ESTIMATES FOR THE MAXWELL FIELD NEAR THE SPATIAL AND NULL INFINITY OF THE SCHWARZSCHILD SPACETIME

It is shown how the gauge of the "regular finite initial value problem at spacelike infinity" can be used to construct a certain type of estimates for the Maxwell field propagating on a Schwarzschild background. These estimates are constructed with the objective of obtaining information about the smoothness near spacelike and null infinity of a wide class of solutions to the Maxwell equations.

Flat space holography

The implementation of holography in gravitational physics has its most concrete realization in the context of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence conjecture, an implication of which is that counterterms from the boundary CFT can be understood as surface terms that render the variational principle finite and well-defined for the gravity theory in the bulk. I discuss recent developments that show how such gravitational counterterms can be deployed for asymptotically flat spacetimes in any spacetime dimension d ≥ 4. These actions yield conserved quantities at spacelike infinity that agree with the usual Arnowitt–Deser–Misner results but are more general. This approach removes the need for ill-defined background subtraction methods and suggests the possibility of obtaining a dual field theory to gravity theories in asymptotically flat spacetimes.PACS Nos.: 04.20.Ha, 04.60.–m, 11.25.Tq

COLLAPSING AND EXPANDING CYLINDRICALLY SYMMETRIC FIELDS WITH LIGHTLIKE WAVE-FRONTS IN GENERAL RELATIVITY

The dynamics of collapsing and expanding cylindrically symmetric gravitational and matter fields with lightlike wave-fronts is studied in General Relativity, using the Barrabés–Israel method. As an application of the general formulae developed, the collapse of a matter field that satisfies the condition RABgAB =0, (A,B = z, φ), in an otherwise flat spacetime background is studied. In particular, it is found that the gravitational collapse of a purely gravitational wave or a null dust fluid cannot be realized in a flat spacetime background. The studies are further specified to the collapse of purely gravitational waves and the general conditions for such collapse are found. It is shown that after the waves arrive at the axis, in general, part of them is reflected to spacelike infinity along the future light cone, and part of it is focused to form spacetime singularities on the symmetry axis. The cases where the collapse does not result in the formation of spacetime singularities are also identified.