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1. An asymptotic framework for gravitational scattering

   https://doi.org/10.1088/1361-6382/acf5c1  

   Compère, Geoffrey ; Gralla, Samuel E. ; Wei, Hongji ( September 2023 , Classical and Quantum Gravity)

   Asymptotically flat spacetimes have been studied in five separate regions: future/past timelike infinity$i^{\pm }$, future/past null infinity, and spatial infinityi⁰. We formulate assumptions and definitions such that the five infinities share a single Bondi–Metzner–Sachs (BMS) group of asymptotic symmetries and associated charges. We show how individual ingoing/outgoing massive bodies may be ascribed initial/final BMS charges and derive global conservation laws stating that the change in total charge is balanced by the corresponding radiative flux. This framework provides a foundation for the study of asymptotically flat spacetimes containing ingoing and outgoing massive bodies, i.e. for generalized gravitational scattering. Among the new implications are rigorous definitions for quantities like initial/final spin, scattering angle, and impact parameter in multi-body spacetimes, without the use of any preferred background structure.

    

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2. The Wald–Zoupas prescription for asymptotic charges at null infinity in general relativity

   https://doi.org/10.1088/1361-6382/ac571a  

   Grant, Alexander M ; Prabhu, Kartik ; Shehzad, Ibrahim ( March 2022 , Classical and Quantum Gravity)

   Abstract We use the formalism developed by Wald and Zoupas to derive explicit covariant expressions for the charges and fluxes associated with the Bondi–Metzner–Sachs symmetries at null infinity in asymptotically flat spacetimes in vacuum general relativity. Our expressions hold in non-stationary regions of null infinity, are local and covariant, conformally-invariant, and are independent of the choice of foliation of null infinity and of the chosen extension of the symmetries away from null infinity. While similar expressions have appeared previously in the literature in Bondi–Sachs coordinates (to which we compare our own), such a choice of coordinates obscures these properties. Our covariant expressions can be used to obtain charge formulae in any choice of coordinates at null infinity. We also include detailed comparisons with other expressions for the charges and fluxes that have appeared in the literature: the Ashtekar–Streubel flux formula, the Komar formulae, and the linkage and twistor charge formulae. Such comparisons are easier to perform using our explicit expressions, instead of those which appear in the original work by Wald and Zoupas. 

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3. Supertranslation-invariant dressed Lorentz charges

   https://doi.org/10.1007/JHEP04(2022)069  

   Javadinezhad, Reza ; Kol, Uri ; Porrati, Massimo ( April 2022 , Journal of High Energy Physics)

   A bstract We present an explicit formula for Lorentz boosts and rotations that commute with BMS supertranslations in asymptotically flat spacetimes. Key to the construction is the use of infrared regularizations and of a unitary transformation that makes observables commute with the soft degrees of freedom. We explicitly verify that our charges satisfy the Lorentz algebra and we check that they are consistent with expectations by evaluating them on the supertranslated Minkowski space and on the boosted Kerr black hole. 

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4. Brown-York charges at null boundaries

   https://doi.org/10.1007/JHEP01(2022)029  

   Chandrasekaran, Venkatesa ; Flanagan, Éanna É. ; Shehzad, Ibrahim ; Speranza, Antony J. ( January 2022 , Journal of High Energy Physics)

   A bstract The Brown-York stress tensor provides a means for defining quasilocal gravitational charges in subregions bounded by a timelike hypersurface. We consider the generalization of this stress tensor to null hypersurfaces. Such a stress tensor can be derived from the on-shell subregion action of general relativity associated with a Dirichlet variational principle, which fixes an induced Carroll structure on the null boundary. The formula for the mixed-index tensor T i j takes a remarkably simple form that is manifestly independent of the choice of auxiliary null vector at the null surface, and we compare this expression to previous proposals for null Brown-York stress tensors. The stress tensor we obtain satisfies a covariant conservation equation with respect to any connection induced from a rigging vector at the hypersurface, as a result of the null constraint equations. For transformations that act covariantly on the boundary structures, the Brown-York charges coincide with canonical charges constructed from a version of the Wald-Zoupas procedure. For anomalous transformations, the charges differ by an intrinsic functional of the boundary geometry, which we explicity verify for a set of symmetries associated with finite null hyper-surfaces. Applications of the null Brown-York stress tensor to symmetries of asymptotically flat spacetimes and celestial holography are discussed. 

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5. A general framework for gravitational charges and holographic renormalization

   https://doi.org/10.1142/S0217751X22501056  

   Chandrasekaran, Venkatesa ; Flanagan, Éanna É. ; Shehzad, Ibrahim ; Speranza, Antony J. ( June 2022 , International Journal of Modern Physics A)

   We develop a general framework for constructing charges associated with diffeomorphisms in gravitational theories using covariant phase space techniques. This framework encompasses both localized charges associated with space–time subregions, as well as global conserved charges of the full space–time. Expressions for the charges include contributions from the boundary and corner terms in the subregion action, and are rendered unambiguous by appealing to the variational principle for the subregion, which selects a preferred form of the symplectic flux through the boundaries. The Poisson brackets of the charges on the subregion phase space are shown to reproduce the bracket of Barnich and Troessaert for open subsystems, thereby giving a novel derivation of this bracket from first principles. In the context of asymptotic boundaries, we show that the procedure of holographic renormalization can be always applied to obtain finite charges and fluxes once suitable counterterms have been found to ensure a finite action. This enables the study of larger asymptotic symmetry groups by loosening the boundary conditions imposed at infinity. We further present an algorithm for explicitly computing the counterterms that renormalize the action and symplectic potential, and, as an application of our framework, demonstrate that it reproduces known expressions for the charges of the generalized Bondi–Metzner–Sachs algebra. 

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