Time-Machine Solutions of Einstein's Equations with Electromagnetic Field

In this paper we investigate the time-machine problem in the electromagnetic field. Based on a metric which is a more general form of Ori＇s, we solve the Einstein＇s equations with the energy-momentum tensors for electromagnetic field, and construct the time-machine solutions, which solve the time machine problem in electromagnetic field.

Einstein转盘引力场精确解

本文解爱因斯坦场方程得出了转盘的度规。

微扰法解Einstein场方程

首先从已知具有对角型度规的Einstein场方程的精确解出发,近似推导了含有微扰条件下的场方程形式;其次,利用这一微扰形式具体计算了静态球对称引力场的外部微扰解,并进而讨论了球状星系外部的引力特征.结果表明,该微扰解不仅可以与内部解衔接,而且在消除微扰的情况下还可以自动恢复到Schwarzchild解的形式.

The Singularities of Gravitational Fields of Static Thin Loop and Double Spheres Reveal the Impossibility of Singularity Black Holes

In the classical Newtonian mechanics, the gravity fields of static thin loop and double spheres are two simple but foundational problems. However, in the Einstein’s theory of gravity, they are not simple. In fact, we do not know their solutions up to now. Based on the coordinate transformations of the Kerr and the Kerr-Newman solutions of the Einstein’s equation of gravity field with axial symmetry, the gravity fields of static thin loop and double spheres are obtained. The results indicate that, no matter how much the mass and density are, there are singularities at the central point of thin loop and the contact point of double spheres. What is more, the singularities are completely exposed in vacuum. Space near the surfaces of thin loop and spheres are highly curved, although the gravity fields are very weak. These results are inconsistent with practical experience and completely impossible. By reasonable analogy, black holes with singularity in cosmology and astrophysics are something illusive. Caused by the mathematical description of curved space-time, they do not exist in real world actually. If there are black holes in the universe, they can only be the types of the Newtonian black holes without singularities, rather than the Einstein’s singularity black holes. In order to escape the puzzle of singularity thoroughly, the description of gravity should return to the traditional form of dynamics in flat space. The renormalization of gravity and the unified description of four basic interactions may be possible only based on the frame of flat space-time. Otherwise, theses problems can not be solved forever. Physicists should have a clear understanding about this problem.

Broken Charges Associated with Classical Spacetime Symmetries under Canonical Transformation in Real Scalar Field Theory

We know from Noether’s theorem that there is a conserved charge for every continuous symmetry. In General Relativity, Killing vectors describe the spacetime symmetries and to each such Killing vector field, we can associate conserved charge through stress-energy tensor of matter which is mentioned in the article. In this article, I show that under simple set of canonical transformation of most general class of Bogoliubov transformation between creation, annihilation operators, those charges associated with spacetime symmetries are broken. To do that, I look at stress-energy tensor of real scalar field theory (as an example) in curved spacetime and show how it changes under simple canonical transformation which is enough to justify our claim. Since doing Bogoliubov transformation is equivalent to coordinate transformation which according to Einstein’s equivalence principle is equivalent to turn on effect of gravity, therefore, we can say that under the effect of gravity those charges are broken.

Einstein’s Pseudo-Tensor in <i>n</i>Spatial Dimensions for Static Systems with Spherical Symmetry

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.

Reciprocity Relation between Alternative Gravity Formulas

We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.

玻色-爱因斯坦凝聚原子与Schr(o|¨)dinger猫态相互作用系统中的保真度

利用全量子理论及量子信息保真度理论,研究了薛定谔猫态光场与玻色爱因斯坦凝聚原子相互作用系统中,量子态保真度随时间的演化特性.讨论了光场强度和玻色爱因斯坦凝聚原子间的耦合强度对量子态保真度的影响.结果表明:光场强度可调制量子态的保真效果,而原子间的耦合常数主要影响量子态保真度的振荡频率.

