Latent solitons, black strings, black branes, and equations of state in Kaluza-Klein models

In Kaluza-Klein models with an arbitrary number of toroidal internal spaces, we investigate soliton solutions which describe the gravitational field of a massive compact object. We single out the physically interesting solution corresponding to a point-like mass. For the general solution we obtain equations of state in the external and internal spaces. These equations demonstrate that the point-like mass soliton has dust-like equations of state in all spaces. We also obtain the PPN parameters, which give the possibility to obtain the formulas for perihelion shift, deflection of light and time delay of radar echoes. Additionally, the gravitational experiments lead to a strong restriction on the parameter of the model: $\tau = -(2.1\pm 2.3)\times 10^{-5}$. The point-like mass solution contradicts this restriction. The condition $\tau=0$ satisfies the experimental limitation and defines a new class of solutions which are indistinguishable from general relativity. We call such solutions latent solitons. Black strings and black branes belong to this class. Moreover, the condition of stability of the internal spaces singles out black strings/branes from the latent solitons and leads uniquely to the black string/brane equations of state $p_i=-\epsilon/2$, in the internal spaces and to the number of the external dimensions $d_0=3$. The investigation of multidimensional static spherically symmetric perfect fluid with dust-like equation of state in the external space confirms the above results.Comment: 8 pages, Revtex4, no figures, minor changes adde

Kaluza-Klein models: can we construct a viable example?

In Kaluza-Klein models, we investigate soliton solutions of Einstein equation. We obtain the formulas for perihelion shift, deflection of light, time delay of radar echoes and PPN parameters. We find that the solitonic parameter k should be very big: |k|\geq 2.3\times10^4. We define a soliton solution which corresponds to a point-like mass source. In this case the soliton parameter k=2, which is clearly contrary to this restriction. Similar problem with the observations takes place for static spherically symmetric perfect fluid with the dust-like equation of state in all dimensions. The common for both of these models is the same equations of state in our three dimensions and in the extra dimensions. All dimensions are treated at equal footing. To be in agreement with observations, it is necessary to break the symmetry between the external/our and internal spaces. It takes place for black strings which are particular examples of solitons with k\to \infty. For such k, black strings are in concordance with the observations. Moreover, we show that they are the only solitons which are at the same level of agreement with the observations as in general relativity. Black strings can be treated as perfect fluid with dust-like equation of state p_0=0 in the external/our space and very specific equation of state p_1=-(1/2)\epsilon in the internal space. The latter equation is due to negative tension in the extra dimension. We also demonstrate that dimension 3 for the external space is a special one. Only in this case we get the latter equation of state. We show that the black string equations of state satisfy the necessary condition of the internal space stabilization. Therefore, black strings are good candidates for a viable model of astrophysical objects (e.g., Sun) if we can provide a satisfactory explanation of negative tension for particles constituting these objects.Comment: 11 pages, Revtex4, no figures, appendix and references adde

ОСУЧАСНЕННЯ ТА МОДЕРНІЗАЦІЯ СИСТЕМИ ЕЛЕКТРОННИХ ПЛАТЕЖІВ НАЦІОНАЛЬНОГО БАНКУ УКРАЇНИ ЗА ЄВРОПЕЙСЬКИМ ДОСВІДОМ У КОНТЕКСТІ ГЛОБАЛІЗАЦІЙНИХ ПРОЦЕСІВ

