Related papers: Quasilocal mass and surface Hamiltonian in spaceti…
In this study, we employ eth-operators and spin-weighted spherical harmonics to express the ADM mass of a static space-time based on the mean values of its components over a a radius-$r$ sphere. While initially derived for standard…
It is shown that under proper conditions in an appropriate coordinate system with a suitable time slicing the Hamiltonian and the Einstein-Hilbert action including all necessary boundary terms can be written on shell in terms of the…
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…
In this paper, we study the limiting behavior of the Brown-York mass and Hawking mass along nearly round surfaces at infinity of an asymptotically flat manifold. Nearly round surfaces can be defined in an intrinsic way. Our results show…
In this paper we consider the positive mass theorem for general initial data sets satisfying the dominant energy condition which are singular across a piecewise smooth surface. We find jump conditions on the metric and second fundamental…
In the following, we offer a novel approach to modeling the observed effects currently attributed to the theoretical concepts of `dark energy', `dark matter', and `dark flow'. Instead of assuming the existence of these theoretical concepts,…
In this note, using the quasilocal formalism of Brown and York, the flow of energy through a closed surface containing a gravitating physical system is calculated in a way that augments earlier results on the subject by Booth and Creighton.…
We give an account of some recent development that connects the concept of mass in general relativity to the geometry of large Riemannian polyhedra, in the setting of both asymptotically flat and asymptotically hyperbolic manifolds.
Witten's proof for the positivity of the ADM mass gives a definition of energy in terms of three-surface spinors. In this paper, we give a generalisation for the remaining six Poincar\'e charges at spacelike infinity, which are the angular…
We study how the standard definitions of ADM mass and Brown-York quasi-local energy generalize to pure Lovelock gravity. The quasi-local energy is renormalized using the background subtraction prescription and we consider its limit for…
We extend the quasilocal formalism of Brown and York to include electromagnetic and dilaton fields and also allow for spatial boundaries that are not orthogonal to the foliation of the spacetime. The extension allows us to study the…
We provide integral formulae for the ADM mass of asymptotically flat hypersurfaces in Riemannian manifolds with a certain warped product structure in a neighborhood of infinity, thus extending Lam's recent results on Euclidean graphs to…
We extend the Brown and York notion of quasilocal energy to include coupled electromagnetic and dilaton fields and also allow for spatial boundaries that are not orthogonal to the foliation of the spacetime. We investigate how the…
We consider the total nonlocal energy associated with a particle at rest in the Hubble flow, i.e., the relational energy between this particle and all connected particles within the causal horizon. The particle, even while at rest, partakes…
We demonstrate that the volume-renormalized mass for asymptotically hyperbolic manifolds recently introduced by the authors can be deduced from a reduced Hamiltonian perspective. In order to do this, we first use Michel's formalism of mass…
The Hamiltonian for dynamic geometry generates the evolution of a spatial region along a vector field. It includes a boundary term which determines both the value of the Hamiltonian and the boundary conditions. The value gives the…
In this work we study the quasilocal energy as in [11] for a constant radius surface in Kerr spacetime in Boyer-Lindquist coordinates. We show that under suitable conditions for isometric embedding, for a stationary observer the quasilocal…
Building on the relativistic Hamiltonian of Sonnleitner and Barnett arXiv:1806.00234 and its post-Newtonian extensions by Schwartz and Giuilini arXiv:1908.06929, we investigate composite atomic systems in dynamical gravitational…
Generalized Smarr relations in terms of quasilocal variables are obtained for Schwarzschild and Reissner-Nordstr\"om black holes. The approach is based on gravitational path integrals with finite boundaries on which, following Brown and…
Consider a triple of "Bartnik data" $(\Sigma, \gamma,H)$, where $\Sigma$ is a topological 2-sphere with Riemannian metric $\gamma$ and positive function $H$. We view Bartnik data as a boundary condition for the problem of finding a compact…