Thick Shell with Different Masses

In the framework of Israel formalism the Oppenheimer-Snyder gravitational collapse and a Schwarzschild cavity are studied. The motion of the Oppenheimer-Snyder thick shell can be represented by an appropriate thin shell if the expansion of the shell is great, which is valid in the flat universe.     

Lanczos Potential for the Gödel Cosmological Model

Using a Lovelock's theorem we obtain the Lanczos spintensor for the Gödel's metric.     

The Hubble parameter in the early universe with viscous QCD matter and finite cosmological constant

The evolution of a flat, isotropic and homogeneous universe is studied. The background geometry in the early phases of the universe is conjectured to be filled with causal bulk viscous fluid and dark energy. The energy density relations obtained from the assumption of covariant conservation of energy‐momentum tensor of the background matter in the early universe are used to derive the basic equation for the Hubble parameter H. The viscous properties described by ultra‐relativistic equations of state and bulk viscosity taken from recent heavy‐ion collisions and lattice QCD calculations have been utilized to give an approximate solution of the field equations. The cosmological constant is conjectured to be related to the energy density of the vacuum. In this treatment, there is a clear evidence for singularity at vanishing cosmic time t indicating the dominant contribution from the dark energy. The time evolution of H seems to last for much longer time than the ideal case, where both cosmological constant and viscosity coefficient are entirely vanishing.     

A neutrino universe with viscosity

A solution of the Einstein field equation corresponding to a distribution of fluid with equation of stateρ = 3p but with a nonvanishing shear viscosity is presented. The solution is spherical symmetric and the flow lines are geodetic.     

Measurements of a Machian transient mass fluctuation

The prediction of a novel transient mass fluctuation expected in relativistic theories of gravitation that satisfy the globally-local Mach condition (that the cosmic gravitational potential is roughly equal to the square of the speed of light) is set forth. Cosmological consequences of the Mach condition are mentioned, and an experiment that tests the prediction is discussed. The apparatus, procedure, and results of this experiment are described. The predicted effect is seen with better than order of magnitude accuracy.     

A new experimental approach to Mach's principle and relativistic graviation

As noted many years ago by Sciama, and more recently by Nordtvedt, Lorentz invariant (relativistic) gravitation at linear order involves a vector potential that is required to properly account for large inertial effects as well as the correct prediction of the classical tests of general relativity theory (GRT). It is pointed out that the linear-order vector aspect of the gravitational potential makes possible a simple, powerful and inexpensive technique for testing the predictions of GRT and associated issues. An experiment using this technique gives preliminary results that, to order of magnitude, corroborate GRT.1. If one demands a theory that satisfies Mach's Principle irrespective of the particular value of _c, one must go to a theory that contains GRT with critical cosmic matter density as a special case. Such a theory (an Einstein-Cartan theory with teleparallelism) has been developed by Treder [2].2. Equation (4) here is Nordtvedt's Eq. (14), in Ref. 3, with GRT PPN parameters chosen.3. The exact value of this correction factor that depends on the way in which energy is distributed between field and sources in turn depends on how the source term for the gravitational field equations is constructed. At least two different source terms that give correct predictions for the various tests of GRT exist. In this connection see Peters [4]. This ambiguity does not mean that it is impossible in principle to determine how energy is distributed between sources and field. Indeed, if one posits the existence of critical cosmic matter density, this experiment can decide the issue.     

