arXiv subjects

Maxim Eingorn

Publications and source records attributed to Maxim Eingorn.

At least 55 records · Page 3Linked to original sources

arXiv2014

Remarks on mechanical approach to observable Universe

We consider the Universe deep inside the cell of uniformity. At these scales, the Universe is filled with inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies), which perturb the background Friedmann model. Here, the mechanical approach (Eingorn & Zhuk, 2012) is the most appropriate to describe the dynamics of the inhomogeneities which is defined, on the one hand, by gravitational potentials of inhomogeneities and, on the other hand, by the cosmological expansion of the Universe. In this paper, we present additional arguments in favor of this approach. First, we estimate the size of the cell of uniformity. With the help of the standard methods of statistical physics and for the galaxies of the type of the Milky Way and Andromeda, we get that it is of the order of 190 Mpc which is rather close to observations. Then, we show that the nonrelativistic approximation (with respect to the peculiar velocities) is valid for $z \lesssim 10$, i.e. approximately for 13 billion years from the present moment. We consider scalar perturbations and, within the $Λ$CDM model, justify the main equations. Moreover, we demonstrate that radiation can be naturally incorporated into our scheme. This emphasizes the viability of our approach. This approach gives a possibility to analyze different cosmological models and compare them with the observable Universe. For example, we indicate some problematic aspects of the spatially flat models. Such models require a rather specific distribution of the inhomogeneities to get a finite potential at any points outside gravitating masses. We also criticize the application of the Schwarzschild-de Sitter solution to the description of the motion of test bodies on the cosmological background.

astro-ph.CO↗

arXiv2014

Many-body problem in Kaluza-Klein models with toroidal compactification

In this paper, we consider a system of gravitating bodies in Kaluza-Klein models with toroidal compactification of extra dimensions. To simulate the astrophysical objects (e.g., our Sun and pulsars) with energy density much greater than pressure, we suppose that these bodies are pressureless in the external/our space. At the same time, they may have nonzero parameters ω_{(\barα-3)} \, (\barα=4,\ldots,D) of the equations of state in the extra dimensions. We construct the Lagrange function of this many-body system for any value of Σ=\sum_{\barα} ω_{(\barα-3)}. Moreover, the gravitational tests (PPN parameters, perihelion and periastron advances) require negligible deviation from the latent soliton value Σ=-(D-3)/2. However, the presence of pressure/tension in the internal space results necessarily in the smearing of the gravitating masses over the internal space and in the absence of the KK modes. This looks very unnatural from the point of view of quantum physics.

gr-qc↗

arXiv2014

Kaluza-Klein multidimensional models with Ricci-flat internal spaces: the absence of the KK particles

In this paper we consider a multidimensional Kaluza-Klein (KK) model with a Ricci-flat internal space, e.g., a Calabi-Yau manifold. We perturb this background metrics by a system of gravitating masses, e.g., astrophysical objects such as our Sun. We suppose that these masses are pressureless in the external space but they have relativistic pressure in the internal space. We show that metric perturbations do not depend on coordinates of the internal space and gravitating masses should be uniformly smeared over the internal space. This means, first, that KK modes corresponding to the metric fluctuations are absent and, second, particles should be only in the ground quantum state with respect to the internal space. In our opinion, these results look very unnatural. According to statistical physics, any nonzero temperature should result in fluctuations, i.e. in KK modes. We also get formulae for the metric correction terms which enable to calculate the gravitational tests: the deflection of light, the time-delay of the radar echoes and the perihelion advance.

gr-qc↗

arXiv2013

Dark matter and dark energy from quark bag model

We calculate the present expansion of our Universe endowed with relict colored objects - quarks and gluons - that survived hadronization either as isolated islands of quark-gluon "nuggets", or spread uniformly in the Universe. In the first scenario, the QNs can play the role of dark matter. In the second scenario, we demonstrate that uniform colored objects can play the role of dark energy providing the late-time accelerating expansion of the Universe.

astro-ph.CO↗

arXiv2013

Many-body problem in Kaluza-Klein models: theory and observational consequences

We consider a system of gravitating bodies in Kaluza-Klein models with toroidal compactification of extra dimensions. To simulate the astrophysical objects (e.g., our Sun and pulsars) with the energy density much greater than the pressure, we suppose that these bodies are pressureless in the external/our space. At the same time, they may have nonzero parameters ω_{(\barα-3)} \, (\barα=4,...,D) of the equations of state in the extra dimensions. We construct the Lagrange function of this many-body system for any value of Σ=\sum_{\barα} ω_{(\barα-3)}. Moreover, the gravitational tests (PPN parameters, perihelion/periastron advance) require negligible deviation from the latent soliton value Σ=-(D-3)/2. However, the presence of pressure/tension in the internal space results necessarily in the smearing of the gravitating masses over the internal space and in the absence of the KK modes. This looks very unnatural from the point of quantum physics.

