Finite temperature Casimir effect in spacetime with extra compactified dimensions

In this Letter, we derive the explicit exact formulas for the finite temperature Casimir force acting on a pair of parallel plates in the presence of extra compactified dimensions within the framework of Kaluza–Klein theory. Using the piston analysis, we show that at any temperature, the Casimir force due to massless scalar field with Dirichlet boundary conditions on the plates is always attractive and the effect of extra dimensions becomes stronger when the size or number of the extra dimensions increases. These properties are not affected by the explicit geometry and topology of the Kaluza–Klein space.     

The Casimir force on a piston in the spacetime with extra compactified dimensions

A Casimir piston for massless scalar fields obeying Dirichlet boundary conditions in high-dimensional spacetimes within the frame of Kaluza–Klein theory is analyzed. We derive and calculate the exact expression for the Casimir force on the piston. We also compute the Casimir force in the limit that one outer plate is moved to the extremely distant place to show that the reduced force is associated with the properties of additional spatial dimensions. The more dimensionality the spacetime has, the stronger the extra-dimension influence is. The Casimir force for the piston in the model including a third plate under the background with extra compactified dimensions always keeps attractive. Further we find that when the limit is taken the Casimir force between one plate and the piston will change to be the same form as the corresponding force for the standard system consisting of two parallel plates in the four-dimensional spacetimes if the ratio of the plate-piston distance and extra dimensions size is large enough.     

二重非交换时空与二重复对称引力理论

通过引入二重复对称度规张量，建立了一种二重复对称引力理论. 从一个二重实的作用量出发，导出了静态球对称二重复度规的具体表达式. 该理论扩展了Moffat结果，不仅自然地得到了双曲复对称引力理 论，而且把著名的Schwarzschild解作为特殊情况包含在其中，并且在线性化的弱场近似下自动摆脱了Moffat理论中存在的负 能鬼态问题. 进一步，通过将二重复坐标推广到满足二重非对易关系以及将Moyal星积二重 化，由此构造出二重非交换复对称引力场作用量. 关键词： 非交换几何 复对称度规 非对易坐标 引力场作用量     

Spherically symmetric vacuum solutions of modified gravity theory in higher dimensions

In this paper we investigate spherically symmetric vacuum solutions of f(R) gravity in a higher-dimensional spacetime. With this objective we construct a system of non-linear differential equations whose solutions depend on the explicit form assumed for the function F(R)=\fracdf(R)dRF(R)=\frac{df(R)}{dR} . We explicit show that for specific classes of this function exact solutions from the field equations are obtained; also we find approximated results for the metric tensor for more general cases admitting F(R) close to the unity.     

The asymptotic behavior of Casimir force in the presence of compactified universal extra dimensions

The Casimir effect for parallel plates in the presence of compactified universal extra dimensions within the frame of Kaluza–Klein theory is analyzed. Having regularized and discussed the expressions of Casimir force in the limit, we show that the nature of Casimir force is repulsive if the distance between the plates is large enough and the higher-dimensional spacetime is, the greater the value of repulsive Casimir force between plates is. The repulsive nature of the force is not consistent with the experimental phenomena.     

Fermionic vacuum polarization in compactified cosmic string spacetime

We investigate the fermionic condensate and the vacuum expectation value (VEV) of the energy-momentum tensor for a charged massive fermionic field in the geometry of a cosmic string compactified along its axis. In addition, we assume the presence of two types of magnetic fluxes: a flux running along the cosmic string and another enclosed by the compact dimension. These fluxes give rise to Aharanov–Bohm-like effects on the VEVs. The VEVs are decomposed into two parts corresponding to the geometry of a straight cosmic string without compactification plus a topological part induced by the compactification of the string axis. Both contributions are even periodic functions of the magnetic fluxes with period equal to the flux quantum. The vacuum energy density is equal to the radial stress for the parts corresponding to the straight cosmic string and the topological one. Moreover, the axial stress is equal to the energy density for the parts corresponding to the straight cosmic string; however, for massive fermionic fields this does not occur for the topological contributions. With respect to the dependence on the magnetic fluxes, both the fermionic condensate and the vacuum energy density, can be either positive or negative. Moreover, for points near the string, the main contribution to the VEVs comes from the straight cosmic string part, whereas at large distances the topological ones dominate. In addition to the local characteristics of the vacuum state, we also evaluate the part in the topological Casimir energy induced by the string.     

Hydrogen atom in space with a compactified extra dimension and potential defined by Gauss’ law

We investigate the consequences of one extra spatial dimension for the stability and energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss’ law, i.e.    proportional to 1/|x|²$1/{\left|x\right|}^2$. The additional spatial dimension is considered to be either infinite or curled-up in a circle of radius R$R$. In both cases, the energy spectrum is bounded from below for charges smaller than the same critical value and unbounded from below otherwise. As a consequence of compactification, negative energy eigenstates appear: if R$R$ is smaller than a quarter of the Bohr radius, the corresponding Hamiltonian possesses an infinite number of bound states with minimal energy extending at least to the ground state of the hydrogen atom.     

Spherically symmetric solutions of Einstein-Maxwell theory with a Gauss-Bonnet term

The low energy expansion of supersymmetric string theory suggests that the leading correction to the Einstein action is given by the Gauss-Bonnet invariant. A generalisation of Birkhoff's theorem in the case of Einstein-Maxwell theory modified by a Gauss-Bonnet term is proved. The only spherically symmetric solutions of the theory are shown to be generalisations of the Reissner-Nordstrom and Robinson-Bertotti solutions. The “Reissner-Nordstrom” solutions have asymptotically flat and asymptotically anti-de Sitter branches, however, the latter are unstable.     

