English
Related papers

Related papers: Another positivity proof and gravitational energy …

200 papers

We present a general framework for reconstructing effective Hamiltonians from known gravitational energy density profiles in curved spacetime. Starting from local thermal equilibrium and Liouville dynamics, we establish an inverse procedure…

General Relativity and Quantum Cosmology · Physics 2025-08-12 Davood Momeni

Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion ("acceleration equal force"), with linear and cubic forces, in N-dimensional space (N being an…

Exactly Solvable and Integrable Systems · Physics 2009-11-10 M. Bruschi , F. Calogero

A covariant hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of hamiltonians accounting for specific properties and…

General Relativity and Quantum Cosmology · Physics 2016-12-21 J. W. van Holten

We prove the following stronger verson of the positivity of quasi-local mass stated in gr-qc/0303019: the quasi-local energy (mass) of each connected component of the boundary of a compact spacelike hypersurface which satisfies the local…

Differential Geometry · Mathematics 2007-05-23 Chiu-Chu Melissa Liu , Shing-Tung Yau

We define a new gauge independent quasi-local mass and energy, and show its relation to the Brown-York Hamilton-Jacobi analysis. A quasi-local proof of the positivity, based on spacetime harmonic functions, is given for admissible closed…

Differential Geometry · Mathematics 2023-09-07 Aghil Alaee , Marcus Khuri , Shing-Tung Yau

A model Hamiltonian is proposed in order to understand the localization-delocalization transition in a quantum dot, where there are two gate voltages: top and side. Considering energetically favorable degrees of freedom only, we achieve a…

Mesoscale and Nanoscale Physics · Physics 2009-10-31 Myung-Hoon Chung

We describe a class of spinor-curvature identities which exist for Riemannian or Riemann-Cartan geometries. Each identity relates an expression quadratic in the covariant derivative of a spinor field with an expression linear in the…

General Relativity and Quantum Cosmology · Physics 2010-04-06 James M. Nester , Roh Suan Tung , Vadim V. Zhytnikov

We calculate the total gravitational energy and the gravitational energy density of the de Sitter space using the definition of localized energy that arises in the framework of the teleparallel equivalent of general relativity. We find that…

General Relativity and Quantum Cosmology · Physics 2009-10-28 J. W. Maluf

The framework of relativistic energy density functionals is extended to include correlations related to restoration of broken symmetries and fluctuations of collective variables. A new implementation is developed for the solution of the…

Nuclear Theory · Physics 2009-04-28 T. Niksic , Z. P. Li , D. Vretenar , L. Prochniak , J. Meng , P. Ring

Using the Sparling form and a geometric construction adapted to spacetimes with a 2-dimensional isometry group, we analyse a quasi-local measure of gravitational energy. We then study the gravitational radiation through spacetime junctions…

General Relativity and Quantum Cosmology · Physics 2018-11-27 Alfonso García-Parrado , Filipe C. Mena

For describing the non-negative gravitational energy-momentum in terms of a pure Bel-Robinson type energy-momentum in a quasilocal 2-surface, both the Bel-Robinson tensor $B$ and tensor $V$ are suitable. We found that this Bel-Robinson type…

General Relativity and Quantum Cosmology · Physics 2013-12-17 Lau Loi So

A quantum-mechanical Hamiltonian with a gravitational potential is derived in the framework of local times. This Hamiltonian is the one used by E. H. Lieb (Bull. Amer. Math. Soc. 22(1990), 1-49) in his explanation of stability and…

General Relativity and Quantum Cosmology · Physics 2008-02-03 Hitoshi Kitada

The 4-index energy-momentum tensors for gravitation and matter are analyzed on the basis of new equations for the gravitational field with the Riemann tensor. Some properties of the such defined gravitational energy are discussed.

General Relativity and Quantum Cosmology · Physics 2012-10-09 Zahid Zakir

Loop quantum gravity in its Hamiltonian form relies on a connection formulation of the gravitational phase space with three key properties: 1.) a compact gauge group, 2.) real variables, and 3.) canonical Poisson brackets. In conjunction,…

General Relativity and Quantum Cosmology · Physics 2024-12-09 Norbert Bodendorfer , Konstantin Eder , Xiangdong Zhang

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…

Differential Geometry · Mathematics 2016-03-10 Po-Ning Chen , Mu-Tao Wang , Shing-Tung Yau

We give an explicit expression for gravitational energy, written solely in terms of physical spacetime geometry, which in suitable limits agrees with the total Arnowitt-Deser-Misner and Trautman-Bondi-Sachs energies for asymptotically flat…

General Relativity and Quantum Cosmology · Physics 2009-10-31 S. R. Lau

In general relativity, the local gravitational energy is best characterised by the quasilocal mass. The small sphere limit of quasilocal mass provides us the most local notion of gravitational energy. In four dimensions, the limits were…

General Relativity and Quantum Cosmology · Physics 2019-09-27 Jinzhao Wang

Gravitational radiation is locally defined where the wavefronts are roughly spherical. A local energy tensor is defined for the gravitational radiation. Including this energy tensor as a source in the truncated Einstein equations describes…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Sean A. Hayward

We establish the quantum stationary Hamilton-Jacobi equation in 3-D and its solutions for three symmetrical potentials, Cartesian symmetry potential, spherical symmetry potential and cylindrical symmetry potential. For the two last…

Quantum Physics · Physics 2007-05-23 T. Djama

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…

General Relativity and Quantum Cosmology · Physics 2007-05-23 James M. Nester , Chiang-Mei Chen , Yu-Heui Wu