Covariant Counterterms and Conserved Charges in Asymptotically Flat Spacetimes

Abstract

Recent work has shown that the addition of an appropriate covariant boundary term to the gravitational action yields a well-defined variational principle for asymptotically flat spacetimes and thus leads to a natural definition of conserved quantities at spatial infinity. Here we connect such results to other formalisms by showing explicitly i) that for spacetime dimension $d\ge 4$ the canonical form of the above-mentioned covariant action is precisely the ADM action, with the familiar ADM boundary terms and ii) that for $d=4$ the conserved quantities defined by counter-term methods agree precisely with the Ashtekar-Hansen conserved charges at spatial infinity.

27 pages; Dedicated to Rafael Sorkin on the occasion of his 60th birthday; v2 minor changes

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• Note on counterterms in asymptotically flat spacetimes
• Asymptotics and Hamiltonians in a First order formalism
• Trace Anomaly and Counterterms in Designer Gravity
• Asymptotic Flatness, Little String Theory, and Holography
• Scalar charges and the first law of black hole thermodynamics
• Gravitational multipole moments from Noether charges
• Actions, topological terms and boundaries in first order gravity: A review
• $\mathbf{O}(D,D)$ Covariant Noether Currents and Global Charges in Double Field Theory
• Dirichlet boundary value problem for Chern-Simons modified gravity
• Quasilocal formalism and thermodynamics of asymptotically flat black objects
• Thermodynamic instability of doubly spinning black objects
• Magnetic Charge Can Locally Stabilize Kaluza-Klein Bubbles
• Charge and Antipodal Matching across Spatial Infinity
• On Asymptotic Flatness and Lorentz Charges
• Finite Charges from the Bulk Action
• On the Stress Tensor for Asymptotically Flat Gravity
• Quasilocal equilibrium condition for black ring
• Aspects of the zero $\Lambda$ limit in the AdS/CFT correspondence
• Harrison transformation and charged black objects in Kaluza-Klein theory
• Boundary Terms Unbound! Holographic Renormalization of Asymptotically Linear Dilaton Gravity
• Asymptotic Flatness, Taub-NUT, and Variational Principle
• Action and Hamiltonians in higher dimensional general relativity: First order framework
• Holographic Renormalization of Gravity in Little String Theory Duals
• Conserved charges in asymptotically de Sitter spacetimes
• Asymptotic Symmetries of Maxwell Theory in Arbitrary Dimensions at Spatial Infinity
• The gravitational Hamiltonian, first order action, Poincaré charges and surface terms
• Black Hole Thermodynamics and Hamilton-Jacobi Counterterm
• First-order action and Euclidean quantum gravity
• Supertranslations and Holographic Stress Tensor
• Supertranslations at Timelike Infinity
• Einstein-Gauss-Bonnet black holes in de Sitter spacetime and the quasilocal formalism
• Bubbles Unbound: Bubbles of Nothing Without Kaluza-Klein
• Celestial IR divergences and the effective action of supertranslation modes
• Asymptotic symmetries and geometry on the boundary in the first order formalism
• Explicit form of the Mann-Marolf surface term in (3+1) dimensions
• Gravitation and tunnelling: Subtleties of the thin-wall approximation and rapid decays
• Affine Gravity, Palatini Formalism and Charges
• Asymptotically Plane Wave Spacetimes and their Actions
• Termodinámica de agujeros negros y campos escalares
• Electric and magnetic aspects of gravitational theories
• Agujeros Negros con Pelo y Dualidad AdS/CFT
• A remark on the quasilocal calculation of tidal heating: energy transfer through the quasilocal surface
• Exact Solutions and Black Hole Stability in Higher Dimensional Supergravity Theories