Search Results (92)

This review examines the role of differential forms, Pfaffian systems, and hypersurfaces in general relativity. These mathematical constructions provide the essential tools for general relativity, in which the curvature of spacetime—described by the Einstein field equations—is most elegantly formulated using the Cartan calculus of differential forms. Another important subject in this discussion is the notion of conformal geometry, where the relevant invariants of a metric are characterized by Élie Cartan’s normal conformal connection. The previous analysis is then used to develop the null surface formulation (NSF) of general relativity, a radical framework that postulates the structure of light cones rather than the metric itself as the fundamental gravitational variable. Defined by a central Pfaffian system, this formulation allows the entire spacetime geometry to be reconstructed from a single scalar function, Z, whose level surfaces are null. Full article

We investigate the geometric and physical properties of the h-almost conformal $\eta$-Ricci–Bourguignon soliton and its gradient form by employing a barotropic equation of state within the framework of $f(\mathcal{R},\mathcal{T})$ gravity. We derive this barotropic equation of state under the assumption that the matter content of $f(\mathcal{R},\mathcal{T})$ gravity is modeled by a barotropic perfect fluid. We also examine the way in which these soliton structures both reveal and limit the underlying symmetries of the spacetime geometry. Furthermore, we obtain modified Poisson and Liouville equations associated with these solitons in such a gravitational setting. Additionally, we explore certain harmonic aspects of the h-almost conformal $\eta$-Ricci–Bourguignon soliton on a spacetime filled with a barotropic perfect fluid, considering a harmonic potential function $\mathrm{\Psi }$. Finally, we present physical interpretations of the conformal pressure $\tilde{p}$ in the context of the h-almost conformal $\eta$-Ricci–Bourguignon soliton within $f(\mathcal{R},\mathcal{T})$ gravity. Full article

By extending the four-dimensional semi-Riemann geometry to higher-dimensional Finsler/Hamilton geometry, the canonical quantization of the fundamental metric tensor of general relativity, i.e., an approach that tackles a geometric quantity, is derived. With this quantization, the smooth continuous Finsler structure is transformed into a quantized Hamilton structure through the kinematics of a free-falling quantum particle with a positive mass, along with the introduction of the relativistic generalized uncertainty principle (RGUP) that generalizes quantum mechanics by integrating gravity. This transformation ensures the preservation of the positive one-homogeneity of both Finsler and Hamilton structures, while the RGUP dictates modifications in the noncommutative relations due to integrating consequences of relativistic gravitational fields in quantum mechanics. The anisotropic conformal transformation of the resulting metric tensor and its inverse in higher-dimensional spaces has been determined, particularly highlighting their translations to the four-dimensional fundamental metric tensor and its inverse. It is essential to recognize the complexity involved in computing the fundamental inverse metric tensor during a conformal transformation, as it is influenced by variables like spatial coordinates and directional orientation, making it a challenging task, especially in tensorial terms. We conclude that the derivations in this study are not limited to the structure in tangent and cotangent bundles, which might include both spacetime and momentum space, but are also applicable to higher-dimensional contexts. The theoretical framework of quantization of general relativity based on quantizing its metric tensor is primarily grounded in the four-dimensional metric tensor and its inverse in pseudo-Riemannian geometry. Full article

The nature of the $F(R,T)$-gravity in conjunction with the quark matter fluid $\left(QMF\right)$ is examined in this research note. In the $F(R,T)$-gravity framework, we derive the equation of state for the $QMF$ in the form of: $F(R,T)=F_1\left(R\right)+F_2\left(T\right)$ and the model of $F\left(R\right)$-gravity. We also discuss how the quark matter supports the Ricci solitons with a conformal vector field in $F(R,T)$-gravity. In this continuing work, we give estimates for the pressure and quark density in the phantom barrier period and the radiation epoch, respectively. Additionally, we use Ricci solitons to identify several black hole prospects and energy requirements for quark matter fluid spacetime ($QMF$-spacetime) connected with $F(R,T)$-gravity. Furthermore, in the $F(R,T)$-gravity model connected with $QMF$, we also discuss some applications of the Penrose singularity theorem in terms of Ricci solitons with a conformal vector field. Finally, we deduce the Schrödinger Equation using the equation of state of the $F(R,T)$-gravity model connected with $QMF$, and we uncover some constraints that imply the existence of compact quark stars of the $Ia$-supernova type in the $QMF$-spacetime with $F(R,T)$-gravity. Full article

