String cosmological models in the Brans-Dicke theory for five-dimensional space-time

We obtain a black hole solution in the Einstein–Gauss–Bonnet theory for the string cloud model in a five-dimensional spacetime. We analyze the event horizons and naked singularities. Later, we compute the Hawking temperature TH, the specific heat C, the entropy S, and the Helmholtz free energy F of the black hole. The entropy was computed using the Wald formulation. In addition, the quantum correction to the Wald's entropy is considered for the string cloud source.We mainly explore the thermodynamical global and local stability of the system with vanishing or non-vanishing cosmological constant. The global thermodynamic phase structure indicates that the Hawking–Page transition is achieved for this model. Further, we observe that there exist stable black holes with small radii and that these regions are enlarged when choosing small values of the string cloud density and of the Gauss–Bonnet parameter. Besides, the rate of evaporation for these black holes are studied, determining whether the evaporation time is finite or not. Then, we concentrate on the dynamical stability of the system, studying the effective potential for s-waves propagating on the string cloud background.

The pure Brans-Dicke (BD) gravity with or without the cosmological constant Λ has been taken as a model theory for dark matter. Indeed, there has been a consensus that unless one modifies either the standard theory of gravity, namely, general relativity, or the standard model for particle physics, or both, one can never achieve a satisfying understanding of the phenomena associated with dark matter and dark energy. Along this line, our dark matter model in this work can be thought of as an attempt to modify the gravity side alone in the simplest fashion to achieve the goal. Among others, it is demonstrated that our model theory can successfully predict the emergence of a dark matter halo-like configuration in terms of a self-gravitating spacetime solution to the BD field equations and reproduce the flattened rotation curve in this dark halo-like object in terms of the non-trivial energy density of the BD scalar field, which was absent in the context of general relativity, where Newton’s constant is strictly a “constant” having no dynamics. Our model theory, however, is not entirely without flaw, such as the prediction of relativistic jets in all types of galaxies, which actually is not the case.

We have studied the plane symmetric cosmological solutions for quark matter coupled with the string cloud and domain walls in the context of Rosen’s (General Relativity and Gravitation 4:435, 1973) bimetric theory. It is observed that, in this theory, string cloud and domain walls do not exist. As we know that, at the early stage of evolution of the universe, domain walls as well as cosmic strings do appear which lead to the formation of galaxies. Thus, it may be said that the bimetric relativity does not help to describe the early era of the universe.

Objectives: To derive the multi-fluid anisotropic Bianchi type-III cosmological model filled with radiation and matter in the presence of Brans-Dicke scalar-tensor theory. Method: In this paper, we have calculated Brans-Dicke field equations in anisotropic Bianchi type -III space times in the presence of matter and radiation which are minimally interacting fields. To obtain the determinate solution of the model, we considered i) the state of the equation , ii) the shear scalar is directly proportional to the expansion scalar i.e., . Also, consider the deceleration parameter, , where with which yields models with constant deceleration parameter. Findings: This solution shows an anisotropic radiation model in Brans-Dicke's theory. Also, it shows accelerated expansion of the universe and transition of the universe from the deceleration phase to the accelerated phase. Novelty: The derived model's many parameters support recent cosmological findings, indicating the model's good discovery. Thus, within the framework of our established model, we are able to comprehend the cosmic development. Keywords: Bianchi type-III, Brans-Dicke theory, Multifluid, Deceleration parameter, Λ CDM

Exact solutions of Bianchi type-II cosmological models with stiff matter are obtained in the Brans-Dicke scalar tensor theory and the behaviour of the models is discussed.

In this study, the homogenous and anisotropic locally rotationally symmetric (LRS) Bianchi type-I universe filled with the bulk viscous and the string cloud matter has been investigated in the Brans-Dicke (BD) scalar-tensor theory. The modified Einstein field equations of the constructed model have been solved by using the relation of the scale factors $A=B^m$ and considering the deceleration parameter to be $q=m-1$. It is found that the string does not survive for the model due to the obtained zero string energy density ($\rho_s=0$) and agrees with some studies in recent years. Moreover, it is possible to say that string matter may be turned into phantom energy over time, depending on the obtained negative rest energy density of the matter. When BD scalar field $\Phi$ is assumed constant, the attained solutions are reduced to General Relativity (GR) solutions for the static vacuum. Thus, the constructed model has not allowed the reduction of the BD solutions to GR solutions, including the matter distributions. In addition, some expansion models for choosing a value of constant $m$ have been obtained and provided. All the results have been analyzed in detail.

