Search Results (33)

The idea of varying constants of nature is very old, and has commanded a lot of attention since first mooted. The variation in the gravitational parameter G and cosmological parameter $\Lambda$ is still an active area of research. Since the idea of a varying G was introduced by Dirac almost a century ago, there are even theories that have variable G such as the Brans–Dicke theory and the scale covariant theory. Both these theories also have a varying $\Lambda$ in their full generalisations. A varying $\Lambda$ was also introduced around the same time as that of varying G. It is interesting to note that a possible solution to the cosmological constant problem can be realised from a dynamic $\Lambda$. In this work, we focus on a varying $\Lambda$ and G framework. In almost all studies in the simplest framework of variables $\Lambda$ and G, it is found that one of them has to increase with time. However, observations and theoretical considerations indicate that both $\Lambda$ and G should decrease with time. In this paper, we propose a solution to this problem, finding theories in which both $\Lambda$ and G decrease with time. Full article

Since the development of Brans–Dicke gravity, it has become well-known that a conformal transformation of the metric can reformulate this theory, transferring the coupling of the scalar field from the Ricci scalar to the matter sector. Specifically, in this new frame, known as the Einstein frame, Brans–Dicke gravity is reformulated as General Relativity supplemented by an additional scalar field. In 1959, Hans Adolf Buchdahl utilized an elegant technique to derive a set of solutions for the vacuum field equations within this gravitational framework. In this paper, we extend Buchdahl’s method to incorporate the cosmological constant and to the scalar-tensor cases beyond the Brans–Dicke archetypal theory, thereby, with a conformal transformation of the metric, obtaining solutions for a version of Brans–Dicke theory that includes a quadratic potential. More specifically, we obtain synchronous solutions in the following contexts: in scalar-tensor gravity with massless scalar fields, Brans–Dicke theory with a quadratic potential, where we obtain specific synchronous metrics to the Schwarzschild–de Sitter metric, the Nariai solution, and a hyperbolically foliated solution. Full article

After a century of cosmological observations, we have a solid standard model of cosmology. However, from a theoretical viewpoint, it is a compelling question if the cosmological data inevitably require an expanding universe independently of the theoretical framework. The possibility of obtaining a viable cosmological model with a constant scale-factor is discussed in the context of the Brans–Dicke class of scalar–tensor theories. It is shown that a flat spatial section requires the presence of a stiff matter fluid. However, some kinematical properties of the standard cosmological model can be reproduced. A realistic scenario may require a more complex class of scalar–tensor theories. Full article

In this paper, we consider homogeneous cosmological solutions in the context of the Weyl geometrical scalar–tensor theory. Firstly, we exhibit an anisotropic Kasner type solution taking advantage of some similarities between this theory and the Brans–Dicke theory. Next, we consider an isotropic model with a flat spatial section sourced by matter configurations described by a perfect fluid. In this model, we obtain an analytical solution for the stiff matter case. For other cases, we carry out a complete qualitative analysis theory to investigate the general behaviour of the solutions, presenting some possible scenarios. In this work, we do not consider the presence of the cosmological constant nor do we take any potential of the scalar field into account. Because of this, we do not find any solution describing the acceleration of the universe. Full article

The many problems faced by the theory of general relativity (GR) have always motivated us to explore the modified theory of GR. Considering the importance of studying the black hole (BH) entropy and its correction in gravity physics, we study the correction of thermodynamic entropy for a kind of spherically symmetric black hole under the generalized Brans–Dicke (GBD) theory of modified gravity. We derive and calculate the entropy and heat capacity. It is found that when the value of event horizon radius $r_{+}$ is small, the effect of the entropy-correction term on the entropy is very obvious, while for larger values $r_{+}$, the contribution of the correction term on entropy can be almost ignored. In addition, we can observe that as the radius of the event horizon increases, the heat capacity of BH in GBD theory will change from a negative value to a positive value, indicating that there is a phase transition in black holes. Given that studying the structure of geodesic lines is important for exploring the physical characteristics of a strong gravitational field, we also investigate the stability of particles’ circular orbits in static spherically symmetric BHs within the framework of GBD theory. Concretely, we analyze the dependence of the innermost stable circular orbit on model parameters. In addition, the geodesic deviation equation is also applied to investigate the stable circular orbit of particles in GBD theory. The conditions for the stability of the BH solution and the limited range of radial coordinates required to achieve stable circular orbit motion are given. Finally, we show the locations of stable circular orbits, and obtain the angular velocity, specific energy, and angular momentum of the particles which move in circular orbits. Full article

