Related papers: Covariant Hamiltonian boundary term: Reference and…

We present a detailed examination of the variational principle for metric general relativity as applied to a ``quasilocal'' spacetime region $\M$ (that is, a region that is both spatially and temporally bounded). Our analysis relies on the…

I modify the quasilocal energy formalism of Brown and York into a purely Hamiltonian form. As part of the reformulation, I remove their restriction that the time evolution of the boundary of the spacetime be orthogonal to the leaves of the…

We present a new formulation and generalization of the classical theory of heat conduction with or without fading memory which includes the usual heat equation subject to a dynamic boundary condition as a special case. We investigate the…

We study asymptotically flat space-times in 3 dimensions for Einstein gravity near future null infinity and show that the boundary is described by Carrollian geometry. This is used to add sources to the BMS gauge corresponding to a…

In General Relativity in Hamiltonian form, change has seemed to be missing, defined only asymptotically, or otherwise obscured at best, because the Hamiltonian is a sum of first-class constraints and a boundary term and thus supposedly…

A set of exact quasi-local conservation equations is obtained in the (1+1)-dimensional description of the Einstein's equations of (3+1)-dimensional spacetimes. These equations are interpreted as quasi-local energy, linear momentum, and…

We discuss the criteria that must be satisfied by a well-posed variational principle. We clarify the role of Gibbons-Hawking-York type boundary terms in the actions of higher derivative models of gravity, such as F(R) gravity, and argue…

The popular Hamilton-Jacobi method first proposed by Brown and York for defining quasilocal quantities such as energy for spatially bound regions assumes that the spatial boundary is orthogonal to the foliation of the spacetime. Such a…

We describe the dynamics of a detector modeled by a harmonic oscillator coupled with an otherwise free quantum field in a curved spacetime in terms of covariant equations of motion leading to local observables. To achieve this, we derive…

Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein's equation appropriately. A…

There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The…

We continue recent work and formulate the gravitational vacuum Einstein equations over a locally finite spacetime by using the basic axiomatics, techniques, ideas and working philosophy of Abstract Differential Geometry. The whole…

Gravity is uniquely situated in between classical topological field theories and standard local field theories. This can be seen in the the quasi-local nature of gravitational observables, but is nowhere more apparent than in gravity's…

Gravitating systems have no well-defined local energy-momentum density. Various quasilocal proposals have been made, however the center-of-mass moment (COM) has generally been overlooked. Asymptotically flat graviating systems have 10 total…

Hamiltonian Boundary Value Methods are a new class of energy preserving one step methods for the solution of polynomial Hamiltonian dynamical systems. They can be thought of as a generalization of collocation methods in that they may be…

We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an…

This article considers the quasi-local conserved quantities with respect to a reference spacetime with a cosmological constant. We follow the approach developed by the authors in [25,26,7] and define the quasi-local energy as differences of…

We focus on three distinct lines of recent developments: edge modes and boundary charges in gravitational physics, relational dynamics in classical and quantum gravity, and quantum reference frames. We argue that these research directions…

A covariant Hamiltonian description of Palatini's gravity on manifolds with boundary is presented. Palatini's gravity appears as a gauge theory satisfying a constraint in a certain topological limit. This approach allows the consideration…

An almost-stationary gauge condition is proposed with a view to Numerical Relativity applications. The time lines are defined as the integral curves of the timelike solutions of the harmonic almost-Killing equation. This vector equation is…