In this paper, we study the thermodynamic behavior of charged AdS black holes in higher-dimensional spacetimes within the framework of conformal holographic extended thermodynamics. This formalism is based on a novel AdS/CFT dictionary in which the conformal rescaling factor of the boundary conformal field theory (CFT) is treated as a thermodynamic parameter, while Newton’s constant is held fixed and the AdS radius is allowed to vary. We explore how variations in the CFT state, represented by its central charge, influence the bulk thermodynamics, phase structure, and stability of black holes in five and six dimensions. Our analysis reveals the emergence of Van der Waals-like phase transitions, critical phenomena governed by the central charge. Additionally, we find that the thermodynamic behavior of AdS black holes is affected by the dimensionality of the bulk spacetime, as we compare higher-dimensional black holes to lower-dimensional ones, such as the BTZ black holes. These findings provide new insights into the role of boundary degrees of freedom in shaping the thermodynamics of gravitational systems via holography. Full article

We investigate the behaviour of photons in Riemann spacetime, focusing on how their velocity and energy are affected by cosmic expansion. Specifically, we examine the differences in energy conservation depending on the cosmological model. Our findings indicate that photons exhibit fundamentally different behaviour based on the chosen metric. In the standard $\Lambda$CDM model, which relies on the Friedmann–Lemaître–Robertson–Walker (FLRW) metric, the energy conservation law for redshifted photons is violated. However, in a cosmological model based on the conformal cosmology (CC) metric, this law remains valid. The CC metric offers additional advantages, as it accurately reproduces the cosmological redshift, cosmic time dilation observed in Type Ia supernova light curves, and flat galaxy rotation curves without requiring the introduction of dark matter. These findings underscore the potential significance of the CC metric in cosmological applications. Full article

The goal of the article is to examine the behavior of bulk viscous fluid string spacetime with a fluid density of the bulk viscous fluid string $\rho$ and a tension of the bulk viscous fluid string $\lambda$. This is known as relativistic bulk viscous fluid string spacetime. We derive some conclusions for bulk viscous fluid string with a vanishing space–matter tensor and a divergence-free matter tensor. We then focus on certain curvature properties for bulk viscous fluid string spacetime, including conformally flat, Ricci recurrent, Ricci semi-symmetric, and pseudo-Ricci-symmetric. Some physical results that align with the equation of state of Ricci semi-symmetric bulk viscous fluid string spacetime are also obtained. Full article

In this paper, we study the conformal symmetry for locally rotationally symmetric Bianchi type I space-time. New exact conformal solutions of Einstein’s field equations for this space-time were obtained. The space-time geometry of these solutions is found to be non-vacuum, conformally flat, and shear-free. We show that in order for LRS Bianchi type I space-time to admit a conformal vector field it must reduce to the FRW space-time. Some physical and kinematic properties of the obtained conformal solutions are also discussed. Full article

