Related papers: Hamiltonian, Energy and Entropy in General Relativ…
Energy-momentum (and angular momentum) for the Metric-Affine Gravity theory is considered from a Hamiltonian perspective (linked with the Noether approach). The important roles of the Hamiltonian boundary term and the many choices involved…
The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasi-local values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found…
We analyse the definition of quasi-local energy in GR based on a Hamiltonian analysis of the Einstein-Hilbert action initiated by Brown-York. The role of the constraint equations, in particular the Hamiltonian constraint on the timelike…
We present the gravitational action and Hamiltonian for a spatially bounded region of an eternal black hole. The Hamiltonian is of the general form $H=H_{+} - H_{-}$, where $H_{+}$ and $H_{-}$ are respectively the Hamiltonians for the…
Energy is a crucial concept within classical and quantum physics. An essential tool to quantify energy is the Hamiltonian. Here, we consider how to define a Hamiltonian in general probabilistic theories, a framework in which quantum theory…
Energy is at best defined quasilocally in general relativity. Quasilocal energy definitions depend on the conditions one imposes on the boundary Hamiltonian, i.e., how a finite region of spacetime is "isolated". Here, we propose a method to…
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…
It is shown that in general the energy ${\cal E}$ and the Hamiltonian ${\cal H}$ of matter fields on the black hole exterior play different roles. ${\cal H}$ is a generator of the time evolution along the Killing time while ${\cal E}$…
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…
The action for a class of three-dimensional dilaton-gravity theories with a cosmological constant can be recast in a Brans-Dicke type action, with its free $\omega$ parameter. These theories have static spherically symmetric black holes.…
The quest to develop a general framework for thermodynamics, suitable for the regime of strong coupling and correlations between subsystems of an autonomous quantum "universe," has entailed diverging definitions for basic quantities,…
In this paper, by arising condition in variation, from equal time to non-equal time, I reconsider how geometrodynamics equations allow to be derived from variational principle in general relativity and then find the variation of extrinsic…
The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free $\omega$ parameter. For a negative…
We construct a Hamiltonian formulation of quasilocal general relativity using an extended phase space that includes boundary coordinates as configuration variables. This allows us to use Hamiltonian methods to derive an expression for the…
A quasi-local energy for Einstein's general relativity is defined by the value of the preferred boundary term in the covariant Hamiltonian formalism. The boundary term depends upon a choice of reference and a time-like displacement vector…
The Hamiltonian for physical systems and dynamic geometry generates the evolution of a spatial region along a vector field. It includes a boundary term which not only determines the value of the Hamiltonian, but also, via the boundary term…
The various roles of boundary terms in the gravitational Lagrangian and Hamiltonian are explored. A symplectic Hamiltonian-boundary-term approach is ideally suited for a large class of quasilocal energy-momentum expressions for general…
The Hamiltonian thermodynamics formalism is applied to the general $d$-dimensional Reissner-Nordstr\"om-anti-de Sitter black hole with spherical, planar, and hyperbolic horizon topology. After writing its action and performing a Legendre…
In this work, we extend the analysis of Brown and York to find the quasilocal energy in a spherical box in the Schwarzschild spacetime. Quasilocal energy is the value of the Hamiltonian that generates unit magnitude proper-time translations…
From a covariant Hamiltonian formulation, using symplectic ideas, we obtain covariant quasilocal energy-momentum boundary expressions for general gravity theories. The expressions depend upon which variables are fixed on the boundary, a…