In the present paper, we focused on exploring the possibility of providing a new class of exact solutions for viable anisotropic stellar systems by means of the massive Brans–Dicke (BD) theory of gravity. In this respect, we used the decoupling of gravitational sources by minimal geometric deformation (MGD) ($e^{-\eta }=\Psi +\beta h$) for compact stellar objects in the realm of embedding class-one space-time to study anisotropic solutions for matter sources through the modified Einstein field equations. For this purpose, we used the ansatz for $\Psi$ relating to the prominent, well-known and well-behaved Finch–Skea model via Karmarkar condition, and the determination scheme for deformation function $h\left(r\right)$ was proposed via mimic requirement on radial pressure component: ${\theta }_1^1\left(r\right)=p_r\left(r\right)$ and matter density: ${\theta }_0^0\left(r\right)=\rho \left(r\right)$ for the anisotropic sector. Moreover, we analyzed the main physical highlights of the anisotropic celestial object by executing several physical tests for the case ${\theta }_1^1\left(r\right)=p_r\left(r\right)$. We have clearly shown how the parameters $\alpha$, $\beta$ and ${\omega }_{BD}$ introduced by massive BD gravity via the MGD approach incorporating the anisotropic profile of the matter distribution have an immense effect on many physical parameters of compact bodies such as LMC X-4, LMC X-4, Her X-1, 4U 1820-30, 4U 1608-52, SAX J1808.4–658 and many others that can be fitted. Full article

In this manuscript, we investigate the cosmological and thermodynamic aspects of the Brans–Dicke theory of gravity for a spatially flat FRW universe. We consider a theoretical model for interacting Kaniadakis holographic dark energy with the Hubble horizon as the infrared cutoff. We deal with two interaction scenarios ($Q_1$ and $Q_2$) between Kaniadakis holographic dark energy and matter. In this context, we study different possible aspects of cosmic evolution through some well-known cosmological parameters such as Hubble $\left(H\right)$, deceleration $\left(q\right)$, jerk $\left(j\right)$, and equation of state $\left({\omega }_d\right)$. For both interaction terms, it is observed that the deceleration parameter exhibits early deceleration to the current accelerating universe and also lies within the suggested range of Planck data. The equation of state parameter shows quintessence behavior (for the first interaction term) and phantom-like behavior (for the second interaction term) of the universe. The jerk parameter represents consistency with the $\Lambda$CDM model for both interaction terms. In the end, we check the thermodynamic behavior of the underlying model. It is interesting to mention here that the generalized second law of thermodynamics holds for both cases of interaction terms. Full article

We studied a superbounce scenario in a set up of the Brans–Dicke (BD) theory. The BD parameter was considered to be time-dependent and was assumed to evolve with the Brans–Dicke scalar field. In the superbounce scenario, the model bounced at an epoch corresponding to a Big Crunch provided the ekpyrotic phase continued until that time. Within the given superbounce scenario, we investigated the evolution of the BD parameter for different equations of state. We chose an axially symmetric metric that has an axial symmetry along the x-axis. The metric was assumed to incorporate an anisotropic expansion effect. The effect of asymmetric expansion and the anisotropic parameter on the evolving and non-evolving parts of the BD parameter was investigated. Full article

