Inflationary Brans-Dicke universe andG

In a recent paper, Mathiazhagan and Johri reduced the field equations for an isotropic, homogeneous, and almost flat universe with a constant vacuum-energy density by Brans-Dicke theory to a pair of coupled differential equations. They also obtained a particular solution of these equations. Further, they used this particular solution of the equations to estimate the value of the gravitational constant. Here we obtain the complete set of solutions of the above-mentioned coupled differential equations and improved the estimate of Mathiazhagan and Johri of the gravitational constant.     

A family of Jordan-Brans-Dicke Kerr solutions

A family of solutions of the vacuum Jordan-Brans-Dicke or scalar-tensor gravitational field equations is given. This family reduces to the Kerr rotating solution of the vacuum Einstein equations when the scalar field is constant. The family does not have spherical symmetry when the rotation is zero and the scalar field is not constant. The method used to generate the new solutions can also be used to obtain vacuum Jordan-Brans-Dicke solutions from any given vacuum stationary, axisymmetric solution.     

Reissner--Nordström-de--Sitter-type Solution by a Gauge Theory of Gravity

We use the theory based on a gravitational gauge group （Wu＇s model） to obtain a spherical symmetric solution of the field equations for the gravitational potential on a Minkowski spacetime. The gauge group, the gauge covariant derivative, the strength tensor of the gauge feld, the gauge invariant Lagrangean with the cosmological constant, the field equations of the gauge potentiaIs with a gravitational energy-momentum tensor as well as with a tensor of the field of a point like source are determined. Finally, a Reissner-Nordstrom-de Sitter-type metric on the gauge group space is obtained.     

洛伦兹破缺的电动力学模型

由于宇宙常数的存在, 时空为渐近de Sitter(dS)的时空. 文中将静态dS度规作为时空的近似刻画, 研究了在此度规下的一个洛伦兹破缺的电动力学模型. 通过张量的标架场分解的方法, 得到了静态dS时空中的电磁场方程. 另外, 分别研究了静态dS时空中点电荷的静电场和圈电流的静磁场, 并且同时讨论了在此模型下的洛伦兹破缺效应.     

Sinh-Gordon Matter Field and a Solvable Model in Two-Dimensional Gravity

The two-dimensional gravity model with a coupling constant k = 4 and a vanishing cosmological constant coupled to a sinh-Gordon matter field is investigated. We find that the classical equations of motion are exactly solvable, and analytically obtain the static solutions of induced metric and scalar curvature. These solutions have some new features and may be used to describe the naked singularities at the horizons.     

Novel Rotating Hairy Black Hole in (2+1)-Dimensions and Shear Viscosity to Entropy Ratio

The novel rotating hairy black hole metric in (2 + 1) dimensions, which is an exact solution to the field equations of the Einstein-scalar AdS theory with a non-minimal coupling, considered in this paper and some hydrodynamics quantities such as diffusion constant and shear viscosity investigated. By using thermodynamics quantities such as temperature and entropy we can use diffusion constant to obtain shear viscosity and then calculate shear viscosity to entropy ratio.     

Stress-energy connection and cosmological constant problem

We study gravitational properties of vacuum energy by erecting a geometry on the stress-energy tensor of vacuum, matter and radiation. Postulating that the gravitational effects of matter and radiation can be formulated by an appropriate modification of the spacetime connection, we obtain varied geometrodynamical equations which properly comprise the usual gravitational field equations with, however, Planck-suppressed, non-local, higher-dimensional additional terms. The prime novelty brought about by the formalism is that, the vacuum energy does act not as the cosmological constant but as the source of the gravitational constant. The formalism thus deafens the cosmological constant problem by channeling vacuum energy to gravitational constant. Nevertheless, quantum gravitational effects, if any, restore the problem via the graviton and graviton-matter loops, and the mechanism proposed here falls short of taming such contributions to cosmological constant.     

Two Charged Particles in the Plane Under a Constant Perpendicular Magnetic Field

We show that a system with two particles of equal masses and opposite electric charge on a plane subject to a constant magnetic field perpendicular to this plane is a completely integrable system. In the classical case, the separation of variables can be performed in oblate coordinates. In the quantum case, we obtain two independent Hill equations of fourth order. Some approximations lead to Mathieu equations, for which the solutions are well known.     

Electrostatic and magnetostatic solutions in a Lorentz-violating electrodynamics model

We propose an effective Lorentz-violating electrodynamics model via the static de Sitter metric, which is deviated from the Minkowski metric by a minuscule amount depending on the cosmological constant. We obtain the electromagnetic field equations via the vierbein decomposition of the tensors. In addition, as an application of the electromagnetic field equations obtained, we derive the solutions of the electrostatic field and the magnetostatic field due to a point charge and a circle current, respectively, and discuss the implication of the effect of Lorentz violation in our electromagnetic theory.PACS 04.20.Cv; 04.40.-b; 98.80.Jk; 11.30.Cp     

Non-perturbative renormalization group calculation of the scalar self-energy

We present the first numerical application of a method that we have recently proposed to solve the Non Perturbative Renormalization Group equations and obtain the n-point functions for arbitrary external momenta. This method leads to flow equations for the n-point functions which are also differential equations with respect to a constant background field. This makes them, a priori, difficult to solve. However, we demonstrate in this paper that, within a simple approximation which turns out to be quite accurate, the solution of these flow equations is not more complicated than that of the flow equations obtained in the derivative expansion. Thus, with a numerical effort comparable to that involved in the derivative expansion, we can get the full momentum dependence of the n-point functions. The method is applied, in its leading order, to the calculation of the self-energy in a 3-dimensional scalar field theory, at criticality. Accurate results are obtained over the entire range of momenta.     