gr-qc↗

arXiv2013

Stable sound wave generation in weakly ionized air medium

We consider the generation of sound waves in the air medium between electrodes at the voltages near electrical breakdown in the presence of the time dependent constituent of the electric field. Within the standard multicomponent hydrodynamic model of the weakly ionized gas it is shown that the generation of sound is possible due to instantaneous character of the ionization equilibrium. The influence of the electronegative ions on the sound intensity is also discussed.

physics.plasm-ph↗

arXiv2013

Kaluza-Klein models with spherical compactification: observational constraints and possible examples

We consider Kaluza-Klein models with background matter in the form of a multicomponent perfect fluid. This matter provides spherical compactification of the internal space with an arbitrary number of dimensions. The gravitating source has the dust-like equation of state in the external/our space and an arbitrary equation of state (with the parameter $Ω$) in the internal space. In the single-component case, tension ($Ω=-1/2$) is the necessary condition to satisfy both the gravitational tests in the solar system and the thermodynamical observations. In the multicomponent case, we propose two models satisfying both of these observations. One of them also requires tension $Ω=-1/2$, but the second one is of special interest because is free of tension, i.e. $Ω=0$. To get this result, we need to impose certain conditions.

gr-qc↗

arXiv2013

Dynamics of astrophysical objects against the cosmological background

In this paper we consider dynamical behavior of astrophysical objects (galaxies and dwarf galaxies) taking into account both gravitational attraction between them and cosmological expansion of the Universe. First, we obtain the general system of equations and apply them to some abstract systems of galaxies. Then we investigate the collision between the Milky Way and Andromeda in future. We distinguish two models. For the first one, we do not take into account the influence of Intra-Group Matter (IGrM). In this case we demonstrate that for currently known parameters of this system the collision is hardly plausible because of the angular momentum. These galaxies will approach the minimum distance of about 290 Kpc in 4.44 Gyr from present and then begin to run away irreversibly from each other. For the second model, we take into account dynamical friction due to IGrM. We find a characteristic value of the IGrM particle velocity dispersion $\tildeσ=2.306$. For $\tildeσ\leq2.306$ the merger will take place, but for the bigger values of $\tildeσ$ the merger can be problematic. If the temperature of the IGrM particles is $10^5$ K, this characteristic value of $\tildeσ$ corresponds to the IGrM particle mass 17 MeV. Therefore, for the IGrM particles with masses less than 17 MeV the merger becomes problematic. We also define the region in the vicinity of our Local Group where the formation of Hubble flows starts. For such processes the zero-acceleration surface (where gravitational attraction is balanced by cosmological accelerated expansion) plays the crucial role. We show that such surface is absent for the Local Group. Instead, we find two points and one circle with zero acceleration. Nevertheless, there is a nearly closed area around the MW and M31 where the absolute value of the acceleration is approximately equal to zero. Hubble flows are formed outside of this area.

astro-ph.CO↗

arXiv2012

Significance of tension for gravitating masses in Kaluza-Klein models

In this letter, we consider the six-dimensional Kaluza-Klein models with spherical compactification of the internal space. Here, we investigate the case of bare gravitating compact objects with the dustlike equation of state $\hat p_0=0$ in the external (our) space and an arbitrary equation of state $\hat p_1=Ω\hat\varepsilon$ in the internal space, where $\hat \varepsilon$ is the energy density of the source. This gravitating mass is spherically symmetric in the external space and uniformly smeared over the internal space. In the weak field approximation, the conformal variations of the internal space volume generate the admixture of the Yukawa potential to the usual Newton's gravitational potential. For sufficiently large Yukawa masses, such admixture is negligible and the metric coefficients of the external spacetime coincide with the corresponding expressions of General Relativity. Then, these models satisfy the classical gravitational tests. However, we show that gravitating masses acquire effective relativistic pressure in the external space. Such pressure contradicts the observations of compact astrophysical objects (e.g., the Sun). The equality $Ω=-1/2$ (i.e. tension) is the only possibility to preserve the dustlike equation of state in the external space. Therefore, in spite of agreement with the gravitational experiments for an arbitrary value of $Ω$, tension ($Ω=-1/2$) plays a crucial role for the considered models.