Exact solutions for Shapovalov wave spacetimes of type I in Brans–Dicke’s scalar-tensor theory of gravity are constructed. Shapovalov wave spacetimes describe gravitational wave models that allow for the the separation of wave variables in privileged coordinate systems. In contrast to general relativity, the vacuum field equations of the Brans–Dicke scalar-tensor theory of gravity lead to exact solutions for type I Shapovalov spaces, allowing for the the construction of observational tests to detect such wave disturbances. Furthermore, the equations for the trajectories of the test particles are obtained for the models considered. Full article

We present a brief description of noncompactified higher-dimensional theories from the perspective of general relativity. More concretely, the Space–Time–Matter theory, or Induced Matter theory, and the reduction procedure used to construct the modified Brans–Dicke theory and the modified Sáez–Ballester theory are briefly explained. Finally, we apply the latter to the Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological models in arbitrary dimensions and analyze the corresponding solutions. Full article

We propose a unimodular version of the Brans–Dicke theory designed with a constrained Lagrangian formulation. The resulting field equations are traceless. The vacuum solutions in the cosmological background reproduce the corresponding solutions of the usual Brans–Dicke theory but with a cosmological constant term. A perturbative analysis of the scalar modes is performed and stable and unstable configurations appear, in contrast with the Brans–Dicke case for which only stable configurations occur. On the other hand, tensorial modes in this theory remain the same as in the traditional Brans–Dicke theory. Full article

This study focuses on the X-ray emission of low-mass black hole binaries in massive Brans–Dicke gravity. First, we compute the accretion disk with the well-known Shakura–Sunyaev model for an optically thick, cool, and geometrically thin disk. Moreover, we assume that the gravitational field generated by the stellar-mass black hole is an analogue of the Schwarzschild space-time of Einstein’s theory in massive Brans–Dicke gravity. We compute the most relevant quantities of interest, i.e., (i) the radial velocity, (ii) the energy and surface density, and (iii) the pressure as a function entirely of the radial coordinate. We also compute the soft spectral component of the X-ray emission produced by the disk. Furthermore, we investigate in detail how the mass of the scalar field modifies the properties of the binary as described by the more standard Schwarzschild solution. Full article

We discuss qualitative features of the conformal relation between certain classes of gravity theories and general relativity, common to different themes such as $f\left(R\right)$, Brans-Dicke-type, and string theories. We focus primarily on the frame relations of the fields involved, slice energy, traceless and Palatini extensions, and selected cosmological applications. Full article

We consider a multi-scalar field model in the Jordan frame, which can be seen as a two-scalar field model where the Brans–Dicke field interacts in the kinetic part with the second scalar field. This theory under a conformal transformation reduces to the hyperbolic inflation. We show that scaling solutions and the de Sitter universe are provided by the theory. In the study of asymptotic dynamics, we determine an attractor where all the fluid sources contribute in the cosmological fluid. This attractor is always a spiral, and it can be seen as the analogue of the hyperbolic inflation in the Jordan frame. Full article

Following Smolin, we proceed to unification of general relativity and quantum theory by operating solely with events, i.e., without appealing to physical systems and space-time. The universe is modelled as a dendrogram (finite tree) expressing the hierarchic relations between events. This is the observational (epistemic) model; the ontic model is based on p-adic numbers (infinite trees). Hence, we use novel mathematics: not only space-time but even real numbers are not in use. Here, the p-adic space (which is zero-dimensional) serves as the base for the holographic image of the universe. In this way our theory is connected with p-adic physics; in particular, p-adic string theory and complex disordered systems (p-adic representation of the Parisi matrix for spin glasses). Our Dendrogramic-Holographic (DH) theory matches perfectly with the Mach’s principle and Brans–Dicke theory. We found a surprising informational interrelation between the fundamental constants, h, c, G, and their DH analogues, h(D), c(D), G(D). DH theory is part of Wheeler’s project on the information restructuring of physics. It is also a step towards the Unified Field theory. The universal potential V is nonlocal, but this is relational DH nonlocality. V can be coupled to the Bohm quantum potential by moving to the real representation. This coupling enhances the role of the Bohm potential. Full article