On the physical interpretation of asymptotically flat gravitational fields

A problem in general relativity is how to extract physical information from solutions to the Einstein equations. Most often information is found from special conditions, e.g., special vector fields, symmetries or approximate symmetries. Our concern is with asymptotically flat space–times with approximate symmetry: the BMS group. For these spaces the Bondi four-momentum vector and its evolution, found at infinity, describes the total energy–momentum and the energy–momentum radiated. By generalizing the simple idea of the transformation of (electromagnetic) dipoles under a translation, we define (analogous to center of charge) the center of mass for asymptotically flat Einstein–Maxwell fields. This gives kinematical meaning to the Bondi four-momentum, i.e., the four-momentum and its evolution which is described in terms of a center of mass position vector, its velocity and spin-vector. From dynamical arguments, a unique (for our approximation) total angular momentum and evolution equation in the form of a conservation law is found. Third Award in the 2008 Essay Competition of the Gravity Research Foundation.     

A new class of asymptotically flat stationary axisymmetric vacuum gravitational fields

We present the full four-dimensional metric for a stationary axisymmetric solution of the vacuum Einstein equations related to the Ernst potential which we obtain by application of anarbitrary number of rank-zero HKX transformations to the general static Weyl solution. The metric function is determined in a completely algebraically way. We perform a suitable Ehlers transformation to ensure asymptotic flatness and give the expression for the total mass of this asymptotically flat solution by analyzing the behavior of the solution on the positive z axis.     

Linearization stability of coupled gravitational and scalar fields in asymptotically flat space-times

Using the methods of Choquet-Bruhat, Fischer and Marsden and using weighted Sobolev spaces developed recently by Christodoulou and Choquet-Bruhat, it is proved that the Einstein field equations coupled with self-gravitating scalar fields are linearization stable in asymptotically flat space-times.     

The topology of asymptotically locally flat gravitational instantons

In this Letter we demonstrate that the intersection form of the Hausel–Hunsicker–Mazzeo compactification of a four-dimensional ALF gravitational instanton is definite and diagonalizable over the integers if one of the Kähler forms of the hyper-Kähler gravitational instanton metric is exact. This leads to their topological classification.     

Sources of gravitational waves in asymptotically flat Einstein-Maxwell spacetime

In this work, the dynamic of isolated systems in general relativity is described when gravitational radiation and electromagnetic fields are present. In this construction, the asymptotic fields received at null infinity together with the regularized null cone cuts equation, and the center of mass of an asymptotically flat Einstein-Maxwell spacetime are used. A set of equations are derived in the low speed regime, linking their time evolution to the emitted gravitational radiation and to the Maxwell fields received at infinity. These equations should be useful when describing the dynamic of compact sources, such as the final moments of binary coalescence and the evolution of the final black hole. Additionally, we compare our equations with those coming from a similar approach given by Newman, finding some differences in the motion of the center of mass and spin of the gravitational system.     

New series of asymptotically flat axisymmetric and stationary gravitational solutions

The equations for the pseudopotential of Harrison's Bäcklund transformations with seed solution an asymptotically flat solution of the Ernst equation are solved. A new series of asymptotically flat solutions of the equations of general relativity is obtained from the determinants of matrices, whose elements are known. The first solution of the series is calculated as a ratio of two sums of monomials. This solution has five arbitrary real constants. For a particular choice of the constants it becomes Kerr's solution.     

Con formally flat gravitational fields of an ideal fluid

The necessary and sufficient conditions are obtained for gravitational fields of an ideal fluid to be conformally Euclidean. The possible types of field are considered.     

Conformally flat gravitational fields produced by an ideal fluid

The problem of finding conformally flat gravitational fields produced by a perfect fluid is solved completely.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No.12, pp.22–25, December, 1980.     