Today for the System of Electronic Payments of the National Bank of Ukraine is actual modernization and updating according to the real needs of payment system participants in the current economic situation in Ukraine. For improvement forms of interbank payments important is a restructuring of the national payment system in accordance with international and EU standards. The article analyzes the functioning of the payment system TARGET2, discloses its advantages and principles of organization. The authors conducted a comparative analysis of payment systems TARGET2 and The System of Electronic Payments of the National Bank of Ukraine, as well as provided recommendations for improving the domestic payment system based on the experience of the European Union The NBU’s Electronic Payment System is quite modern and efficient, but the existence of a certain time in the payment process, insufficient level of regulatory and information support of the electronic payment system participants and its control lead to the possibility of opaque financial transactions in the system itself. The lack of organizational and financial mechanisms today is also a serious drawback in his work. In Ukraine, the technological level of the NBU system of calculations does not quite allow to use qualitatively most of the means of supporting intraday liquidity. This is a significant disadvantage of EPS compared to its foreign counterpart TARGET2. An analysis of the functioning of TARGET2 and SEP enabled us to examine in more detail the positives and negatives of both payment systems. A significant advantage of TARGET2 is its liquidity management system, which, under certain conditions, is an effective tool in the planning of settlement operations. This allows system members to prevent problems during the calculations and to solve them effectively. Optimization of liquidity management in the SEP is negligible. The National Bank of Ukraine, unlike the European Central Bank, does not provide full information on EPS, which indicates the closedness of the payment system and the NBU’s unwillingness to provide the most transparent settlement mechanism. Today, the TARGET2 settlement system is more modern and open compared to the NBU’s Electronic Payment System.На сьогодні для Системи електронних платежів Національного банку України актуальною є модернізація та осучаснення відповідно до реальних потреб учасників платіжної системи в умовах сучасної економічної ситуації в Україні. Для вдосконалення форм міжбанківських розрахунків важливою є перебудова національної платіжної системи відповідно до міжнародних стандартів і стандартів ЄС. Проведено аналіз функціонування платіжної системи ТАРГЕТ2, розкрито її переваги і принципи організації. Проведено порівняльний аналіз платіжних систем ТАРГЕТ2 та системи електронних платежів Національного банку, а також надано рекомендації щодо вдосконалення вітчизняної платіжної системи на основі досвіду Європейського Союзу. Система електронних платежів НБУ є досить сучасною та ефективною, але існування певного часу у проходженні платежу, недостатньо високий рівень нормативного та інформаційного забезпечення учасників системи електронних платежів та її контролю призводять до можливості непрозорих фінансових операцій у самій системі. В Україні технологічний рівень розрахункової системи НБУ не зовсім дозволяє якісно використовувати більшість із засобів підтримки внутрішньоденної ліквідності, що є значним недоліком СЕП у порівнянні з її зарубіжним аналогом — ТАРГЕТ2. Аналіз функціонування ТАРГЕТ2 та СЕП надав змогу більш детально розглянути позитивні і негативні моменти обох платіжних систем. Значною перевагою ТАРГЕТ2 є система управління ліквідністю, що за певних умов є дієвим інструментом при плануванні розрахункових операцій. Це дозволяє учасникам системи попереджувати виникнення проблем під час розрахунків та ефективно розв’язувати їх. Оптимізація управління ліквідністю у СЕП є незначною. Національний банк України, на відміну від Європейського центрального банку, надає інформацію стосовно СЕП не в повному обсязі, що свідчить про закритість платіжної системи та неготовність НБУ забезпечувати максимально прозорий механізм розрахунків. На сьогодні система розрахунків ТАРГЕТ2 є більш сучасною та відкритою у порівнянні із Cистемою електронних платежів НБУ

Problems with Time-Varying Extra Dimensions or "Cardassian Expansion" as Alternatives to Dark Energy

It has recently been proposed that the Universe might be accelerating as a consequence of extra dimensions with time varying size. We show that although these scenarios can lead to acceleration, they run into serious difficulty when taking into account limits on the time variation of the four dimensional Newton's constant. On the other hand, models of ``Cardassian'' expansion based on extra dimensions which have been constructed so far violate the weak energy condition for the bulk stress energy, for parameters that give an accelerating universe.Comment: 8 pages, minor changes. To appear in Physical Review

Multidimensional cosmological models: cosmological and astrophysical implications and constraints

