null-infinity for the Rarita-Schwinger field with magnetic term

In this paper we study the magnetic charges of the free massless Rarita-Schwinger field in four dimensional asymptotically flat space-time. This is the first step towards extending the study of the dual BMS charges to supergravity. The magnetic charges appear due to the addition of a boundary term in the action. This term is similar to the theta term in Yang-Mills theory. At null-infinity an infinite dimensional algebra is discovered, both for the electric and magnetic charge.

Charge algebra for non-abelian large gauge symmetries at O(r)

Asymptotic symmetries of gauge theories are known to encode infrared properties of radiative fields. In the context of tree-level Yang-Mills theory, the leading soft behavior of gluons is captured by large gauge symmetries with parameters that are O(1) in the large r expansion towards null infinity. This relation can be extended to subleading order provided one allows for large gauge symmetries with O(r) gauge parameters. The latter, however, violate standard asymptotic field fall-offs and thus their interpretation has remained incomplete. We improve on this situation by presenting a relaxation of the standard asymptotic field behavior that is compatible with O(r) gauge symmetries at linearized level. We show the extended space admits a symplectic structure on which O(1) and O(r) charges are well defined and such that their Poisson brackets reproduce the corresponding symmetry algebra.

A new look at the Bondi-Sachs energy-momentum

How does one compute the Bondi mass on an arbitrary cut of null infinity I when it is not presented in a Bondi system? What then is the correct definition of the mass aspect? How does one normalise an asymptotic translation computed on a cut which is not equipped with the unit-sphere metric? These are questions which need to be answered if one wants to calculate the Bondi-Sachs energy-momentum for a space-time which has been determined numerically. Under such conditions there is not much control over the presentation of I so that most of the available formulations of the Bondi energy-momentum simply do not apply. The purpose of this article is to provide the necessary background for a manifestly conformally invariant and gauge independent formulation of the Bondi energy-momentum. To this end we introduce a conformally invariant version of the GHP formalism to rephrase all the well-known formulae. This leads us to natural definitions for the space of asymptotic translations with its Lorentzian metric, for the Bondi news and the mass-aspect. A major role in these developments is played by the “co-curvature”, a naturally appearing quantity closely related to the Gauß curvature on a cut of I.

Staticity and regularity for zero rest-mass fields near spatial infinity on flat spacetime

Linear zero-rest-mass fields generically develop logarithmic singularities at the critical sets where spatial infinity meets null infinity. Friedrich's representation of spatial infinity is ideally suited to study this phenomenon. These logarithmic singularities are an obstruction to the smoothness of the zero-rest-mass field at null infinity and, in particular, to peeling. In the case of the spin-2 field it has been shown that these logarithmic singularities can be precluded if the initial data for the field satisfies a certain regularity condition involving the vanishing, at spatial infinity, of a certain spinor (the linearised Cotton spinor) and its totally symmetrised derivatives. In this article we investigate the relation between this regularity condition and the staticity of the spin-2 field. It is shown that while any static spin-2 field satisfies the regularity condition, not every solution satisfying the regularity condition is static. This result is in contrast with what happens in the case of General Relativity where staticity in a neighbourhood of spatial infinity and the smoothness of the field at future and past null infinities are much more closely related.

Free data at spacelike $${\mathscr {I}}$$ and characterization of Kerr-de Sitter in all dimensions

We study the free data in the Fefferman–Graham expansion of asymptotically Einstein $$(n+1)$$ ( n + 1 ) -dimensional metrics with non-zero cosmological constant. We analyze the relation between the electric part of the rescaled Weyl tensor at $${\mathscr {I}}$$ I , D, and the free data at $${\mathscr {I}}$$ I , namely a certain traceless and transverse part of the n-th order coefficient of the expansion $$\mathring{g}_{(n)}$$ g ˚ ( n ) . In the case $$\Lambda <0$$ Λ < 0 and Lorentzian signature, it was known [23] that conformal flatness at $${\mathscr {I}}$$ I is sufficient for D and $$\mathring{g}_{(n)}$$ g ˚ ( n ) to agree up to a universal constant. We recover and extend this result to general signature and any sign of non-zero $$\Lambda $$ Λ . We then explore whether conformal flatness of $${\mathscr {I}}$$ I is also neceesary and link this to the validity of long-standing open conjecture that no non-trivial purely magnetic $$\Lambda $$ Λ -vacuum spacetimes exist. In the case of $${\mathscr {I}}$$ I non-conformally flat we determine a quantity constructed from an auxiliary metric which can be used to retrieve $$\mathring{g}_{(n)}$$ g ˚ ( n ) from the (now singular) electric part of the Weyl tensor. We then concentrate in the $$\Lambda >0$$ Λ > 0 case where the Cauchy problem at $${\mathscr {I}}$$ I of the Einstein vacuum field equations is known to be well-posed when the data at $${\mathscr {I}}$$ I are analytic or when the spacetime has even dimension. We establish a necessary and sufficient condition for analytic data at $${\mathscr {I}}$$ I to generate spacetimes with symmetries in all dimensions. These results are used to find a geometric characterization of the Kerr-de Sitter metrics in all dimensions in terms of its geometric data at null infinity.