On asymptotically flat space-times

The allowed asymptotic behavior of the Ricci tensor is determined for asymptotically flat space-times. With the aid of Penrose's conformai technique the asymptotic behavior of the components of the metric tensor, Weyl tensor, and spin coefficients in a suitable frame is calculated for such a space-time. For Einstein-Maxwell space-times these results reduce to those of Exton, Newman, Penrose, Unti, and Kozarzewski.     

Null surface quantization and quantum theory of massless fields in asymptotically flat space-time

The quantum theory of massless fields in an asymptotically simple space-time is developed. The Schwinger dynamical principle and the Penrose conformal technique are exploited to derive the commutation relations on proper null surfaces in a curved space-time and on null infinities. The explicit expression for theS matrix in an asymptotically simple space-time is presented. The general expression for a density matrix describing particles created in an external field is also given and its possible applications are discussed briefly.     

An asymptotically flat vacuum solution

An asympototically flat algebraically general vacuum metric is obtained. The solution is characterized by two commuting spacelike Killing vectors with flat integral surfaces and depends on one arbitrary function.     

Note on asymptotically flat empty spaces

The algebraic programming system FORMAC is used to extend asymptotic solutions of the Newman-Penrose equations. The expansions are then applied to metrics with geodesic rays and to the Newman-Penrose conserved terms. It is shown how the expansion may prove useful in finding new solutions to the field equations.This paper presents results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS7-100, sponsored by the National Aeronautics and Space Administration.     

Gravity theories with asymptotically flat instantons

We construct explicitly a gravitational instanton which is asymptotically flat and globally euclidean. The instanton is a solution of euclidean gravity coupled to a scalar field in first-order formulation. The presence of a zero in the vierbeins and the consequent non-vanishing torsion allow us to obtain non-trivial topological excitations of the metric field without changing the topologically trivial structure of the underlying (euclidean) spacetime.     

Axisymmetric gravitational fields

In this review paper Einstein equations for axisymmetric vacuum fields are introduced in the form given by Lewis. Following Ernst they are reduced to one complex potential equation. Weyl-type, Schwarzschild, Kerr, Tomimatsu-Sato solutions, and their NUT-like generalizations are then discussed.     

Maximal hypersurfaces in stationary asymptotically flat spacetimes

Existence of maximal hypersurfaces and of foliations by maximal hypersurfaces is proven in two classes of asymptotically flat spacetimes which possess a one parameter group of isometries whose orbits are timelike near infinity.. The first class consists of strongly causal asymptotically flat spacetimes which contain no black hole or white hole (but may contain ergoregions where the Killing orbits fail to be timelike). The second class of spacetimes possess a black hole and a white hole, with the black and white hole horizons intersecting in a compact 2-surfaceS.Supported in part by KBN grant #2 1047 9101Supported in part by NSF grant PHY-8918388.     

Real structures in asymptotically flat ℋ spaces

A real structure is defined in asymptotically flat ? spaces and investigated in connection with the equations of motion in ? space.     

On maximal surfaces in asymptotically flat space-times

Existenc of maximal and almost maximal hypersurfaces in asymptotically flat space-times is established under boundary conditions weaker than those considered previously. We show in particular that every vacuum evolution of asymptotically flat data for the Einstein equations can be foliated by slices maximal outside a spatially compact set and that every (strictly) stationary asymptotically flat space-time can be foliated by maximal hypersurfaces. Amongst other uniqueness results, we show that maximal hypersurfaces can be used to partially fix an asymptotic Poincaré group.Supported in part by the NSF grant PHY 8503072 to Yale University     

Quasinormal frequencies of asymptotically flat two-dimensional black holes

We discuss whether the minimally coupled massless Klein-Gordon and Dirac fields have well defined quasinormal modes in single horizon, asymptotically flat two-dimensional black holes. To get the result we solve the equations of motion in the massless limit and we also calculate the effective potentials of Schrödinger type equations. Furthermore we calculate exactly the quasinormal frequencies of the Dirac field propagating in the two-dimensional uncharged Witten black hole. We compare our results on its quasinormal frequencies with other already published.