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Abstract The Spi framework provides a 4-dimensional approach to investigate the asymptotic properties of gravitational fields as one recedes from isolated systems in any space-like direction, without reference to a Cauchy surface [1]. It is well suited to unify descriptions at null and spatial infinity because I $$ \mathcal{I} $$ arises as the null cone of i°. The goal of this work is to complete this task by introducing a natural extension of the asymptotic conditions at null and spatial infinity of [2], by ‘gluing’ the two descriptions appropriately. Space-times satisfying these conditions are asymptotically flat in both regimes and thus represent isolated gravitating systems. They will be said to be Asymptotically Minkowskian at i°. We show that in these space-times the Spi group S $$ \mathfrak{S} $$ as well as the BMS group B $$ \mathcal{B} $$ naturally reduce to a single Poincaré group, denoted by p i ° $$ {\mathfrak{p}}_{i^{{}^{\circ}}} $$ to highlight the fact that it arises from the gluing procedure at i°. The asymptotic conditions are sufficiently weak to allow for the possibility that the Newman-Penrose component Ψ 1 ° $$ {\Psi}_1^{{}^{\circ}} $$ diverges in the distant past along I $$ \mathcal{I} $$ +. This can occur in astrophysical sources that are not asymptotically stationary in the past, e.g. in scattering situations. Nonetheless, as we show in the companion paper [5], the energy momentum and angular momentum defined at i° equals the sum of that defined at a cross-section C of I $$ \mathcal{I} $$ + and corresponding flux across I $$ \mathcal{I} $$ + to the past of C, when the quantities refer to the preferred Poincaré subgroup p i ° $$ {\mathfrak{p}}_{i^{{}^{\circ}}} $$ .

Abstract In a companion paper [1] we introduced the notion of asymptotically Minkowski spacetimes. These space-times are asymptotically flat at both null and spatial infinity, and furthermore there is a harmonious matching of limits of certain fields as one approaches i ° in null and space-like directions. These matching conditions are quite weak but suffice to reduce the asymptotic symmetry group to a Poincaré group p i ° $$ {\mathfrak{p}}_{i{}^{\circ}} $$ . Restriction of p i ° $$ {\mathfrak{p}}_{i{}^{\circ}} $$ to future null infinity I + $$ {\mathcal{I}}^{+} $$ yields the canonical Poincaré subgroup p i ° bms $$ {\mathfrak{p}}_{i{}^{\circ}}^{\textrm{bms}} $$ of the BMS group B $$ \mathfrak{B} $$ selected in [2, 3] and that its restriction to spatial infinity i°, the canonical subgroup p i ° spi $$ {\mathfrak{p}}_{i{}^{\circ}}^{\textrm{spi}} $$ of the Spi group S $$ \mathfrak{S} $$ selected in [4, 5]. As a result, one can meaningfully compare angular momentum that has been defined at i° using p i ° spi $$ {\mathfrak{p}}_{i{}^{\circ}}^{\textrm{spi}} $$ with that defined on I + $$ {\mathcal{I}}^{+} $$ using p i ° bms $$ {\mathfrak{p}}_{i{}^{\circ}}^{\textrm{bms}} $$ . We show that the angular momentum charge at i° equals the sum of the angular momentum charge at any 2-sphere cross-section S of I + $$ {\mathcal{I}}^{+} $$ and the total flux of angular momentum radiated across the portion of I + $$ {\mathcal{I}}^{+} $$ to the past of S. In general the balance law holds only when angular momentum refers to SO(3) subgroups of the Poincaré group p i ° $$ {\mathfrak{p}}_{i{}^{\circ}} $$ .

Abstract In a companion paper [1] we showed that the symmetry group G $$ \mathfrak{G} $$ of non-expanding horizons (NEHs) is a 1-dimensional extension of the Bondi-Metzner-Sachs group B $$ \mathfrak{B} $$ at I $$ \mathcal{I} $$ +. For each infinitesimal generator of G $$ \mathfrak{G} $$ , we now define a charge and a flux on NEHs as well as perturbed NEHs. The procedure uses the covariant phase space framework in presence of internal null boundaries N $$ \mathcal{N} $$ along the lines of [2–6]. However, N $$ \mathcal{N} $$ is required to be an NEH or a perturbed NEH. Consequently, charges and fluxes associated with generators of G $$ \mathfrak{G} $$ are free of physically unsatisfactory features that can arise if N $$ \mathcal{N} $$ is allowed to be a general null boundary. In particular, all fluxes vanish if N $$ \mathcal{N} $$ is an NEH, just as one would hope; and fluxes associated with symmetries representing ‘time-translations’ are positive definite on perturbed NEHs. These results hold for zero as well as non-zero cosmological constant. In the asymptotically flat case, as noted in [1], I $$ \mathcal{I} $$ ± are NEHs in the conformally completed space-time but with an extra structure that reduces G $$ \mathfrak{G} $$ to B $$ \mathfrak{B} $$ . The flux expressions at N $$ \mathcal{N} $$ reflect this synergy between NEHs and I $$ \mathcal{I} $$ +. In a forthcoming paper, this close relation between NEHs and I $$ \mathcal{I} $$ + will be used to develop gravitational wave tomography, enabling one to deduce horizon dynamics directly from the waveforms at I $$ \mathcal{I} $$ +.

Abstract It is well-known that blackhole and cosmological horizons in equilibrium situations are well-modeled by non expanding horizons (NEHs) [1–3]. In the first part of the paper we introduce multipole moments to characterize their geometry, removing the restriction to axisymmetric situations made in the existing literature [4]. We then show that the symmetry group G $$ \mathfrak{G} $$ of NEHs is a 1-dimensional extension of the BMS group B $$ \mathfrak{B} $$ . These symmetries are used in a companion paper [5] to define charges and fluxes on NEHs, as well as perturbed NEHs. They have physically attractive properties. Finally, it is generally not appreciated that I $$ \mathcal{I} $$ ± of asymptotically flat space-times are NEHs in the conformally completed space-time. Forthcoming papers will (i) show that I $$ \mathcal{I} $$ ± have a small additional structure that reduces G $$ \mathfrak{G} $$ to the BMS group B $$ \mathfrak{B} $$ , and the BMS charges and fluxes can be recovered from the NEH framework; and, (ii) develop gravitational wave tomography for the late stage of compact binary coalescences: reading-off the dynamics of perturbed NEHs in the strong field regime (via evolution of their multipoles), from the waveform at I $$ \mathcal{I} $$ +.