To describe properties of the high frequency gravitational wave （HFGW） propagating through the vacuum gravitational field in Robertson-Walker background space-time, we calculated its energy momentum pseudo-tensor （...To describe properties of the high frequency gravitational wave （HFGW） propagating through the vacuum gravitational field in Robertson-Walker background space-time, we calculated its energy momentum pseudo-tensor （EMPT） in the limit of short wavelengths by taking the Brill-Hartle average on the second order perturbation of the Einstein tensor over several wavelengths. By rewriting the EMPT as a form of perfect fluid, the dynamical back-reaction of HIFGW on the background spacetime was discussed. The result shows that the energy density of HFGW, which is in the gauge we chose, is positive definite. The HFGW serves as a source for curving the background space-time and affects the dynamical evolution and time evolution of the scale factor of the Robertson-Walker metric.展开更多
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
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
It is shown that a novel anomaly associated with transverse Waxd-Takahashi identity exists for a pseudo- tensor current in QED, and the anomaly gives rise to a topological index of a Dirac operator in terms of an Atiy...It is shown that a novel anomaly associated with transverse Waxd-Takahashi identity exists for a pseudo- tensor current in QED, and the anomaly gives rise to a topological index of a Dirac operator in terms of an Atiyah- Singer index theorem.展开更多
基金the National Basic Research Program of China (No.2003 CB 716300)the National Natural Science Foundation of China (No.10575140)+1 种基金the Nature Science Foundation of Chongqing (No. 8562)the Foundation of China Academy of Engineering Physics.
文摘To describe properties of the high frequency gravitational wave （HFGW） propagating through the vacuum gravitational field in Robertson-Walker background space-time, we calculated its energy momentum pseudo-tensor （EMPT） in the limit of short wavelengths by taking the Brill-Hartle average on the second order perturbation of the Einstein tensor over several wavelengths. By rewriting the EMPT as a form of perfect fluid, the dynamical back-reaction of HIFGW on the background spacetime was discussed. The result shows that the energy density of HFGW, which is in the gauge we chose, is positive definite. The HFGW serves as a source for curving the background space-time and affects the dynamical evolution and time evolution of the scale factor of the Robertson-Walker metric.
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.
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(10775059)
文摘It is shown that a novel anomaly associated with transverse Waxd-Takahashi identity exists for a pseudo- tensor current in QED, and the anomaly gives rise to a topological index of a Dirac operator in terms of an Atiyah- Singer index theorem.
