Abstract
New boundary conditions for asymptotically flat spacetimes are given at spatial infinity. These boundary conditions are invariant under the BMS group, which acts non trivially. The boundary conditions fulfill all standard consistency requirements: (i) they make the symplectic form finite; (ii) they contain the Schwarzchild solution, the Kerr solution and their Poincaré transforms, (iii) they make the Hamiltonian generators of the asymptotic symmetries integrable and well-defined (finite). The boundary conditions differ from the ones given earlier in the literature in the choice of the parity conditions. It is this different choice of parity conditions that makes the action of the BMS group non trivial. Our approach is purely Hamiltonian and off-shell throughout.
Highlights
2.1 Fall-off at spatial infinity — RT parity conditionsOur starting point are the standard Hamiltonian boundary conditions for asymptotically flat spacetimes, given on spatial slices that asymptote hyperplanes equipped with asymptotically cartesian coordinates xi = (x, y, z) at spatial infinity (r → ∞ with r2 = xixi)
We propose in this paper new boundary conditions at spatial infinity that fulfill this purpose
We show that the canonical generators of the asymptotic symmetries are well-defined with the new parity conditions
Summary
Our starting point are the standard Hamiltonian boundary conditions for asymptotically flat spacetimes, given on spatial slices that asymptote hyperplanes equipped with asymptotically cartesian coordinates xi = (x, y, z) at spatial infinity (r → ∞ with r2 = xixi) On any such hypersurface, the spatial metric gij and its conjugate momentum πij behave as gij. In addition to containing the Schwarzschild and Kerr solutions and being invariant under (at least) the Poincare transformations, consistent boundary conditions should fulfill two addition requirements:. The general boundary conditions (2.1) and (2.2) fail on both accounts For that reason, they must be strengthened, but in way that does not eliminate the Schwarzschild or Kerr solutions and keeps the Poincare transformations among the asymptotic symmetries. There is no room for the full BMS algebra with the parity conditions of [6]
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