Holographic forced fluid dynamics in non-relativistic limit

We study the thermodynamics and non-relativistic hydrodynamics of the holographic fluid on a finite cutoff surface in the Gauss–Bonnet gravity. It is shown that the isentropic flow of the fluid is equivalent to a radial component of gravitational field equations. We use the non-relativistic fluid expansion method to study the Einstein–Maxwell-dilaton system with a negative cosmological constant, and obtain the holographic incompressible forced Navier–Stokes equations of the dual fluid at AdS boundary and at a finite cutoff surface, respectively. The concrete forms of external forces are given.     

Large numbers hypothesis. IV. The cosmological constant and quantum physics

In standard physics quantum field theory is based on a flat vacuum space-time. This quantum field theory predicts a nonzero cosmological constant. Hence the gravitational field equations do not admit a flat vacuum space-time. This dilemma is resolved using the units covariant gravitational field equations. This paper shows that the field equations admit a flat vacuum space-time with nonzero cosmological constant if and only if the canonical LNH is valid. This allows an interpretation of the LNH phenomena in terms of a time-dependent vacuum state. If this is correct then the cosmological constant must be positive.     

The dynamical evolution of 3-space in a higher dimensional steady state universe

We investigate a class of cosmological solutions of Einstein’s field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject to two constraints that (i) the total volume scale factor of the universe is constant and (ii) the effective energy density is constant. We obtain various interesting new dynamics for the external space that yield a time varying deceleration parameter including oscillating cases when the flat/curved external and curved/flat internal spaces are considered. We also comment on how the universe would be conceived by an observer in four dimensions who is unaware of the extra dimensions.     

Discretizing constant curvature surfaces via loop group factorizations: The discrete sine- and sinh-Gordon equations

The sine- and sinh-Gordon equations are the harmonic map equations for maps of the (Lorentz) plane into the 2-sphere. Geometrically they correspond to the integrability equations for surfaces of constant Gauss and constant mean curvature. There is a well-known dressing action of a loop group on the space of harmonic maps. By discretizing the vacuum solutions we obtain via the dressing action completely integrable discretizations (in both variables) of the sine- and sinh-Gordon equations. For the sine-Gordon equation we get Hirota's discretization. Since we work in a geometric context we also obtain discrete models for harmonic maps into the 2-sphere and discrete models of constant Gauss and mean curvature surfaces.     

Symmetric Variations of the Metric and Extrema of the Action for Pure Gravity

Symmetries of generalized gravitational actions, yielding field equations which typically involve at most second-order derivatives of the metric, are considered. The field equations for several different higher-derivative theories in the first-order formalism are derived, and variations of a generic set of higher-order curvature terms appearing in string effective actions are studied. It is shown that there often exists a particular set of solutions to the field equations of pure gravity theories, consisting of different combinations of curvature tensors, which satisfies the vacuum equations with cosmological constant. Implications of generalized symmetries of the field equations derived from the superstring effective action for the cosmological constant problem are discussed.     

Magnetically charged regular black hole in a model of nonlinear electrodynamics

We obtain a magnetically charged regular black hole in general relativity. The source to the Einstein field equations is nonlinear electrodynamic field in a physically reasonable model of nonlinear electrodynamics (NED). “Physically” here means the NED model is constructed on the basis of three conditions: the Maxwell asymptotic in the weak electromagnetic field limit; the presence of vacuum birefringence phenomenon; and satisfying the weak energy condition (WEC). In addition, we analyze the thermodynamic properties of the regular black hole in two ways. According to the usual black hole thermodynamics, we calculate the heat capacity at constant charge, from which we know the smaller black hole is more stable. We also employ the horizon thermodynamics to discuss the thermodynamic quantities, especially the heat capacity at constant pressure.     

Field Equations due to a Constant Modification in General Relativity

In this article, by adding a constant to Einstein-Hilbert action, we derive field equations for a non-vacuum space. Also we derive a general solution for these field equations, considering a de Sitter like initial geometric constraint. It is shown that how this additional constant can affect usual gravitational field equations, which are derived from general relativity.     

Rigorous construction of planar diagram field theories in four dimensional Euclidean space

Asymptotically free quantum field theories with planar Feynman diagrams [such as SU(∞) gauge theory] are considered in 4 dimensional Euclidean space. It is shown that if all particles involved have non-vanishing masses and if the coupling constant(s) γ (org ²) are small enough (λ≦λ^crit), then an absolutely convergent procedure exists to obtain Green functions that uniquely solve the Dyson-Schwinger equations.     

Abelian Higgs model with a Chern-Simons term in 3-dimensional gravitation

We consider the Abelian Higgs model with a Chern-Simons term coupled to the Einstein theory of gravitation in 3-dimensional space-time. We seek a finite solution, regular everywhere, having a stationary, cylindrically symmetric metric. We analyze these field equations and we suggest that such a solution exists. We find that the asymptotic metric of this solution corresponds to that which describes gravitationally a massive particle with spin. We obtain explicitly the expression of the spin. We give only the expression of the mass in the first order with respect to the gravitational coupling constant.