Physics with large extra dimensions

The recent understanding of string theory opens the possibility that the string scale can be as low as a few TeV. The apparent weakness of gravitational interactions can then be accounted by the existence of large internal dimensions, in the sub-millimeter region. Furthermore, our world must be confined to live on a brane transverse to these large dimensions, with which it interacts only gravitationally. In my lecture, I describe briefly this scenario which gives a new theoretical framework for solving the gauge hierarchy problem and the unification of all interactions. I also discuss a minimal embedding of the standard model, gauge coupling unification and proton stability. On leave from: Centre de Physique Théorique, Ecole Polytechnique, 91128 Palaiseau, Cedex, France.     

Anisotropic cosmology with extra dimensions

We present an exact solution of the n-dimensional (n > 4) vacuum Einstein field equations with a Bianchi type I metric. The solution may be interpreted as a four-dimensional anisotropic cosmological model. The extra dimensions are related to the energy density and pressures in the model. The physics of the results is discussed at the end of the paper.     

Spherically symmetric solutions in Macroscopic Gravity

Schwarzschild’s solution to the Einstein Field Equations was one of the first and most important solutions that lead to the understanding and important experimental tests of Einstein’s theory of General Relativity. However, Schwarzschild’s solution is essentially based on an ideal theory of gravitation, where all inhomogeneities are ignored. Therefore, any generalization of the Schwarzschild solution should take into account the effects of small perturbations that may be present in the gravitational field. The theory of Macroscopic Gravity characterizes the effects of the inhomogeneities through a non-perturbative and covariant averaging procedure. With similar assumptions on the geometry and matter content, a solution to the averaged field equations as dictated by Macroscopic Gravity are derived. The resulting solution provides a possible explanation for the flattening of galactic rotation curves, illustrating that Dark Matter is not real but may only be the result of averaging inhomogeneities in a spherically symmetric background.     

Spherically symmetric collapse in quantum gravity

The problem of classical singularities is revised on the basis of the quantum-gravity effective equations. We find a simple rule for establishing the Birkhoff theorem in spherically symmetric problems. All exact solutions of the lagrangian with C²_αβγσ are obtained. Spherically symmetric collapse of the thin null shell of mass M is considered in the framework of a local theory describing vacuum polarization effects. The boundary-value problem is set and the asymptotic solution is obtained. It is found that the shell collapses to r = 0 without the rise of a singularity, and begins expanding. The global behaviour of the solution is obtained for small M. For large M it is conjectured that the event horizon does not form, and the apparent horizon is closed. An object forms, possessing the observable properties of a black hole, but living a finite time.     

Spherically symmetric nonstatic perfect fluid solutions with shear

In this paper we investigate solutions of Einstein's field equations for the spherically symmetric perfect fluid case with shear and with vanishing acceleration. If these solutions have shear, they must necessarily be nonstatic. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three known classes of solutions. The fourth class of solutions with shear leads to a generalized Emden-Fowler equation. This equation is discussed by means of Lie's method of point symmetries.     

Spherically symmetric solutions with heat flow in general relativity

Some new solutions of shear-free imperfect fluid spheres with heat flux in the radial direction are obtained. They have isotropic pressure and could be the generalizations of earlier solutions of Nariai and of Banerjee and Banerji for perfect fluid without dissipation.     

Spherically symmetric solutions in five-dimensional general relativity

The most general time-independent spherically symmetric (in the usual three space dimensions) solution to the five-dimensional vacuum Einstein equations is found, subject to the existence of a Killing vector in the fifth direction. The significance of these solutions is discussed within the context of a previously proposed extension of the Kaluza-Klein model in which the universe, although (4+1)-dimensional, has evolved over cosmic times into an effectively (3+l)-dimensional one.     

Quantum noncommutative gravity in two dimensions

We study quantisation of noncommutative gravity theories in two dimensions (with noncommutativity defined by the Moyal star product). We show that in the case of noncommutative Jackiw–Teitelboim gravity the path integral over gravitational degrees of freedom can be performed exactly even in the presence of a matter field. In the matter sector, we study possible choices of the operators describing quantum fluctuations and define their basic properties (e.g., the Lichnerowicz formula). Then we evaluate two leading terms in the heat kernel expansion, calculate the conformal anomaly and the Polyakov action (as an expansion in the conformal field).     

Gauged supergravities in various spacetime dimensions

In this review article we study the gaugings of extended supergravity theories in various space‐time dimensions. These theories describe the low‐energy limit of non‐trivial string compactifications. For each theory under consideration we review all possible gaugings that are compatible with supersymmetry. They are parameterized by the so‐called embedding tensor which is a group theoretical object that has to satisfy certain representation constraints. This embedding tensor determines all couplings in the gauged theory that are necessary to preserve gauge invariance and supersymmetry. The concept of the embedding tensor and the general structure of the gauged supergravities are explained in detail. The methods are then applied to the half‐maximal (N = 4) supergravities in d = 4 and d = 5 and to the maximal supergravities in d = 2 and d = 7. Examples of particular gaugings are given. Whenever possible, the higher‐dimensional origin of these theories is identified and it is shown how the compactification parameters like fluxes and torsion are contained in the embedding tensor.     

Spherically symmetric solutions of Einstein-Maxwell theory with null fluid

Solutions of the Einstein-Maxwell equations with the addition of terms representing charged null fluid emitting from a spherically symmetric body are found. One type of solution is a simple extension of that found by Bonnor and Vaidya while the other represents a null electromagnetic field with null electric current.