A new gravitational energy tensor

The Bel-Robinson tensor is the most used gravitational energy tensor; however, it has the dimensions of energy squared. How to construct tensors with the dimensions of energy by using Lancoz tensors is shown here. The resulting tensors have a large number of arbitrary parameters, frequently have spacelike currents, and frequently do not reduce to familiar pseudo-energy tensors in the weak field limit. Two particular examples of interest are one with well-behaved currents and one which reduces to an energy pseudo-tensor in the weak field limit.     

Comparison of various gravitational energy tensors

In this paper we make a comparison of various energy tensors of the gravitational field, obtained by introducing various auxiliary structures into the discussion. Notwithstanding differences in initial positions, the best-known investigations have led to the same result.Translated from Izvestiya VUZ. Fizika, No. 6, pp. 12–15, June, 1973.In conclusion the author expresses deep thanks to Prof. V. I. Hodichev for discussion of results of the work.     

The possibility of negative gravitational energy

The status and physical importance of the question “Can the energy of gravitational fields be negative?” is discussed. To study this question further a particular model of a gravitational shock wave has been developed. The energy corresponding to this model is a scalar functional of the two-geometry of the shock front. Values of the energy for special choices of the shock front have been calculated. These cases all give rise to positive energy, the energy becoming more positive as the shock front becomes more curved. However, no general proof is known to show that the energy is positive for all choices of two-geometries.     

On energy transfer by gravitational waves

The solutions of Møller's tetrad equations are found for the three types of exact gravitational waves, for which Møller's energy-momentum complex gives vanishing densities of gravitational energy and energy current.     

A new gravitational model for dark energy

A new gravitational model for dark energy is presented based on the model of de Sitter gauge theory of gravity. In the model, in addition to the cosmological constant, the homogeneous and isotropic torsion and its coupling with curvature play an important role for dark energy. The model may supply the universe with a natural transit from decelerating expansion to accelerating expansion.     

Holographic dark energy with varying gravitational constant

We investigate the holographic dark energy scenario with a varying gravitational constant, in flat and non-flat background geometry. We extract the exact differential equations determining the evolution of the dark energy density-parameter, which include G-variation correction terms. Performing a low-redshift expansion of the dark energy equation of state, we provide the involved parameters as functions of the current density parameters, of the holographic dark energy constant and of the G-variation.     

A new gravitational model for dark energy

A new gravitational model for dark energy is presented based on the model of de Sitter gauge theory of gravity.In the model,in addition to the cosmological constant,the homogeneous and isotropic torsion and its coupling with curvature play an important role for dark energy.The model may supply the universe with a natural transit from decelerating expansion to accelerating expansion.     

The positivity of gravitational energy and global supersymmetry

The concept of gravitational energy and the proof of its positivity are reviewed. The relationship between Witten's proof of the positivity of mass and supergravity is explained with reference to the group of global supersymmetries of a spacetime. A formula for the mass is given, in terms of the change of the supercharge under global supersymmetry, which has a simple positivity theorem and which reduces to Witten's expression. An interpretation of Witten's constraint on the spinors used in his proof is given.     

Equipartition energy, Noether energy and boundary term in gravitational action

In the study of horizon thermodynamics and emergent gravity two natural expressions for energy, E = 2T S (equipartition energy) and E = T S (Noether energy) arise which differ by a factor 2. I clarify the role of these two expressions in different contexts and show how E = T S is also closely related to the Noether charge arising from the boundary term of the Einstein–Hilbert action.     

Experimental facts and gravitational energy in general relativity

It is shown that the nonrotating coordinates wherein the energy-momentum is globally conserved share the experimental features of the inertial frames. The falling of matter in a spherically symmetric gravitational field is studied in the light of the energy-momentum conservation valid in these coordinates.Deceased.     

Strong gravitational lensing constraints on holographic dark energy

Strong gravitational lensing(SGL) has provided an important tool for probing galaxies and cosmology. In this paper, we use the SGL data to constrain the holographic dark energy model, as well as models that have the same parameter number, such as the w CDM and Ricci dark energy models. We find that only using SGL is difficult to effectively constrain the model parameters.However, when the SGL data are combined with CBS(CMB+BAO+SN) data, the reasonable estimations can be given and the constraint precision is improved to a certain extent, relative to the case of CBS only. Therefore, SGL is an useful way to tighten constraints on model parameters.     

On Lynden-Bell and Katz's definition of gravitational field energy

The covariant definition of gravitational field energy given by Lynden-Bell and Katz is expressed in terms of Israel's theory of surface layers in general relativity. In this way an expression, valid for arbitrary radial coordinates, of the gravitational field energy in a static, spherically symmetric space-time, is deduced. This expression is applied to the Schwarschild and Reissner-Nordström space-times, and leads here to the same results as those given by Einstein's pseudotensor expression in isotropic coordinates.     

One-dimensional gravitational gas: Estimate of ground state energy

The ground state energy E(N) increases with N at most as $\text{N}{}^{\mathrm{<mtext>5</mtext><mtext>3</mtext>}}$.     

On gravitational radiation and the energy flux of matter

A suitable derivative of Einstein's equations in the framework of the teleparallel equivalent of general relativity (TEGR) yields a continuity equation for the gravitational energy‐momentum. In particular, the time derivative of the total gravitational energy is given by the sum of the total fluxes of gravitational and matter fields energy. We carry out a detailed analysis of the continuity equation in the context of Bondi and Vaidya's metrics. In the former space‐time the flux of gravitational energy is given by the well known expression in terms of the square of the news function. It is known that the energy definition in the realm of the TEGR yields the ADM (Arnowitt‐Deser‐Misner) energy for appropriate boundary conditions. Here we show that the same energy definition also describes the Bondi energy. The analysis of the continuity equation in Vaidya's space‐time shows that the variation of the total gravitational energy is determined by the energy flux of matter only.