A stationary apparent weight shift from a transient Machian mass fluctuation

A transient mass fluctuation, predicted by Lorentz-invariant theories of gravitation wherein inertia is gravitationally induced, can be combined with a synchronous thrust to produce a stationary change in the apparent weight of an object. A substantial effect of this sort—on the order of tenths of a gram or more—should be achievable in laboratory scale apparatus. A detailed derivation of the predicted transient mass fluctuation is given in an appendix.1. This does not mean, however, that it is impossible to directly detect the expected weight fluctuations at higher than low audio frequencies. In fact, in preliminary work toward the experiment described below, L. Shen, K. Wanser, and I have detected evidence of the effect at ultrasonic frequencies employing very unusual capacitors (high energy density ceramic multiplate chip capacitors with strongly suppressed first- and second-order electromechanical effects) mounted on an aluminum pedestal which acts as the spring in the system. The minute displacements produced are detected with a laser interferometer. This work will be described fully in a separate paper.2. Such a transformer can be made with, for example, an Amidon T 300A-26 powdered iron torus. Powdered iron is preferable to ferrite because of its superior flux saturation and energy loss characteristics at the frequencies in question.3. Einstein[7] was the first to point out (in 1912) that the simplest formalism for the gravitational field that incorporates Machian gravitational induction of inertia is that based on the analogy with the electromagnetic field, that is, a Lorentz-invariant four-vector potential theory. Many years later, Sciama[5] showed explicitly how such a theory could account for well-known inertial reaction effects, provided that the mean matter density of the universe were the right value (in fact, just cosmologically critical density). Later he showed that a general relativistic tensor formalism yielded the same conclusions[8]. And, as I have pointed out elsewhere[1–3], Nordtvedt's PPN formalism with GRT parameters chosen yields the same result when the effect of cosmic matter is included.4. Contributions from the Hubble flow tov and thusj are ignored here, since upon integration they vanish by symmetry. Hubble flow does, however, make _c a function ofr. 5. The advanced solutions of the wave equation required to account for inertia in the Lorentz gauge can be avoided if one chooses by using the Coulomb gauge with its action-at-a-distance characteristic. Asserting the equivalent of the Coulomb gauge to get instantaneous inertial reaction forces, as Trederet al.[9] point out, suggests an interesting generalization of GRT.6. This procedure for going from a particle to a continuous media representation is not in general valid, since in all frames, except the rest frame, will involve elements of the stress tensor. Those contributions, however, are of orderv ² /c ² and are here ignored.7. One may find this result troublesome, for one may think thatø is only fixed up to an additive constant. While this is true in linear theories, as discussed below, it is not true in nonlinear theories. Let me also point out here the similarity of Eq. (A12) and the field equations obtained by Trederet al.[9, pp. 70-73] in a higher-derivative manifestly Machian Einstein-Cartan theory of gravitation where the same potential-like coupling of gravity and matter occurs.8. Equation (A13) only applies in the instantaneous rest frame of the test particle. In all other frames of reference one obtains a term involving the time derivative of the acceleration. Terms of this sort, of course, are not normally allowed in dynamics. They are the signature of self-forces and radiation reaction effects. But this should come as no surprise, for the effect arises from the gravitational self-energy interaction when inertial reaction forces are stimulated.     

Cosmological Constant and Stability of the Cosmological Models

The importance of cosmological constant for the cosmological models is given. The variations of the cosmological model for parameters λ and k were discussed respectively. Near λ = 0, the cosmological model is unstable with the change of λ, and near λ = β = 0, the cosmological model is unstable with the change of k. So when we consider the stable cosmological model, we must consider the nonzero cosmological constant.     

Black hole physics in globally hyperbolic space-times

The usual definition of a black hole is modified to make it applicable in a globally hyperbolic space-time. It is shown that in a closed globally hyperbolic universe the surface area of a black hole must eventually decrease. The implications of this breakdown of the black hole area theorem are discussed in the context of thermodynamics and cosmology. A modified definition of surface gravity is also given for non-stationary universes. The limitations of these concepts are illustrated by the explicit example of the Kerr-Vaidya metric.     

Quintessence and Dark Matter Created by Weyl–Dirac Geometry

A spatially closed universe undergoing at present accelerated expansion, having a non-vanishing cosmological constant, and filled with luminous- and dark matter is described in terms of the Integrable Weyl–Dirac theory. It is shown that, during the dust-dominated period, dark matter and the quintessence pressure, the latter giving rise to acceleration: both are created by the Dirac gauge function. The behavior of two models: a nearly flat one and a well closed are considered in appropriate gauges, and plausible scenarios are obtained. The outcome of the present paper, together with results of a previous work,⁽³¹⁾ provide a geometrically based, classical, singularity-free model of the universe, that has originated from a pure geometric Weyl–Dirac entity, passed a prematter period, the radiation-dominated era, and continues its development in the present dust period.     

Modified entropic gravity revisited

Inspired by Verlinde’s idea,some modified versions of entropic gravity have been suggested.Extending them in a unified formalism,herein we derive the generalized gravitational equations accordingly.From gravitational equations,the energy-momentum conservation law and cosmological equations are investigated.The covariant conservation law of energy-momentum tensor severely constrains viable modifications of entropic gravity.A discrepancy arises when two independent methods are applied to the homogeneous isotropic universe,posing a serious challenge to modified models of entropic gravity.     

A Solution to Einstein's Equations for the Mixmaster Universe in Complex General Relativity

Starting from Einstein's equations of the Classical General Relativity, new kinds of solutions for the Mixmaster model are explored. By dispensing with the extension to the complex variable field, which is usual in problems such as the Laplace equation or the harmonic oscillator, in a similar manner to that of Quantum Mechanics, the equations appear to have solutions that belong to the complex General Relativity. A first integral is performed by establishing a separation of the first derivatives. Then a second integral is obtained once the respective equations with separate variables are found and whose integrals provide a family of complex solutions. However, reality conditions do not seem to be easily imposed at this stage. Above all, it is significant that the classical Einstein's equations for the debatably integrable Mixmaster model present complex solutions.     