We investigate four-dimensional effective theories which are obtained by dimensional reduction of multidimensional cosmological models with factorizable geometry and consider the interaction between conformal excitations of the internal space (geometrical moduli excitations) and Abelian gauge fields. It is assumed that the internal space background can be stabilized by minima of an effective potential. The conformal excitations over such a background have the form of massive scalar fields (gravitational excitons) propagating in the external spacetime. We discuss cosmological and astrophysical implications of the interaction between gravexcitons and four-dimensional photons as well as constraints arising on multidimensional models of the type considered in our paper. In particular, we show that due to the experimental bounds on the variation of the fine structure constant, gravexcitons should decay before nucleosynthesis starts. For a successful nucleosynthesis the masses of the decaying gravexcitons should be m>10^4 GeV. Furthermore, we discuss the possible contribution of gravexcitons to UHECR. It is shown that, at energies of about 10^{20}eV, the decay length of gravexcitons with masses m>10^4 GeV is very small, but that for m <10^2 GeV it becomes much larger than the Greisen-Zatsepin-Kuzmin cut-off distance. Finally, we investigate the possibility for gravexciton-photon oscillations in strong magnetic fields of astrophysical objects. The corresponding estimates indicate that even the high magnetic field strengths of magnetars are not sufficient for an efficient and copious production of gravexcitons.Comment: 16 pages, LaTeX2e, minor changes, improved references, to appear in PR

Anisotropic Inflation and the Origin of Four Large Dimensions

In the context of (4+d)-dimensional general relativity, we propose an inflationary scenario wherein 3 spatial dimensions grow large, while d extra dimensions remain small. Our model requires that a self-interacting d-form acquire a vacuum expectation value along the extra dimensions. This causes 3 spatial dimensions to inflate, whilst keeping the size of the extra dimensions nearly constant. We do not require an additional stabilization mechanism for the radion, as stable solutions exist for flat, and for negatively curved compact extra dimensions. From a four-dimensional perspective, the radion does not couple to the inflaton; and, the small amplitude of the CMB temperature anisotropies arises from an exponential suppression of fluctuations, due to the higher-dimensional origin of the inflaton. The mechanism triggering the end of inflation is responsible, both, for heating the universe, and for avoiding violations of the equivalence principle due to coupling between the radion and matter.Comment: 24 pages, 2 figures; uses RevTeX4. v2: Minor changes and added references. v3: Improved discussion of slow-rol

Hilbert space of wormholes

Wormhole boundary conditions for the Wheeler--DeWitt equation can be derived from the path integral formulation. It is proposed that the wormhole wave function must be square integrable in the maximal analytic extension of minisuperspace. Quantum wormholes can be invested with a Hilbert space structure, the inner product being naturally induced by the minisuperspace metric, in which the Wheeler--DeWitt operator is essentially self--adjoint. This provides us with a kind of probabilistic interpretation. In particular, giant wormholes will give extremely small contributions to any wormhole state. We also study the whole spectrum of the Wheeler--DeWitt operator and its role in the calculation of Green's functions and effective low energy interactions.Comment: 23 pages, 2 figures available upon request, REVTE

Stabilization of internal spaces in multidimensional cosmology

Effective 4-dimensional theories are investigated which were obtained under dimensional reduction of multidimensional cosmological models with a minimal coupled scalar field as matter source. Conditions for the internal space stabilization are considered and the possibility for inflation in the external space is discussed. The electroweak as well as the Planck fundamental scale approaches are investigated and compared with each other. It is shown that there exists a rescaling for the effective cosmological constant as well as for gravitational exciton masses in the different approaches.Comment: 12 pages, LaTeX2e, to appear in Phys.Rev.D, note adde

Solutions to the Wheeler-Dewitt Equation Inspired by the String Effective Action

The Wheeler-DeWitt equation is derived from the bosonic sector of the heterotic string effective action assuming a toroidal compactification. The spatially closed, higher dimensional Friedmann-Robertson-Walker (FRW) cosmology is investigated and a suitable change of variables rewrites the equation in a canonical form. Real- and imaginary-phase exact solutions are found and a method of successive approximations is employed to find more general power series solutions. The quantum cosmology of the Bianchi IX universe is also investigated and a class of exact solutions is found.Comment: 21 pages of plain LaTeX, Fermilab-Pub-93/100-

Fresnel coefficients as hyperbolic rotations

We describe the action of a plane interface between two semi-infinite media in terms of a transfer matrix. We find a remarkably simple factorization of this matrix, which enables us to express the Fresnel coefficients as a hyperbolic rotation.Comment: 6 pages, 3 figure