gr-qc↗

arXiv2012

Hubble flows and gravitational potentials in observable Universe

In this paper, we consider the Universe deep inside of the cell of uniformity. At these scales, the Universe is filled with inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies), which disturb the background Friedmann model. We propose mathematical models with conformally flat, hyperbolic and spherical spaces. For these models, we obtain the gravitational potential for an arbitrary number of randomly distributed inhomogeneities. In the cases of flat and hyperbolic spaces, the potential is finite at any point, including spatial infinity, and valid for an arbitrary number of gravitating sources. For both of these models, we investigate the motion of test masses (e.g., dwarf galaxies) in the vicinity of one of the inhomogeneities. We show that there is a distance from the inhomogeneity, at which the cosmological expansion prevails over the gravitational attraction and where test masses form the Hubble flow. For our group of galaxies, it happens at a few Mpc and the radius of the zero-acceleration sphere is of the order of 1 Mpc, which is very close to observations. Outside of this sphere, the dragging effect of the gravitational attraction goes very fast to zero.

astro-ph.CO↗

arXiv2012

Observational constraints on Kaluza-Klein models with $d$-dimensional spherical compactification

We investigate Kaluza-Klein models in the case of spherical compactification of the internal space with an arbitrary number of dimensions. The gravitating source has the dust-like equation of state in the external/our space and an arbitrary equation of state (with the parameter $Ω$) in the internal space. We get the perturbed (up to $O(1/c^2)$) metric coefficients. For the external space, these coefficients consist of two parts: the standard general relativity expressions plus the admixture of the Yukawa interaction. This admixture takes place only for some certain condition which is equivalent to the condition for the internal space stabilization. We demonstrate that the mass of the Yukawa interaction is defined by the mass of the gravexciton/radion. In the Solar system, the Yukawa mass is big enough for dropping the admixture of this interaction and getting good agreement with the gravitational tests for any value of $Ω$. However, the gravitating body acquires the effective relativistic pressure in the external space which vanishes only in the case of tension $Ω=-1/2$ in the internal space.

gr-qc↗

arXiv2012

Remarks on gravitational interaction in Kaluza-Klein models

In these remarks, we clarify the problematic aspects of gravitational interaction in a weak-field limit of Kaluza-Klein models. We explain why some models meet the classical gravitational tests, while others do not. We show that variation of the total volume of the internal spaces generates the fifth force. This is the main reason of the problem. It happens for all considered models (linear with respect to the scalar curvature and nonlinear $f(R)$, with toroidal and spherical compactifications). We explicitly single out the contribution of the fifth force to nonrelativistic gravitational potentials. In the case of models with toroidal compactification, we demonstrate how tension (with and without effects of nonlinearity) of the gravitating source can fix the total volume of the internal space, resulting in the vanishing fifth force and consequently in agreement with the observations. It takes place for latent solitons, black strings and black branes. We also demonstrate a particular example where non-vanishing variations of the internal space volume do not contradict the gravitational experiments. In the case of spherical compactification, the fifth force is replaced by the Yukawa interaction for models with the stabilized internal space. For large Yukawa masses, the effect of this interaction is negligibly small, and considered models satisfy the gravitational tests at the same level of accuracy as general relativity.

gr-qc↗

arXiv2012

Exact and asymptotic black branes with spherical compactification

In the six-dimensional Kaluza-Klein model with the multidimensional cosmological constant $Λ_6$, we obtain the black brane with spherical compactification of the internal space. The matter source for this exact solution consists of two parts. First, it is a fine-tuned homogeneous perfect fluid which provides spherical compactification of the internal space. Second, it is a gravitating massive body with the dustlike equation of state in the external space and tension $\hat p_1=-(1/2)\hat\varepsilon$ in the internal space. This solution exists both in the presence and absence of $Λ_6$. In the weak-field approximation, we also get solutions of the linearized Einstein equations for the model with spherical compactification. Here, the gravitating matter source has the dustlike equation of state in the external space and an arbitrary equation of state $\hat p_1=Ω\hat\varepsilon$ in the internal space. In the case $Λ_6>0$ and $Ω\neq -1/2$, these approximate solutions tend asymptotically to the weak-field limit of the exact black brane solution. Both the exact and asymptotic black branes satisfy the gravitational experiments at the same level of accuracy as general relativity.

gr-qc↗

arXiv2012

Weak-field limit of Kaluza-Klein models with spherical compactification: problematic aspects