A Spherical Relativistic Anisotropic Compact Star Model

We provide solutions to Einsteins field equations for a model of a spherically symmetric anisotropic fluid distribution, relevant to the description of compact stars. The central matter-energy density, radial and tangential pressures, red shift and speed of sound are positive definite and are decreasing monotonically with increasing radial distance from the center of matter distribution of astrophysical object. The causality condition is satisfied for complete fluid distribution. The central value of anisotropy is zero and is increasing monotonically with increasing radial distance from the center of the distribution. The adiabatic index is increasing with increasing radius of spherical fluid distribution. The stability conditions in relativistic compact star are also discussed in our investigation. The solution is representing the realistic objects such as SAXJ1808.4-3658, HerX-1, 4U1538-52, LMC X-4, CenX-3, VelaX-1, PSRJ1614-2230 and PSRJ0348+0432 with suitable conditions.

Class of Charged Fluid Balls in General Relativity

In the present study, we have obtained a new analytical solution of combined Einstein-Maxwell field equations describing the interior field of a ball having static spherically symmetric isotropic charged fluid within it. The charge and electric field intensity are zero at the center and monotonically increasing towards the boundary of the fluid ball. Besides these, adiabatic index is also increasing towards the boundary and becomes infinite on it. All other physical quantities such as pressure, density, adiabatic speed of sound, charge density, adiabatic index are monotonically decreasing towards the surface. Causality condition is obeyed at the center of ball. In the limiting case of vanishingly small charge, the solution degenerates into Schwarzchild uniform density solution for electrically neutral fluid. The solution joins smoothly to the Reissner-Nordstrom solution over the boundary. We have constructed a neutron star model by assuming the surface density . The mass of the neutron star comes with radius 14.574 km.

Mass as the Fifth Dimension of the Universe

Newton considered three-dimensional universe endowed with flat space Euclidean geometry, and treated the time as an outside parameter and established his dynamics of the universe. Einstein along with space, considered time, and generated a four-dimensional universe endowed with non-Euclidean curved space-time geometry with time as its fourth dimension, and set up his field equations. Schwarzschild solved Einstein’s field equations around a star in space, which is, otherwise, flat, and obtained a solution. We, along with space and time, considered mass which also included energy according to Einstein’s mass-energy equivalence relation: E = mc2, and generated a five-dimensional universe with the mass as its fifth dimension, and solved the Einstein’s field equations, in some simple cases, and obtained solutions around a star in space, which is otherwise, flat.

Self-Similar Solutions of the Kantowski-Sachs Model with a Perfect Fluid in General Relativity

Exact self-similar solutions to Einstein’s field equations for the Kantowski-Sachs space-time are determined. The self-similarity property is applied to determine the functional form of the unknown functions that define the gravitational model and to reduce the order of the field equations. The consequences of matter, described by the energy-momentum tensor, are investigated in the case of a perfect fluid. Some physical features and kinematical properties of the obtained model are studied.

Friedmann-Like Cosmological Equations for the Accelerated Expansion of the Universe

In recent papers [1] [2] [3], we framed suitable axioms for Space called Super Space by Wheeler [4]. Using our axioms in Newtonian formalism and considering the density of the universe to be constant in time, we showed in the above references that at t = 0 the radius of the universe need not be zero. And thus, we avoided the problem of singularity. We further showed that the Hubble factor is no longer constant in time and goes on decreasing as confirmed by experiments. We pointed out in the above references that Space is the source of dark energy which is responsible for the accelerated expansion of the universe. With a view to improving the above-mentioned results quantitatively, in this paper, we are discussing the consequences of our axioms using Einstein’s field equations of general theory of relativity. Friedmann-like Cosmological equations with Dark Energy built-in are derived. This derivation is obtained using Robertson-Walker line element and by introducing a suitable expression for Energy-Momentum tensor in terms of matter and Dark energy contents of the universe. The solutions of our cosmological equations obtained here, show that the radius of the universe cannot reach zero but has a minimum value and there is also maximum value for the radius of the universe. The inflationary expansion of the very early universe emerges from our theory.

Light-Cone Coordinate System in General Relativity

If there exists a null gradient field in 3 + 1 dimensional space-time, we can set up a kind of light-cone coordinate system in the space-time. In such coordinate system, the metric takes a simple form, which is helpful for simplifying and solving the Einstein’s field equation. This light-cone coordinate system has wonderful properties and has been used widely in astrophysics to calculate parameters. We discuss the structure of space-time with light-cone coordinate system in detail. We show how to construct the light-cone coordinate system and obtain the conditions of its existence, and then explain their geometrical and physical meanings.

