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.     

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.     

A new gravitational energy expression with a simple positivity proof

We present a new four-dimensionally covariant expression whose integral at space-like infinity gives the total energy for Einstein's theory of gravity. It is easy to show that the integral of its divergence over a space-like hypersurface is positive thereby providing a simple demonstration that Einstein gravity has positive energy.     

Minimal and nonminimal gravitational interactions,and the asymmetric energy momentum tensor

Minimal and nonminimal gravitational couplings are discussed in terms of the translation gauge fields b _k , which are necessary to describe the gravitational interaction of the spin 1/2 field. For this purpose we carry out the extension of the conventional tetrad formalism of general relativity. Our general framework contains four arbitrary parameters; one of them represents the asymmetry of the affine connection (or equivalently that of the energymomentum tensor) and the others measure possible deviations from Einstein's gravitational Lagrangian, which will be responsible for spin effects. We also discuss the physical meaning of the invariance requirement with respect to the Poincaré gauge transformation that uniquely leads us within the present framework to Einstein's theory of gravity.An abridged version of the present paper was presented at the 6th International Conference on Gravitation and Relativity at Copenhagen, July 1972.Y. Nishina Memorial Foundation Fellow, on leave of absence from the University of Tokyo, Japan.     

A new geometrical gravitational theory

A geometrical gravitational theory based on the connection ={ } + ln + ln –g ln is developed. The field equations for the new theory are uniquely determined apart from one unknown dimensionless parameter ₂. The geometry on which our theory is based is an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metricg and two gauge scalars and. Physically the gravitational potential corresponds tog in the same way as in general relativity, the gravitational coupling constant to ^–2, and the gravitational mass tou(, ), which is a coscalar of power –1 algebraically made of and. The theory satisfies the weak equivalence principle, but breaks the strong one generally. We shall find outu(, )= on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus we have the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power –4 algebraically made of andu(, ), so it is dynamical, too. Finally we give spherically symmetric exact solutions. The permissible range of the unknown parameter ₂ is experimentally determined by applying the solutions to the solar system.     

A new AF gravitational instanton

It has long been conjectured that the Euclidean Schwarzschild and Euclidean Kerr instantons are the only non-trivial asymptotically flat (AF) gravitational instantons. In this Letter, we show that this conjecture is false by explicitly constructing a new two-parameter AF gravitational instanton with a U(1)×U(1) isometry group, using the inverse-scattering method. It has Euler number χ=3 and Hirzebruch signature τ=1, and its global topology is CP² with a circle S¹ removed appropriately. Various other properties of this gravitational instanton are also discussed.     

Localization of gravitational energy

In the general relativity theory gravitational energy-momentum density is usually described by a pseudo-tensor with strange transformation properties so that one does not have localization of gravitational energy. It is proposed to set up a gravitational energy-momentum density tensor having a unique form in a given coordinate system by making use of a bimetric formalism. Two versions are considered: (1) a bimetric theory with a flat-space background metric which retains the physics of the general relativity theory and (2) one with a background corresponding to a space of constant curvature which introduces modifications into general relativity under certain conditions. The gravitational energy density in the case of the Schwarzschild solution is obtained.     

Lorentz transformation of three dimensional gravitational wave tensor

Recently there has been more and more interest in the gravitational wave(GW) of moving sources. This paper introduces a Lorentz transformation problem of GWs. Although the BondiMetzner-Sachs(BMS) theory has in principle already included the Lorentz transformation of GWs, the transformation of the three-dimensional GW tensor has not been explicitly calculated before. Within four-dimensional spacetime, GWs have the properties of ‘boost weight zero’ and‘spin weight 2’. This fact makes the Lorentz t...     

The energy-momentum tensor of a static gravitational field

The method of a tetrad field proposed by Rayski was used to determine the energy-momentum tensor for an approximate solution of the Einstein equations in the static case, from which it follows that the static gravitational field has non-zero mass but zero momentum, as was to be expected.In conclusion the author thanks P. Burcev for fruitful discussions and great interest in this work.     

物质纯重力场部分的能量-动量张量研究

认为物质的质量(能量)存在形式可分为两部分，一部分是以纯物质形式存在的，另一部分是以纯重力场形式存在的.物质质量(能量)这两种形式各自对应着相应的能量 动量张量，物质总的能量-动量张量可表示为Tμν=T(Ⅰ)μν+T(Ⅱ)μν,这里，T(Ⅰ)μν，T（Ⅱ）μν分别代表物质纯物质部分和纯重力场部分的能量-动量张量.通过类比电磁理论，定义：ωμ≡-c2gμ0/g00,并引入一个反对称张量Dμν=ωμ/xν-ων/xμ，则物质纯重力场部分的能量-动量张量为T(Ⅱ)μν=(DμρDρν-gμνDαβDαβ/4 关键词： 能量-动量张量 纯重力场 重力场方程 标量重力势 矢量重力势     

On the emergence of gravitational dynamics from tensor networks

Tensor networks are used to describe the ground state wavefunction of the quantum many-body system. Recently, it has been shown that a tensor network can generate the anti-de Sitter(AdS)geometry by using the entanglement renormalization approach, which provides a new way to realize bulk reconstruction in the AdS/conformal field theory correspondence. However,whether the dynamical connections can be found between the tensor network and gravity is an important unsolved problem. In this paper, we g...     

Energy-momentum-stress tensor and gravitational field of uniformly rotating masses

Beginning with a general ansatz for the energy-momentum-stress tensor of masses in uniform rotation we determine uniquely the energy tensor and the gravitational field of two particular systems; namely, a thin, rotating, hollow cylinder and a spinning rod (dumb-bell). All calculations are made within the framework of linearised theory, but no restriction is made upon angular velocity, except that given by the velocity of light.This work was supported by the Deutsche Forschungsgemeinschaft.     

Multidirectional,multipolarization antennas for scalar and tensor gravitational radiation

Summary Some gravitational radiation antenna designs are discussed which are capable of distinguishing between the spin zero scalar radiation predicted by the Brans-Dicke theory of gravitation and the spin two tensor radiation predicted by the Einstein theory of gravitation. The antennas will also give information concerning the direction to the source of radiation, and will measure the polarization of the tensor radiation. The designs consist of symmetric masses with approapriately spaced and oriented transducers. The transducers are combined to give orthogonal outputs. Linear combinations of these orthogonal outputs then are uniquely associated with the various possible combinations of radiation type, propagation, direction and polarization, orientation. Essay submitted to the 1969 Awards for Essays on Gravity, Gravity Research Foundation, New Boston, New Hampshire.     

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.     

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.     

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.