The locally rotationally symmetric Bianchi-type II string cosmological models with bulk viscosity are obtained, where an equation of state, , and a relation between metric potentials, , are adopted. The physical featu...The locally rotationally symmetric Bianchi-type II string cosmological models with bulk viscosity are obtained, where an equation of state, , and a relation between metric potentials, , are adopted. The physical features of the models are also discussed. In special cases the model reduces to the string models without viscosity that was previously given in the literatures.展开更多
This article suggests a new metric theory of gravitation, in which metric field is determined not only by matter and nongravitational field but also by vector graviton field, and in principle there is no need to intro...This article suggests a new metric theory of gravitation, in which metric field is determined not only by matter and nongravitational field but also by vector graviton field, and in principle there is no need to introduce the Einstein's tensor. In order to satisfy automatically the geodesic postulate, an additional coordinate condition is needed. For the spherically symmetric static field, it leads us to quite different conclusions from those of Einstein's general relativity in the interior region of the surface of infinite redshift. Accurate to the first order of , it obtains the same results about the four experimental tests of general relativity.展开更多
Gravity and electromagnetism are two sides of the same coin, which is the clue of this unification. Gravity and electromagnetism are represented by two mathematical structures, symmetric and antisymmetric respectively...Gravity and electromagnetism are two sides of the same coin, which is the clue of this unification. Gravity and electromagnetism are represented by two mathematical structures, symmetric and antisymmetric respectively. Einstein gravitational field equation is the symmetric mathematical structure. Electrodynamics Lagrangian is three parts, for electromagnetic field, Dirac field and interaction term. The definition of canonical energy momentum tensor was used for each term in Electrodynamics Lagrangian to construct the antisymmetric mathematical structure; symmetric and antisymmetric gravitational field equations are two sides of the same Lagrangian.展开更多
The relation between microtubules architecture in the cytoskeletal structure inside the dendrites and soma and the emergence of neuron function and firing action potential crosses the tiny line between physics and bio...The relation between microtubules architecture in the cytoskeletal structure inside the dendrites and soma and the emergence of neuron function and firing action potential crosses the tiny line between physics and biology. As decoherence is a fundamental mechanism in some biological process such as photosynthesis and others examples, the gravitational quantum approach may contribute to elucidate if neuron function really emerges from quantum coherence in neuronal microtubules. The Einstein equation correlates the stress-energy tensor Tμv to a specific divergence-free combination Ricci tensor Rμv and the metric. In the semiclassical formulation, we have Gμv = Rμv -1/2gμvR=8πG/C^4〈ψ｜μvψ〉 which describes the quantum field in curved space-time geometry. But for a more precise equation in relation to the stress-energy tensor, we know that in a non-zero temperature, the wave-function is not enough to describe the physical reality. A more precise equation demands a formulation in the density-matrix form but for now there is no Diosi-Penrose model with density-matrix formulation. Such a density-matrix description can be viewed as a probability mixture of different wave-functions. Using some algebra and rules related to the mathematical manipulation of the density-matrix applied to operators, such the stress energy tensor, we found the von Neumann-Einstein equation for the general relativity equation in the density matrix operator form, Gμv = 8πG/C^4Tr[pTμv]. Thus density-matrix operator--instead of just a wave function of pure states--applied to the stress-energy tensor gives the curvature of space time, given by Einstein tensor, Gμv. The quantum fluctuation in the gravitational space-time field might feed back to decohere the quantum density-matrix. As long as decoherence can be viewed as the loss of information from a system to the environment, the density-matrix p is also related to that process and considering the measurement problem, density-matrix /garter is a more complete description of the possible outcome of the measurement. It is possible that some characteristics of the special microtubulin-associated proteins （MAP） that capes the dendritic-somatic microtubulins which could induces longer-lived nuclear spin states prevented from de-polymerization and suitable for long term information encode and memory. Understand the mechanism by which the hyper-phosphorylation in type tau-MAP displacements from microtubulins results in neurofibrillary tangles and cognitive dysfunctions in Alzheimer＇s disease.展开更多
A-manifolds and/3-manifolds, introduced by Gray （1978）, are two significant classes of Einstein-like Riemannian manifolds. A Riemannian manifold is Ricci parallel if and only if it is simultaneously an A-manifold an...A-manifolds and/3-manifolds, introduced by Gray （1978）, are two significant classes of Einstein-like Riemannian manifolds. A Riemannian manifold is Ricci parallel if and only if it is simultaneously an A-manifold and a B-manifold. The present paper proves that both focal submanifolds of each isoparametric hypersurface in unit spheres with g = 4 distinct principal curvatures are A-manifolds. As for the focal submanifolds with g = 6, m = 1 or 2, only one is an A-manifold, and neither is a B-manifold.展开更多
Einstein＇s equation,in its standard form,breaks down at the Big Bang singularity.A new version,equivalent to Einstein＇s whenever the latter is defined,but applicable in wider situations,is proposed.The new equation ...Einstein＇s equation,in its standard form,breaks down at the Big Bang singularity.A new version,equivalent to Einstein＇s whenever the latter is defined,but applicable in wider situations,is proposed.The new equation remains smooth at the Big Bang singularity of the Friedmann-Lemaatre-Robertson-Walker model.It is a tensor equation defined in terms of the Ricci part of the Riemann curvature.It is obtained by taking the Kulkarni-Nomizu product between Einstein＇s equation and the metric tensor.展开更多
With the usual definitions for the entropy and the temperature associated with the apparent horizon, we discuss the first law of the thermodynamics on the apparent in the general scalar-tensor theory of gravity with t...With the usual definitions for the entropy and the temperature associated with the apparent horizon, we discuss the first law of the thermodynamics on the apparent in the general scalar-tensor theory of gravity with the kinetic term of the scalar field nonminimally coupling to Einstein tensor. We show the equivalence between the first law of thermodynamics on the apparent horizon and Friedmann equation for the general models, by using a mass-like function which is equal to the Misner-Sharp mass on the apparent horizon. The results further support the universal relationship between the first law of thermodynamics and Friedmann equation.展开更多
文摘The locally rotationally symmetric Bianchi-type II string cosmological models with bulk viscosity are obtained, where an equation of state, , and a relation between metric potentials, , are adopted. The physical features of the models are also discussed. In special cases the model reduces to the string models without viscosity that was previously given in the literatures.
