Related papers: Positive Gravitattional Energy in Arbitrary Dimens…
In their proof of the positive energy theorem, Schoen and Yau showed that every asymptotically flat spacelike hypersurface M of a Lorentzian manifold which is flat along M can be isometrically imbedded with its given second fundamental form…
It is shown how can be made the classification of all tensors constructed from the Riemann tensor that verify the conservation of gravitational energy momentum. More precisely we explain that there exists a unique tensor of degree n in the…
We use various results concerning isometry groups of Riemannian and pseudo-Riemannian manifolds to prove that there are spaces on which differential structure can act as a source of gravitational force (Brans conjecture). The result is…
The simplest variant of gauge gravitation theory in Riemann-Cartan spacetime leading to the solution of the problem of cosmological singularity and dark energy problem is investigated. It is shown that this theory by certain restrictions on…
It is well-known that Einstein gravity is kinematic (no non-trivial vacuum solution;i.e. Riemann vanishes whenever Ricci does so) in $3$ dimension because Riemann is entirely given in terms of Ricci. Could this property be universalized for…
We consider generalized energy conditions in modified theories of gravity by taking into account the further degrees of freedom related to scalar fields and curvature invariants. The latter are usually recast as generalized {\it geometrical…
In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for…
We investigate the energy of a theory with a unit vector field (the "aether") coupled to gravity. Both the Weinberg and Einstein type energy-momentum pseudotensors are employed. In the linearized theory we find expressions for the energy…
General classical theories of material fields in an arbitrary Riemann-Cartan space are considered. For these theories, with the help of equations of balance, new non-trivially generalized, manifestly generally covariant expressions for…
We generalize the cosmic energy equation to the case when massive particles interact via a modified gravitational potential of the form phi(a, r), which is allowed to explicitly depend upon the cosmological time through the expansion factor…
We study gravitational theory in 1+2 spacetime dimensions which is determined by the Lagrangian constructed as a sum of the Einstein-Hilbert term plus the two (translational and rotational) gravitational Chern-Simons terms. When the…
There are constructed exact solutions of the quantum-mechanical equation for a spin S=1 particle in 2-dimensional Riemannian space of constant positive curvature, spherical plane, in presence of an external magnetic field, analogue of the…
We study transverse asymptotically flat spacetimes without horizons that arise from brane matter sources. We assume that asymptotically there is a spatial translation Killing vector that is tangent to the brane. Such spacetimes are…
We prove that under suitable assumptions, the constant term in the Green function of the Paneitz-Branson operator on a compact Riemannian manifold $(M,g)$ is positive unless $(M,g)$ is conformally diffeomophic to the standard sphere. The…
We prove the positive mass theorem on conical manifold with small cone angle and co-dimensional two singularities under the assumption that the ambient manifold admits a spin structure and locally conformal flat
The positive energy theorem for weighted asymptotically flat spin manifolds was proved by Baldauf and Ozuch \cite{BO}, and for non-spin case by Chu and Zhu \cite{CZh}. In this paper, we generalize the positive energy theorem for…
It is shown that a simple model for 4-dimensional quantum gravity based on a 3-dimensional generalization of anyon superconductivity can be regarded as a discrete form of Polyakov's string theory. This suggests that there is a universal…
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…
An energy condition, in the context of a wide class of spacetime theories (including general relativity), is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that…
We prove the spacetime positive mass theorem in dimensions less than eight. This theorem states that for any asymptotically flat initial data set satisfying the dominant energy condition, the ADM energy-momentum vector $(E,P)$ of the…