Wormholes are non-trivial topological structures that arise as exact solutions to Einstein’s field equations, theoretically connecting distinct regions of spacetime via a throat-like geometry. While static traversable wormholes necessarily require exotic matter that violates the classical energy conditions, subsequent studies have sought to minimize such violations by introducing time-dependent geometries embedded within cosmological backgrounds. This review provides a comprehensive survey of evolving wormhole solutions, emphasizing their formulation within both general relativity and alternative theories of gravity. We explore key developments in the construction of non-static wormhole spacetimes, including those conformally related to static solutions, as well as dynamically evolving geometries influenced by scalar fields. Particular attention is given to the wormholes embedded into Friedmann–Lemaître–Robertson–Walker (FLRW) universes and de Sitter backgrounds, where the interplay between the cosmic expansion and wormhole dynamics is analyzed. We also examine the role of modified gravity theories, especially in hybrid metric–Palatini gravity, which enable the realization of traversable wormholes supported by effective stress–energy tensors that do not violate the null or weak energy conditions. By systematically analyzing a wide range of time-dependent wormhole solutions, this review identifies the specific geometric and physical conditions under which wormholes can evolve consistently with null and weak energy conditions. These findings clarify how such configurations can be naturally integrated into cosmological models governed by general relativity or modified gravity, thereby contributing to a deeper theoretical understanding of localized spacetime structures in an expanding universe. Full article

We present a review of recent developments in cosmological models based on Finsler geometry, as well as geometric extensions of general relativity formulated within this framework. Finsler geometry generalizes Riemannian geometry by allowing the metric tensor to depend not only on position but also on an additional internal degree of freedom, typically represented by a vector field at each point of the spacetime manifold. We examine in detail the possibility that Finsler-type geometries can describe the physical properties of the gravitational interaction, as well as the cosmological dynamics. In particular, we present and review the implications of a particular implementation of Finsler geometry, based on the Barthel connection, and of the $(\alpha ,\beta )$ geometries, where $\alpha$ is a Riemannian metric, and $\beta$ is a one-form. For a specific construction of the deviation part $\beta$, in these classes of geometries, the Barthel connection coincides with the Levi–Civita connection of the associated Riemann metric. We review the properties of the gravitational field, and of the cosmological evolution in three types of geometries: the Barthel–Randers geometry, in which the Finsler metric function F is given by $F=\alpha +\beta$, in the Barthel–Kropina geometry, with $F={\alpha }^2/\beta$, and in the conformally transformed Barthel–Kropina geometry, respectively. After a brief presentation of the mathematical foundations of the Finslerian-type modified gravity theories, the generalized Friedmann equations in these geometries are written down by considering that the background Riemannian metric in the Randers and Kropina line elements is of Friedmann–Lemaitre–Robertson–Walker type. The matter energy balance equations are also presented, and they are interpreted from the point of view of the thermodynamics of irreversible processes in the presence of particle creation. We investigate the cosmological properties of the Barthel–Randers and Barthel–Kropina cosmological models in detail. In these scenarios, the additional geometric terms arising from the Finslerian structure can be interpreted as an effective geometric dark energy component, capable of generating an effective cosmological constant. Several cosmological solutions—both analytical and numerical—are obtained and compared against observational datasets, including Cosmic Chronometers, Type Ia Supernovae, and Baryon Acoustic Oscillations, using a Markov Chain Monte Carlo (MCMC) analysis. A direct comparison with the standard $\Lambda$CDM model is also carried out. The results indicate that Finslerian cosmological models provide a satisfactory fit to the observational data, suggesting they represent a viable alternative to the standard cosmological model based on general relativity. Full article

The cosmic time dilation observed in Type Ia supernova light curves suggests that the passage of cosmic time varies throughout the evolution of the Universe. This observation implies that the rate of proper time is not constant, as assumed in the standard FLRW metric, but instead is time-dependent. Consequently, the commonly used FLRW metric should be replaced by a more general framework, known as the Conformal Cosmology (CC) metric, to properly account for cosmic time dilation. The CC metric incorporates both spatial expansion and time dilation during cosmic evolution. As a result, it is necessary to distinguish between comoving and proper (physical) time, similar to the distinction made between comoving and proper distances. In addition to successfully explaining cosmic time dilation, the CC metric offers several further advantages: (1) it preserves Lorentz invariance, (2) it maintains the form of Maxwell’s equations as in Minkowski spacetime, (3) it eliminates the need for dark matter and dark energy in the Friedmann equations, and (4) it successfully predicts the expansion and morphology of spiral galaxies in agreement with observations. Full article