Stationary, axially symmetric Brans-Dicke-Maxwell solutions are reexamined in the framework of the Brans-Dicke (BD) theory. We see that, employing a particular parametrization of the standard axially symmetric metric simplifies the procedure of obtaining the Ernst equations for axially symmetric electrovacuum space-times for this theory. This analysis also permits us to construct a two parameter extension in both Jordan and Einstein frames of an old solution generating technique frequently used to construct axially symmetric solutions for BD theory from a seed solution of general relativity. As applications of this technique, several known and new solutions are constructed including a general axially symmetric BD-Maxwell solution of Plebanski-Demianski with vanishing cosmological constant, i.e. the Kinnersley solution and general magnetized Kerr-Newman--type solutions. Some physical properties and the circular motion of test particles for a particular subclass of Kinnersley solution, i.e., a Kerr-Newman-NUT--type solution for BD theory, are also investigated in some detail.

Stability of horizon with pressure and volume of d-dimensional charged AdS black holes with cloud of strings and quintessence

In this paper it is shown that in Brans–Dicke theory, if one considers a non-minimal coupling between the matter and scalar field, can give rise to a bouncing universe (i.e., an expanding universe preceded by a contracting universe). Two examples of such universes have been considered in a spatially flat Friedmann–Robertson–Walker universe and their physical properties have been studied.

A string cosmological models with magnetic field along X and Z-axis are investigated in the context of Ruban’s space time. To obtain a determinant solution, equation of state for string model and relation between metric potential is considered. The physical and geometrical aspects are also discussed.

The quasinormal modes for a scalar field in the background spacetime corresponding to a black hole, with a cloud of strings, in Einstein–Gauss–Bonnet gravity, and the tensor quasinormal modes corresponding to perturbations in such spacetime, were both calculated using the WKB approximation. In the obtained results, we emphasize the role played by the parameter associated with the string cloud, comparing them with the results already obtained for the Boulware–Deser metric. We also study how the Gauss–Bonnet correction to general relativity affects the results for the quasinormal modes, comparing them with the same background in general relativity.

Ricci scalar being zero is equivalent to the vacuum field equation in Finsler space-time. The Schwarzschild metric can be concluded from the field equation's solution if the space-time conserves spherical symmetry. This research aims to investigate Finslerian Schwarzschild-de Sitter space-time. Recent studies based on Finslerian space-time geometric models are becoming more prevalent because the local anisotropic structure of space-time influences the gravitational field and gives rise to modified cosmological relations. We suggest a gravitational field equation with a non-zero cosmological constant in Finslerian geometry and apprehend that the presented Finslerian gravitational field equation corresponds to the non-zero Ricci scalar. In Finsler geometry, the peer of spherical symmetry is the Finslerian sphere. Assuming space-time to conserve the “Finslerian sphere” symmetry, the counterpart of the Riemannian sphere (Finslerian sphere) must have a constant flag curvature (λ). It is demonstrated that the Finslerian covariant derivative of the geometric part of the gravitational field equation is preserved under a condition using the Chern connection. According to the string theory, string clouds can be defined as a pool of strings made due to symmetry breaking in the universe's early stages. We find that for λ ≠ 1, this solution resembles a black hole surrounded by a cloud of strings. Furthermore, we investigate null and time-like geodesics for λ = 1. In this regard, the photon geodesics are obtained that are the closest paths to the photon sphere of the first photons visible at the black hole shadow limit. Also, circular orbit conditions are obtained for the effective potential.

We study string cosmological models with attached particles in LRS BI type space time. The dynamical and physical properties of such universes are studied, and the possibility that during the evolution of the universe the strings disappear, leaving only the particles, is also discussed. It is found that bulk viscosity plays a large role in the evolution of the universe. In these models we find critical instances of when there was a “Bounce". The studied models are found to be of an inflationary type, and since a desirable feature of a meaningful string cosmological model is the presence of an inflationary epoch in the very early stages of evolution, our models can be thought of as realistic universes.

Invariance of the Brans-Dicke scalar-tensor theory of gravity under scale transformations of the second kind is discussed. It is shown that the requirement of scale invariance of the second kind leads to the unique value −32 of the adjustable parameter ω in the Brans-Dicke theory. It is further shown that, in order to obtain a consistent set of equations, matter must be coupled to the scalar-tensor field in such a way that the whole theory can be transformed into the usual Einstein tensor theory. This is accomplished by performing a space-time dependent scale change such that the transformed scalar field is everywhere a constant.

Triaxial testing was used on a suite of shales of varied age and geographic distribution in order to ascertain static and dynamic elastic properties, strength and frictional response. The shales were also fully characterized in terms of composition, fabric elements, standard and exotic physical and petrophysical properties, including dielectrics and nuclear magnetic resonance. Empirical correlations were made between static mechanical properties and the other properties measured in order to determine empirical strength correlations for a global and a local shale population. For the global population, dynamic elastic properties were poor empirical predictors of shale strength. Better correlations could be obtained with physical properties such as cation exchange capacity and porosity. Good porosity‐velocity and impedance correlations were obtained however from the global shale population. Dynamic properties were better predictors of strength and static elastic properties in a local shale population where the rocks have shared similar compactional and diagenetic histories.