Effects on the Structure of the Universe of an Accelerating Expansion

Recent experimental results from supernovae Ia observations have been interpreted to show that the rate of expansion of the universe is increasing. Other recent experimental results find strong indications that the universe is flat. In this paper, I investigate some solutions of Einstein's field equations which go smoothly between Schwarzschild's relativistic gravitational solution near a mass concentration to the Friedmann-Lemaître expanding universe solution. In particular, the static, curved-space extension of the Lemaître-Schwarzschild solution in vacuum is given. Uniqueness conditions are discussed. One of these metrics preserves the cosmological equation. We find that when the rate of expansion of the universe is increasing, space is broken up into domains of attraction. Outside a domain of attraction, the expansion of the universe is strong enough to accelerate a test particle away from the domain boundary. I give a domain-size–mass relationship. This relationship may very well be important to our understanding of the large scale structure of the universe.     

Mysteries of R^ik=0： A novel paradigm in Einstein＇s theory of gravitation

Despite a century-long effort, a proper energy-stress tensor of the gravitational field, could not have been discovered. Furthermore, it has been discovered recently that the standard formulation of the energy-stress tensor of matter, suffers from various inconsistencies and paradoxes, concluding that the tensor is not consistent with the geometric formulation of gravitation [Astrophys. Space Sci., 2009, 321： 151; Astrophys. Space Sei., 2012, 340： 373]. This perhaps hints that a consistent theory of gravitation should not have any bearing on the energy-stress tensor. It is shown here that the so-called ＂vacuum＂ field equations Rik = 0 do not represent an empty spacetime, and the energy, momenta and angular momenta of the gravitational and the matter fields are revealed through the geometry, without including any formulation thereof in the field equations. Though, this novel discovery appears baffling and orthogonal to the usual understanding, is consistent with the observations at all scales, without requiring the Moreover, the resulting theory circumvents the besides explaining some unexplained puzzles. hypothetical dark matter, dark energy or inflation long-standing problems of the standard cosmology     

Primary Matter Creation in a Weyl–Dirac Cosmological Model

In the framework of an integrable Weyl–Dirac (W–D) theory a cosmological model is proposed. It describes a universe that began its expansion from a primary pre-Planckian geometric entity containing no matter. During the pre-Planckian period, from R ₀ =5.58×10 ^–36 cm to R_I=5.58×10 ^–34 cm, this embryonic universe has undergone a very rapid expansion and cosmic matter was created by geometry. At R_I the universe was already filled with matter having the Planckian density _P and being in the state of prematter (P=–), while the Weylian geometric elements were insignificant. This state is the Planckian egg that has served as the initial state of the singularity-free cosmological model ⁽¹⁾ considered in the framework of Einstein's general theory of relativity. The W–D character of the geometry and the cosmological constant are significant in the pre-Planckian period during the matter creation. In the dust-dominated period a relic of the W–D geometry causes a global dark matter effect. In between the pre-Planckian and dust period one has Einstein's framework and is negligible.     

Bianchi type I string cosmologies

By making use of Letelier’s form of energy—momentum tensor for a cloud of stringdust we present some classes of solutions of general relativistic field equations which describe cosmological string-dust models in Bianchi type I space-time. Some of the classes of models obey Takabayashi’s equation of state whereas a class of models exhibits inflation in the initial stage. Two of the classes presented here have Kasner’s space-time as past asymptote     

Radial Quantization in Rotating Space–Times

We examine the time discontinuity in rotating space–times for which the topology of time is S¹. A kinematic restriction is enforced that requires the discontinuity to be an integral number of the periodicity of time. Quantized radii emerge for which the associated tangential velocities are less than the speed of light. Using the de Broglie relationship, we show that quantum theory may determine the periodicity of time. A rotating Kerr–Newman black hole and a rigidly rotating disk of dust are also considered; we find that the quantized radii do not lie in the regions that possess CTCs.     

A Possible Modification of Einstein's Theory of General Relativity

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 GM/r, it obtains the same results about the four experimental tests of general relativity.     

Semiempirical Shell Model Masses with Magic Proton Number Z=126 for Translead Elements

A highly extrapolatable semiempirical shell model mass equation applicable to translead elements up to Z=126 is presented. The equation is applied to the recently discovered superheavy nuclei ²⁹³118 and ²⁸⁹114 and their decay products. This revised version was published online in July 2006 with corrections to the Cover Date.