Gravitational Space-Time Curve Generation via Accelerated Charged Particles

A force with an acceleration that is equal to multiples greater than the speed of light per unit time is exerted on a cloud of charged particles. The particles are resultantly accelerated to within an infinitesimal fraction of the speed of light. As the force or acceleration increases, the particles’ velocity asymptotically approaches but never achieves the speed of light obeying relativity. The asymptotic increase in the particles’ velocity toward the speed of light as acceleration increasingly surpasses the speed of light per unit time does not compensate for the momentum value produced on the particles at sub-light velocities. Hence, the particles’ inertial mass value must increase as acceleration increases. This increase in the particles’ inertial mass as the particles are accelerated produce a gravitational field which is believed to occur in the oscillation of quarks achieving velocities close to the speed of light. The increased inertial mass of the density of accelerated charged particles becomes the source mass (or Big “M”) in Newton’s equation for gravitational force. This implies that a space-time curve is generated by the accelerated particles. Thus, it is shown that the acceleration number (or multiple of the speed of light greater than 1 per unit of time) and the number of charged particles in the cloud density are surjectively mapped to points on a differential manifold or space-time curved surface. Two aspects of Einstein’s field equations are used to describe the correspondence between the gravitational field produced by the accelerated particles and the resultant space-time curve. The two aspects are the Schwarzchild metric and the stress energy tensor. Lastly, the possibility of producing a sufficient acceleration or electromagnetic force on the charged particles to produce a gravitational field is shown through the Lorentz force equation. Moreover, it is shown that a sufficient voltage can be generated to produce an acceleration/force on the particles that is multiples greater than the speed of light per unit time thereby generating gravity.

Time-periodic solutions of the Einstein's field equations Ⅰ:general framework

In this paper,we develop a new algorithm to find the exact solutions of the Einstein's field equations.Time-periodic solutions are constructed by using the new algorithm.The singularities of the time-periodic solutions are investigated and some new physical phenomena,such as degenerate event horizon and time-periodic event horizon,are found.The applications of these solutions in modern cosmology and general relativity are expected.

Time-periodic solutions of the Einstein's field equations II:geometric singularities

In this paper,we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish,keep finite or take the infinity at some points in these space-times,respectively.The singularities of these new time-periodic solutions are investigated and some new physical phenomena are discovered.

Time-periodic solutions of the Einstein's field equations Ⅲ:physical singularities

In this paper we construct a new time-periodic solution of the vacuum Einstein's field equations, this solution possesses physical singularities, i.e., the norm of the solution's Riemann curvature tensor takes the infinity at some points. We show that this solution is intrinsically time-periodic and describes a time-periodic universe with the "time-periodic physical singularity". By calculating the Weyl scalars of this solution, we investigate new physical phenomena and analyze new singularities for this universal model.

A NEW CLASS OF SOLUTIONS OF VACUUM EINSTEIN'S FIELD EQUATIONS WITH COSMOLOGICAL CONSTANT

In this paper, a new class of solutions of the vacuum Einstein＇s field equa- tions with cosmological constant is obtained. This class of solutions possesses the naked physical singularity. The norm of the Riemann curvature tensor of this class of solutions takes infinity at some points and the solutions do not have any event horizon around the singularity.

两种GRACE地球重力场精度评定方法的检验

基于改进的能量守恒法,分别利用先验地球重力场模型法(PEM)和最小二乘协方差阵法(LSM)评定了120阶GRACE地球重力场的精度,模拟结果表明:1)基于美国JPL公布的GRACE轨道参数和核心载荷精度指标,在120阶处分别采用PEM和LSM恢复地球引力位系数的精度为5.192×10-10和6.633×10-10;2)分别基于PEM和LSM恢复120阶地球引力位系数的模拟精度和德国GFZ公布的EIGEN-GRACE02S地球重力场模型的实测精度在各阶处符合较好,从而证明了基于PEM和LSM评定地球重力场恢复精度的有效性;3)通过基于PEM和LSM分别恢复地球引力位系数的模拟精度在各阶处的符合性,验证了基于能量守恒法结合预处理共轭梯度迭代法恢复120阶GRACE地球重力场算法的可靠性。