文摘This article suggests a new metric theory of gravitation, in which metric field is determined not only by matter and nongravitational field but also by vector graviton field, and in principle there is no need to introduce the Einstein's tensor. In order to satisfy automatically the geodesic postulate, an additional coordinate condition is needed. For the spherically symmetric static field, it leads us to quite different conclusions from those of Einstein's general relativity in the interior region of the surface of infinite redshift. Accurate to the first order of , it obtains the same results about the four experimental tests of general relativity.
文摘Gravity and electromagnetism are two sides of the same coin, which is the clue of this unification. Gravity and electromagnetism are represented by two mathematical structures, symmetric and antisymmetric respectively. Einstein gravitational field equation is the symmetric mathematical structure. Electrodynamics Lagrangian is three parts, for electromagnetic field, Dirac field and interaction term. The definition of canonical energy momentum tensor was used for each term in Electrodynamics Lagrangian to construct the antisymmetric mathematical structure; symmetric and antisymmetric gravitational field equations are two sides of the same Lagrangian.
文摘The relation between microtubules architecture in the cytoskeletal structure inside the dendrites and soma and the emergence of neuron function and firing action potential crosses the tiny line between physics and biology. As decoherence is a fundamental mechanism in some biological process such as photosynthesis and others examples, the gravitational quantum approach may contribute to elucidate if neuron function really emerges from quantum coherence in neuronal microtubules. The Einstein equation correlates the stress-energy tensor Tμv to a specific divergence-free combination Ricci tensor Rμv and the metric. In the semiclassical formulation, we have Gμv = Rμv -1/2gμvR=8πG/C^4〈ψ｜μvψ〉 which describes the quantum field in curved space-time geometry. But for a more precise equation in relation to the stress-energy tensor, we know that in a non-zero temperature, the wave-function is not enough to describe the physical reality. A more precise equation demands a formulation in the density-matrix form but for now there is no Diosi-Penrose model with density-matrix formulation. Such a density-matrix description can be viewed as a probability mixture of different wave-functions. Using some algebra and rules related to the mathematical manipulation of the density-matrix applied to operators, such the stress energy tensor, we found the von Neumann-Einstein equation for the general relativity equation in the density matrix operator form, Gμv = 8πG/C^4Tr[pTμv]. Thus density-matrix operator--instead of just a wave function of pure states--applied to the stress-energy tensor gives the curvature of space time, given by Einstein tensor, Gμv. The quantum fluctuation in the gravitational space-time field might feed back to decohere the quantum density-matrix. As long as decoherence can be viewed as the loss of information from a system to the environment, the density-matrix p is also related to that process and considering the measurement problem, density-matrix /garter is a more complete description of the possible outcome of the measurement. It is possible that some characteristics of the special microtubulin-associated proteins （MAP） that capes the dendritic-somatic microtubulins which could induces longer-lived nuclear spin states prevented from de-polymerization and suitable for long term information encode and memory. Understand the mechanism by which the hyper-phosphorylation in type tau-MAP displacements from microtubulins results in neurofibrillary tangles and cognitive dysfunctions in Alzheimer＇s disease.
基金supported by National Natural Science Foundation of China(Grant No.11301027)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130003120008)+1 种基金the Beijing Natural Science Foundation(Grant No.1144013)the Fundamental Research Funds for the Central Universities(Grant No.2012CXQT09)
文摘A-manifolds and/3-manifolds, introduced by Gray （1978）, are two significant classes of Einstein-like Riemannian manifolds. A Riemannian manifold is Ricci parallel if and only if it is simultaneously an A-manifold and a B-manifold. The present paper proves that both focal submanifolds of each isoparametric hypersurface in unit spheres with g = 4 distinct principal curvatures are A-manifolds. As for the focal submanifolds with g = 6, m = 1 or 2, only one is an A-manifold, and neither is a B-manifold.
文摘Einstein＇s equation,in its standard form,breaks down at the Big Bang singularity.A new version,equivalent to Einstein＇s whenever the latter is defined,but applicable in wider situations,is proposed.The new equation remains smooth at the Big Bang singularity of the Friedmann-Lemaatre-Robertson-Walker model.It is a tensor equation defined in terms of the Ricci part of the Riemann curvature.It is obtained by taking the Kulkarni-Nomizu product between Einstein＇s equation and the metric tensor.
基金supported by the National Natural Science Foundation of China(Grant Nos.11175270 and 11475065)the Program for New Century Excellent Talents in University(Grant No.NCET-12-0205)
文摘With the usual definitions for the entropy and the temperature associated with the apparent horizon, we discuss the first law of the thermodynamics on the apparent in the general scalar-tensor theory of gravity with the kinetic term of the scalar field nonminimally coupling to Einstein tensor. We show the equivalence between the first law of thermodynamics on the apparent horizon and Friedmann equation for the general models, by using a mass-like function which is equal to the Misner-Sharp mass on the apparent horizon. The results further support the universal relationship between the first law of thermodynamics and Friedmann equation.
