Bondi-Sachs Formalism
Thomas Mädler, Jeffrey Winicour
TL;DR
The Bondi–Sachs formalism provides a metric-based, null-cone approach to General Relativity that reveals gravitational radiation as a nonlinear energy-loss process. By formulating the spacetime in outgoing null coordinates, it derives a hierarchical set of Einstein equations whose asymptotic $1/r$ expansion yields key quantities: the mass aspect $M$, angular-momentum aspect $L_A$, and the radiative shear and news tensor. This framework leads to the Bondi mass loss formula and clarifies the structure of asymptotic symmetries through the BMS group, including the crucial role of supertranslations. The worldtube–null-cone formulation further enables a bridge to numerical relativity via mixed initial-boundary data, underpinning waveform extraction and gravitational-memory studies with broad applications in modern gravitational-wave science.
Abstract
The Bondi-Sachs formalism of General Relativity is a metric-based treatment of the Einstein equations in which the coordinates are adapted to the null geodesics of the spacetime. It provided the first convincing evidence that gravitational radiation is a nonlinear effect of general relativity and that the emission of gravitational waves from an isolated system is accompanied by a mass loss from the system. The asymptotic behaviour of the Bondi-Sachs metric revealed the existence of the symmetry group at null infinity, the Bondi-Metzner-Sachs group, which turned out to be larger than the Poincare group.