In the present article, we classify conformally flat weakly Ricci-symmetric space-times and obtain that they represent Robertson–Walker space-times. Furthermore, we provethat a Ricci-recurrent weakly Ricci-symmetric space-time is static and a Ricci-semi-symmetric weakly Ricci-symmetric space-time does not exist. Further, we acquire the conditions under which a weakly Ricci-symmetric twisted space-time becomes a generalized Robertson–Walker space-time. Also, we examine the effect of conformally flat weakly Ricci-symmetric space-time solutions in $f(R,G)$ gravity by considering two models, and we see that the null, weak and strong energy conditions are verified, but the dominant energy condition fails, which is also consistent with present observational studies that reveal the universe is expanding. Finally, we apply the flat Friedmann–Robertson–Walker metric to deduce a relation between deceleration, jerk and snap parameters. Full article

This research note presents the properties of the $F(R,T)$-gravity model in combination with magnetized strange quark matter. We obtain the equation of state for the magnetized strange quark matter in the $F(R,T)$-gravity model endowed with the Lagrangian through of Ricci curvature. We also examine the Ricci solitons supported by a time-like conformal vector field in $F(R,T)$-gravity, attached with magnetized strange quark matter fluid. Within this ongoing research, we give an estimate of the total quark pressure and total density in the phantom barrier and the radiation epochs of the Universe. Finally, using Ricci solitons, we study the various energy conditions, some black holes criteria, and Penrose’s singularity theorem for magnetized strange quark matter fluid spacetime coupled with the $F(R,T)$-gravity model. Full article

In this work, we obtained exact solutions of Einstein’s field equations for plane symmetric cosmological models by assuming that they admit conformal motion. The space-time geometry of these solutions is found to be nonsingular, non-vacuum and conformally flat. We have shown that in the case of a perfect fluid, these solutions have an energy-momentum tensor possessing dark energy with negative pressure and the energy equation of state is $\rho +p=0$. We have shown that a fluid has acceleration, rotation, shear-free, vanishing expansion, and rotation. In the case of a cosmic string cloud, we found that the tension density and particle density decrease as the fluid moves along the direction of the strings, then vanish at infinity. We shown that the exact conformal solution for a static plane symmetric model reduces to the well-known anti-De Sitter space-time. We obtained that the space-time under consideration admits a conformal vector field orthogonal to the 4-velocity vector and does not admits a vector parallel to the 4-velocity vector. Some physical and kinematic properties of the resulting models are also discussed. Full article

According to general relativity, the cosmological redshift may be caused by other mechanisms than the source moving away from the observer. It can occur on a global scale, similar to the gravitational redshift near massive stars. In principle, these are differences in the time-dependent global metric field between the source in the past and the observer in the present. In this paper we attempt a new interpretation of the simple solution of Einstein’s equations within a fully conformal metric for the case of a time-independent energy-momentum tensor. The scaling factor here acts identically on all four space-time coordinates and the speed of light is independent of the conformal time. The fully conformal metric is interpreted here as a universal geometric background which is scale invariant and acts universally on all objects, including gauges and clocks, regardless of their dimensions and internal interactions. The associated scale invariant exponential expansion is thus only relative and all observers at different times are completely equal. The model introduces the concept of the appearent age of the universe, which is the limiting consequence of time dilation into the past, and corresponds to the present value of the age of the universe H⁻¹ according to the standard model. This appearent age is the same for all observers, and the Hubble constant is thus a true universal constant, invariant to time translations. The motivation of this work was to test the possibility of the above cosmological redshift mechanism in confrontation with astrophysical data. Probably the most important consequence is the generalized formulation and interpretation of the Hubble-Lemaître law z(r) = (e^Hr/c − 1), which shows good agreement with astrophysical data even for the most distant supernovae. Confronting the conformal metric model with some astrophysical data shows an interesting agreement with the observed spatial distribution of astrophysical sources such as γ-ray bursts and quasars. On a cosmological scale, the above fully conformal metric naturally determines the global energy density, spatial flatness, and solves the horizon problem and Olbers’ paradox in infinite spacetime. Full article