Related papers: Estimating total momentum at finite distances
We define the asymptotic flatness and discuss asymptotic symmetry at null infinity in arbitrary dimensions using the Bondi coordinates. To define the asymptotic flatness, we solve the Einstein equations and look at the asymptotic behavior…
We relate Bondi systems near space-like infinity to another type of gauge conditions. While the former are based on null infinity, the latter are defined in terms of Einstein propagation, the conformal structure, and data on some Cauchy…
We present the first numerical simulations of asymptotically flat space-times whose computational domain includes past and future null-infinity. As an application, we explore the scattering of a gravitational wave in a black hole…
The cosmological constant $\Lambda$ used to be a freedom in Einstein's theory of general relativity, where one had a proclivity to set it to zero purely for convenience. The signs of $\Lambda$ or $\Lambda$ being zero would describe…
In this short paper, we review recent progress on the positive mass theorem for spacelike hypersurfaces which approach to null infinity in asymptotically flat spacetimes. We use it to prove, if the functions $c(u, \theta, \psi)$, $d(u,…
We review old and recent finite de Finetti theorems in total variation distance and in relative entropy, and we highlight their connections with bounds on the difference between sampling with and without replacement. We also establish two…
The supertranslation ambiguity of angular momentum at null infinity creates a technical difficulty in choosing the proper definition for this conserved quantity. As a result, many different approaches are found in the literature. This…
The total momentum of $N$ interacting bosons or fermions in a cube equipped with periodic boundary conditions is a conserved quantity. Its eigenvalues follow a probability distribution, determined by the thermal equilibrium state. While in…
By taking into account both quantum mechanical and general relativistic effects, I derive an equation that describes some limitations on the measurability of space-time distances. I then discuss possible features of quantum gravity which…
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…
In this note we introduce the notion of factorial moment distance for non-negative integer-valued random variables and we compare it with the total variation distance. Furthermore, we study the rate of convergence in the classical matching…
Recently some authors concluded that the energy and momentum of the Fiedman universes, flat and closed, are equal to zero locally and globally (flat universes) or only globally (closed universes). The similar conclusion was also done for…
The astronomical observations indicate that the universe expands with acceleration and it has a finite event horizon. The recent CMB observations confirm the universe is homogeneous, isotropic and asymptotically flat. The total…
A higher (even spacetime) dimensional generalization of the Bondi energy has recently been proposed by gr-qc/0304054 within the framework of conformal infinity and Hamiltonian formalizm. The gauge condition employed in gr-qc/0304054 to…
Due to the absence of symmetries under time and spatial translations in a general curved spacetime, the energy and momentum of matter is not conserved as it is in flat space. This means, for example, that the flux of matter energy through a…
To study quantum gravity in asymptotically flat spacetimes, one would like to understand the algebra of observables at null infinity. Here we show that the Bondi mass cannot be observed in finite retarded time, and so is not contained in…
The recent astronomical observations indicate that the expanding universe having a finite particle horizon is homogeneous, isotropic and asymptotically flat. The Euclidean geometry of the universe enables to determine the total kinetic and…
In this contribution, we suggest the approach that geometric concepts ought to be defined in terms of physical operations involving quantum matter. In this way it is expected that some (presumably nocive) idealizations lying deep within the…
The continuum of real numbers has served well as a model for physical space in mechanics and field theories. However it is a well-motivated and popular idea that at the fundamental Planck scale the combination of gravitational and quantum…
We present an introduction to mass and angular momentum in General Relativity. After briefly reviewing energy-momentum for matter fields, first in the flat Minkowski case (Special Relativity) and then in curved spacetimes with or without…