It was noted earlier that the general relativity field equations for static systems with spherical symmetry can be put into a linear form when the source energy density equals radial stress. These linear equations lea...It was noted earlier that the general relativity field equations for static systems with spherical symmetry can be put into a linear form when the source energy density equals radial stress. These linear equations lead to a delta function energymomentum tensor for a point mass source for the Schwarzschild field that has vanishing self-stress, and whose integral therefore transforms properly under a Lorentz transformation, as though the particle is in the flat space-time of special relativity (SR). These findings were later extended to n spatial dimensions. Consistent with this SR-like result for the source tensor, Nordstrom and independently, Schrodinger, found for three spatial dimensions that the Einstein gravitational energy-momentum pseudo-tensor vanished in proper quasi-rectangular coordinates. The present work shows that this vanishing holds for the pseudo-tensor when extended to n spatial dimensions. Two additional consequences of this work are: 1) the dependency of the Einstein gravitational coupling constant κ on spatial dimensionality employed earlier is further justified;2) the Tolman expression for the mass of a static, isolated system is generalized to take into account the dimensionality of space for n ≥ 3.展开更多
This document reviews the Landau-Liftshifts reformulation of General relativity with a representation of the available mass of a graviton. From looking at a conservation law, using the Landau-Liftshifs formulation, we...This document reviews the Landau-Liftshifts reformulation of General relativity with a representation of the available mass of a graviton. From looking at a conservation law, using the Landau-Liftshifs formulation, we obtain conditions for initial mass, in the Pre-Planckian regime of space-time. In doing so, we also indicate a metric tensor and metric pseudo tensor delineation of causal discontinuity.展开更多
We introduce a new notion of pseudo-anti commuting Ricci tensor for real hypersurfaces in the noncompact complex hyperbolic quadric Q^(m?)= SO_2~0,_m/SO_2SO_m and give a complete classi?cation of these hypersurfaces.
In this paper, we consider Osserman conditions on lightlike warped product (sub-)manifolds with respect to the Jacobi Operator. We define the Jacobi operator for lightlike warped product manifold and introduce a study...In this paper, we consider Osserman conditions on lightlike warped product (sub-)manifolds with respect to the Jacobi Operator. We define the Jacobi operator for lightlike warped product manifold and introduce a study of lightlike warped product Osserman manifolds. For the coisotropic case with totally degenerates first factor, we prove that this class consists of Einstein and locally Osserman lightlike warped product.展开更多
The restoration of pseudo-spin symmetry（PSS） along the N = 32 and N = 34 isotonic chains and the physics behind are studied by applying the relativistic Hartree-Fock theory with the effective Lagrangian PKA1. Taking...The restoration of pseudo-spin symmetry（PSS） along the N = 32 and N = 34 isotonic chains and the physics behind are studied by applying the relativistic Hartree-Fock theory with the effective Lagrangian PKA1. Taking the proton pseudo-spin partners(π2s1/2, π1d3/2) as candidates, the systematic restoration of PSS along both isotonic chains is found from sulphur（S） to nickel（Ni）, while an obvious PSS violation from silicon（Si） to sulphur is discovered near the drip lines. The effects of the tensor force components are investigated, introduced naturally by the Fock terms, which can only partially interpret the systematics from calcium to nickel, whereas they fail for the overall trends. Further analysis following the Schr?dinger-like equation of the lower component of Dirac spinor shows that contributions from the Hartree terms dominate the overall systematics of the PSS restoration. Such effects can be self-consistently interpreted by the evolution of the proton central density profiles along both isotonic chains. In particular, the PSS violation is found to tightly relate to the dramatic changes from the bubble-like density profiles in silicon to the central-bumped ones in sulphur.展开更多
文摘It was noted earlier that the general relativity field equations for static systems with spherical symmetry can be put into a linear form when the source energy density equals radial stress. These linear equations lead to a delta function energymomentum tensor for a point mass source for the Schwarzschild field that has vanishing self-stress, and whose integral therefore transforms properly under a Lorentz transformation, as though the particle is in the flat space-time of special relativity (SR). These findings were later extended to n spatial dimensions. Consistent with this SR-like result for the source tensor, Nordstrom and independently, Schrodinger, found for three spatial dimensions that the Einstein gravitational energy-momentum pseudo-tensor vanished in proper quasi-rectangular coordinates. The present work shows that this vanishing holds for the pseudo-tensor when extended to n spatial dimensions. Two additional consequences of this work are: 1) the dependency of the Einstein gravitational coupling constant κ on spatial dimensionality employed earlier is further justified;2) the Tolman expression for the mass of a static, isolated system is generalized to take into account the dimensionality of space for n ≥ 3.
文摘This document reviews the Landau-Liftshifts reformulation of General relativity with a representation of the available mass of a graviton. From looking at a conservation law, using the Landau-Liftshifs formulation, we obtain conditions for initial mass, in the Pre-Planckian regime of space-time. In doing so, we also indicate a metric tensor and metric pseudo tensor delineation of causal discontinuity.
基金supported by National Research Foundation of Korea (Grant No. NRF2015-R1A2A1A-01002459)
文摘We introduce a new notion of pseudo-anti commuting Ricci tensor for real hypersurfaces in the noncompact complex hyperbolic quadric Q^(m?)= SO_2~0,_m/SO_2SO_m and give a complete classi?cation of these hypersurfaces.
文摘In this paper, we consider Osserman conditions on lightlike warped product (sub-)manifolds with respect to the Jacobi Operator. We define the Jacobi operator for lightlike warped product manifold and introduce a study of lightlike warped product Osserman manifolds. For the coisotropic case with totally degenerates first factor, we prove that this class consists of Einstein and locally Osserman lightlike warped product.
基金Supported by National Natural Science Foundation of China(11675065,11711540016)
文摘The restoration of pseudo-spin symmetry（PSS） along the N = 32 and N = 34 isotonic chains and the physics behind are studied by applying the relativistic Hartree-Fock theory with the effective Lagrangian PKA1. Taking the proton pseudo-spin partners(π2s1/2, π1d3/2) as candidates, the systematic restoration of PSS along both isotonic chains is found from sulphur（S） to nickel（Ni）, while an obvious PSS violation from silicon（Si） to sulphur is discovered near the drip lines. The effects of the tensor force components are investigated, introduced naturally by the Fock terms, which can only partially interpret the systematics from calcium to nickel, whereas they fail for the overall trends. Further analysis following the Schr?dinger-like equation of the lower component of Dirac spinor shows that contributions from the Hartree terms dominate the overall systematics of the PSS restoration. Such effects can be self-consistently interpreted by the evolution of the proton central density profiles along both isotonic chains. In particular, the PSS violation is found to tightly relate to the dramatic changes from the bubble-like density profiles in silicon to the central-bumped ones in sulphur.
