Dust-like Equation Of State Research Articles

Black branes and black strings in the astrophysical and cosmological context

We consider Kaluza–Klein models where internal spaces are compact flat or curved Einstein spaces. This background is perturbed by a compact gravitating body with the dust-like equation of state (EoS) in the external/our space and an arbitrary EoS parameter Ω in the internal space. Without imposing any restrictions on the form of the perturbed metric and the distribution of the perturbed energy densities, we perform the general analysis of the Einstein and conservation equations in the weak-field limit. All conclusions follow from this analysis. For example, we demonstrate that the perturbed model is static and perturbed metric preserves the block-diagonal form. In a particular case Ω=−1/2, the found solution corresponds to the weak-field limit of the black strings/branes. The black strings/branes are compact gravitating objects which have the topology (four-dimensional Schwarzschild spacetime) × (d-dimensional internal space) with d≥1. We present the arguments in favour of these objects. First, they satisfy the gravitational tests for the parameterized post-Newtonian parameter γ at the same level of accuracy as General Relativity. Second, they are preferable from the thermodynamical point of view. Third, averaging over the Universe, they do not destroy the stabilization of the internal space. These are the astrophysical and cosmological aspects of the black strings/branes.

Weak-field limit of Kaluza\u2013Klein models with spherically symmetric static scalar field: observational constraints

In a multidimensional Kaluza–Klein model with Ricci-flat internal space, we study the gravitational field in the weak-field limit. This field is created by two coupled sources. First, this is a point-like massive body which has a dust-like equation of state in the external space and an arbitrary parameter varOmega of equation of state in the internal space. The second source is a static spherically symmetric massive scalar field centered at the origin where the point-like massive body is. The found perturbed metric coefficients are used to calculate the parameterized post-Newtonian (PPN) parameter gamma . We define under which conditions gamma can be very close to unity in accordance with the relativistic gravitational tests in the solar system. This can take place for both massive or massless scalar fields. For example, to have gamma approx 1 in the solar system, the mass of scalar field should be mu gtrsim 5.05times 10^{-49}g sim 2.83times 10^{-16}eV. In all cases, we arrive at the same conclusion that to be in agreement with the relativistic gravitational tests, the gravitating mass should have tension: varOmega = -,1/2.

Космологические модели с вращением типа VIII по Бьянкис источниками-жидкостями

Within the general theory of relativity the Bianchi type VIII cosmological models with rotationand expansion have been built. The first case includes a field of radiation, the second one -a perfect fluid with dust-like equation of state. Perfect anisotropic fluid imitates the rotatingdark energy. Static and dynamic cosmological modes have been observed, at the same timethe equations of state are partly postulated in the first case for the anisotropic fluid and inthe second case - for the perfect isotropic fluid, that imitates baryon matter. The analysisof absence of closed time-like curves has been done, so the models have been proved to becasual when the metric parameters satisfy the found conditions. Also the conditions, when theanisotropic fluid’s equation of state becomes vacuum-like, the energy of the fluid dominatesand it becomes asymptotically isotropic, have been cleared out. Specialities of the oscillatingmode have been observed. The order of present angular velocity value, calculated within thecosmological models, has been found to be quite satisfactory when expanding from the Plank scale to the present size of observed part of the Universe. The found solutions may be used foreffects taking place nowadays and also during the inflationary stage.

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 it is free of tension, i.e. Ω = 0. To obtain this result, we need to impose certain conditions.

Exact and asymptotic black branes with spherical compactification

In the six-dimensional Kaluza-Klein model with the multidimensional cosmological constant $\Lambda_6$, 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 $\Lambda_6$. 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 $\hat p_1=\Omega \hat\varepsilon$ in the internal space. In the case $\Lambda_6>0$ and $\Omega\neq -1/2$, 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.

Asymptotic latent solitons, black strings, and black branes inf(R)gravity

We investigate nonlinear $f(R)$ theories in the Kaluza-Klein models with toroidal compactification of extra dimensions. A pointlike matter source has the dustlike 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.

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. Each ${d}_{i}$-dimensional torus has its own scale factor ${C}_{i}$, $i=1,\dots{},N$, which is characterized by a parameter ${\ensuremath{\gamma}}_{i}$. We single out the physically interesting solution corresponding to a pointlike mass. For the general solution we obtain equations of state in the external and internal spaces. These equations demonstrate that the pointlike mass soliton has dustlike equations of state in all spaces. We also obtain the parametrized post-Newtonian 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 parameters of the model: $\ensuremath{\tau}=\ensuremath{\sum}_{i=1}^{N}{d}_{i}{\ensuremath{\gamma}}_{i}=\ensuremath{-}(2.1\ifmmode\pm\else\textpm\fi{}2.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. The pointlike mass solution with ${\ensuremath{\gamma}}_{1}=\dots{}={\ensuremath{\gamma}}_{N}=(1+\ensuremath{\sum}_{i=1}^{N}{d}_{i}{)}^{\ensuremath{-}1}$ contradicts this restriction. The condition $\ensuremath{\tau}=0$ 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 with ${\ensuremath{\gamma}}_{i}=0$ 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 ${p}_{i}=\ensuremath{-}\ensuremath{\epsilon}/2$, $i=1,\dots{},N$, 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 a dustlike equation of state in the external space confirms the above results.

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.