We investigate classical gravitational tests for the Kaluza-Klein model with spherical compactification of the internal two-dimensional space. In the case of the absence of a multidimensional bare cosmological constant, the only matter which corresponds to the proposed metric ansatz is a perfect fluid with the vacuum equation of state in the external space and the dust-like equation of state in the internal space. We perturb this background by a compact massive source with the dust-like equation of state in both external and internal spaces (e.g., a point-like mass), and obtain the metric coefficients in the weak-field approximation. It enables to calculate the parameterized post-Newtonian parameter $γ$. We demonstrate that $γ=1/3$ which strongly contradicts the observations.

gr-qc↗

arXiv2012

Weak-field limit of Kaluza-Klein models with spherical compactification: experimental constraints

We investigate the classical gravitational tests for the six-dimensional Kaluza-Klein model with spherical (of a radius $a$) compactification of the internal space. The model contains also a bare multidimensional cosmological constant $Λ_6$. The matter, which corresponds to this ansatz, can be simulated by a perfect fluid with the vacuum equation of state in the external space and an arbitrary equation of state with the parameter $ω_1$ in the internal space. For example, $ω_1=1$ and $ω_1=2$ correspond to the monopole two-forms and the Casimir effect, respectively. In the particular case $Λ_6=0$, the parameter $ω_1$ is also absent: $ω_1=0$. In the weak-field approximation, we perturb the background ansatz by a point-like mass. We demonstrate that in the case $ω_1>0$ the perturbed metric coefficients have the Yukawa type corrections with respect to the usual Newtonian gravitational potential. The inverse square law experiments restrict the parameters of the model: $a/\sqrt{ω_1}\lesssim 6\times10^{-3}\ {cm}$. Therefore, in the Solar system the parameterized post-Newtonian parameter $γ$ is equal to 1 with very high accuracy. Thus, our model satisfies the gravitational experiments (the deflection of light and the time delay of radar echoes) at the same level of accuracy as General Relativity. We demonstrate also that our background matter provides the stable compactification of the internal space in the case $ω_1>0$. However, if $ω_1=0$, then the parameterized post-Newtonian parameter $γ=1/3$, which strongly contradicts the observations.

gr-qc↗

arXiv2011

Asymptotic latent solitons, black strings and black branes in f(R)-gravity

We investigate nonlinear f(R) theories in the Kaluza-Klein models with toroidal compactification of extra dimensions. A point-like matter source has the dust-like equation of state in our three dimensions and nonzero equations of state in the extra dimensions. We obtain solutions of linearized Einstein equations with this matter source taking into account effects of nonlinearity of the model. There are two asymptotic regions where solutions satisfy the gravitational tests at the same level of accuracy as General Relativity. According to these asymptotic regions, there are two classes of solutions. We call these solutions asymptotic latent solitons. The asymptotic latent solitons from the first class generalize the known result of the linear theory. The asymptotic black strings and black branes are particular cases of these asymptotic solutions. The second class of asymptotic solitons exists only in multidimensional nonlinear models. The main feature for both of these classes of solutions is that the matter sources have tension in the extra dimensions.

gr-qc↗

arXiv2011

Non-relativistic limit of Randall-Sundrum model: solutions, applications and constraints

In the Randall-Sundrum model with one brane, we found the approximate and exact solutions for gravitational potentials and accelerations of test bodies in these potentials for different geometrical configurations. We applied these formulas for calculation of the gravitational interaction between two spheres and found the approximate and exact expressions for the relative force corrections to the Newton's gravitational force. We demonstrated that the difference between relative force corrections for the approximate and exact cases increases with the parameter $l$ (for the fixed distance $r$ between centers of the spheres). On the other hand, this difference increases with decreasing of the distance between the centers of the spheres (for the fixed curvature scale parameter $l$). We got the upper limit for the curvature scale parameter $l\lesssim 10\, μ$m. For these values of $l$, the difference between the approximate and exact solutions is negligible.

gr-qc↗

arXiv2011

Weak-field limit of f(R)-gravity in three and more spatial dimensions

We investigate a point-like massive source in non-linear f(R) theories in the case of arbitrary number of spatial dimensions D\geq 3. If D>3 then extra dimensions undergo toroidal compactification. We consider a weak-field approximation with Minkowski and de Sitter background solutions. In both these cases point-like massive sources demonstrate good agreement with experimental data only in the case of ordinary three-dimensional (D=3) space. We generalize this result to the case of perfect fluid with dust-like equations of state in the external and internal spaces. This perfect fluid is uniformly smeared over all extra dimensions and enclosed in a three-dimensional sphere. In ordinary three dimensional (D=3) space, our formulas are useful for experimental constraints on parameters of f(R) models.

gr-qc↗