Related papers: Evolution of angular momentum and center of mass a…
Associated to the unique 4-parametric subgroup of translations, normal to the Bondi-Metzner-Sachs group, there exists a generator of the temporal translation asymptotic symmetry. Such a descriptor of the motion along the conformal orbit…
We consider smooth null cones in a vacuum spacetime that extend to future null infinity. For such cones that are perturbations of shear-free outgoing null cones in Schwarzschild spacetimes, we prove bounds for the Bondi energy, momentum,…
It is a long-standing problem in general relativity that the notion of angular momentum of an isolated system has supertranslation ambiguity. In this paper, we argue that the ambiguity is essentially because of the gravitational wave…
We compute the motions of null infinity to which the components of the angular momentum of the gravitational field, as defined by Penrose, are conjugate. We find that the boosts are supplemented by anomalous translations. If $c_{ab}$ is the…
There are two important statements regarding the Trautman-Bondi mass at null infinity: one is the positivity, and the other is the Bondi mass loss formula, which are both global in nature. In this note, we compute the limit of the Wang-Yau…
We show that the BMS-supertranslations and their associated supermomenta on past null infinity can be related to those on future null infinity, proving the conjecture of Strominger for a class of spacetimes which are asymptotically-flat in…
We show that for isolated relativistic systems with spin the conservation of total angular momentum implies that, instead of the center of mass, it is a modified center of mass and spin which behaves inertially. This requires a change in…
Utilizing recent mathematical advances in proving stability of Minkowski spacetime with minimal decay rates and nonlinear stability of Kerr black holes with small angular momentum, we investigate the detailed asymptotic behaviors of…
The law of balance of angular momentum is shown to imply the existence of absolute time, a fundamental physical quantity that is independent of the motion or position of the observer. Absolute time implies the notion of absolute…
If the angular momentum of the molecular cloud core were conserved during the star formation process, a new-born star would rotate much faster than its fission speed. This constitutes the angular momentum problem of new-born stars. In this…
Generalized definitions for angular and linear momentum are given and shown to reduce to the ADM (at spatial infinity) definitions and the definitions at null infinity in the appropriate limit. These definitions are used to express angular…
We exhibit a Hamiltonian formulation, both for electromagnetism and gravitation, in which it is not required that the Bondi "news" vanish, but only that the incoming news be equal to the outgoing ones. This requirement is implemented by…
Dray and Streubel proposed a definition of angular momentum in general relativity based on `Bondi-Metzner-Sachs (BMS) charges'. I show here that the natural definition of center of mass in this program has an infinite-dimensional ambiguity.…
Conservation laws have many applications in numerical relativity. However, it is not straightforward to define local conservation laws for general dynamic spacetimes due the lack of coordinate translation symmetries. In flat space, the rate…
A major issue in general relativity, from its earliest days to the present, is how to extract physical information from any solution or class of solutions to the Einstein equations. Though certain information can be obtained for arbitrary…
We present a definition of angular momentum for radiative spacetimes which does not suffer from any ambiguity of supertranslations. We succeed in providing an appropriate notion of {\it intrinsic} angular momentum; and at the same time a…
When a system emits gravitational radiation, the Bondi mass decreases. If the Bondi energy is Hamiltonian, it can thus only be a time dependent Hamiltonian. In this paper, we show that the Bondi energy can be understood as a time-dependent…
Some models of modified gravity and their observational manifestations are considered. It is shown, that gravitating systems with mass density rising with time evolve to a singular state with infinite curvature scalar. The universe…
The asymptotic symmetry of an isolated gravitating system, or the Bondi-Metzner-Sachs (BMS) group, contains an infinite-dimensional subgroup of supertranslations. Despite decades of study, the difficulties with the "supertranslation…
Angular momentum can be defined by rearranging the Komar surface integral in terms of a twist form, encoding the twisting around of space-time due to a rotating mass, and an axial vector. If the axial vector is a coordinate vector and has…