Search Results (54)

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

In a previous study we investigated the spherically symmetric Schwarzschild and Schwarzschild–de Sitter solutions within a Finsler–Randers-type geometry. In this work, we extend our analysis to charged and rotating solutions, focusing on the Reissner–Nordström and Kerr-like metrics in the Finsler–Randers gravitational framework. In particular, we extract the modified gravitational field equations and we examine the geodesic equations, analyzing particle trajectories and quantifying the deviations from their standard counterparts. Moreover, we compare the results with the predictions of general relativity, and we discuss how potential deviations from Riemannian geometry could be reached observationally. Full article

This paper discusses the nonlinear stability of a thin-shell wormhole from a regular black hole in Bardeen–de Sitter spacetime in the $f\left(R\right)$ gravity framework. The stability is examined under the linear perturbation about static solution and a nonlinear variable equation of state, such as the modified generalized Chaplygin gas. The stability solutions for a suitable choice of different parameters included in the variable equation of state and $f\left(R\right)$ gravity models, as well as the metric space–time, are illustrated. Full article

This work explores the geometry of extremal Kerr-Newman black holes by analyzing their mass/energy relationships and the conditions ensuring black hole existence. Using differential geometry in $E^3$, we examine the topology of the event horizon surface and identify two distinct families of extremal black holes, each defined by unique proportionalities between their core parameters: mass (m), charge (Q), angular momentum (L), and the irreducible mass ($m_{ir}$). In the first family, these parameters are proportionally related to the irreducible mass by irrational numbers, with a characteristic flat Gaussian curvature at the poles. In the second family, we uncover a more intriguing structure where m, Q, and L are connected to $m_{ir}$ through coefficients involving the golden ratio $-{\varphi }_{-}$. Within this family lies a unique black hole whose physical parameters converge on the golden ratio, including the irreducible mass and polar Gauss curvature. This black hole represents the highest symmetry achievable within the constraints of the Kerr-Newman metric. This remarkable symmetry invites further speculation about its implications, such as the potential determination of the dark energy density parameter ${\Omega }_{\Lambda }$ for Kerr-Newman-de Sitter black holes. Additionally, we compute the maximum energy that can be extracted through reversible transformations. We have determined that the second, golden-ratio-linked family allows for a greater energy yield than the first. Full article

We investigate the implications of different quantization approaches in Loop Quantum Cosmology for the primordial power spectrum of tensor modes. Specifically, we consider the hybrid and dressed metric approaches to derive the effective mass that governs the evolution of the tensor modes. Our study comprehensively examines the two resulting effective masses and how to estimate them in order to obtain approximated analytic solutions to the tensor perturbation equations. Since Loop Quantum Cosmology incorporates preinflationary effects in the dynamics of the perturbations, we do not have at our disposal a standard choice of privileged vacuum, like the Bunch–Davies state in quasi-de Sitter inflation. We then select the vacuum state by a recently proposed criterion which removes unwanted oscillations in the power spectrum and guarantees an asymptotic diagonalization of the Hamiltonian in the ultraviolet. This vacuum is usually called the NO-AHD (from the initials of Non-Oscillating with Asymptotic Hamiltonian Diagonalization) vacuum. Consequently, we compute the power spectrum by using our analytic approximations and by introducing a suitable numerical procedure, adopting in both cases an NO-AHD vacuum. With this information, we compare the different spectra obtained from the hybrid and the dressed metric approaches, as well as from the analytic and numerical procedures. In particular, this proves the remarkable accuracy of our approximations. Full article

In developing his cosmological model of 1917, de Sitter theoretically predicted the phenomenon of cosmological redshift (the de Sitter effect), which he did long before the discovery of this phenomenon in observations. The de Sitter effect is gravitational by its nature, as it is due to differences between the coordinate systems of the observer and the distant source. However, the relationship between the redshift and distance derived from the de Sitter metric is at odds with observations, since this relationship is nonlinear (quadratic) for small redshifts, while the observed relationship between the same quantities is strictly linear. This paper discusses the possibility that cosmological redshift is gravitational by its nature, as in de Sitter’s 1917 model. At the same time, here, as in de Sitter’s model, an elliptical space is used, the main characteristic of which is the identification of its antipodal points. But, unlike de Sitter’s model, here, in order to ensure strict linear dependence of the redshift on distance, the origin of the reference system is transferred to the observer’s antipodal point. The Schwarzschild–de Sitter metric used in this model allows you to estimate the curvature of space from observational data. To achieve this, a theoretical Hubble diagram is built within the framework of the model with the Schwarzschild–de Sitter metric, which is compared with observations from the Pantheon+ catalogue of type Ia supernovae and the Amati catalogue of gamma-ray bursts in the redshift range of $0<z<8$. As a result of this comparison, we found that the lower estimate of the radius of curvature of space was quite large: $2.4\times {10}^{15}$ Mpc. This means that the observational data indicate a negligible curvature of space. 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

It is already known that a simple nonlocal de Sitter gravity model, which we denote as $\sqrt{dS}$ gravity, contains an exact vacuum cosmological solution that mimics dark energy and dark matter and is in very good agreement with the standard model of cosmology. This success of $\sqrt{dS}$ gravity motivated us to investigate how it works at a lower-than-cosmic scale—galactic and the solar system. This paper contains our investigation of the corresponding Schwarzschild–de Sitter metric of the $\sqrt{dS}$ gravity model. To obtain an exact solution, it is necessary to solve the corresponding nonlinear differential equation, which is a very complicated and difficult problem. What we obtained is a solution to a linearized equation, which is related to space metrics far from the massive body, where the gravitational field is weak. The obtained approximate solution is of particular interest for examining the possible role of nonlocal de Sitter gravity $\sqrt{dS}$ in describing the effects in galactic dynamics that are usually attributed to dark matter. This solution was tested on the Milky Way and the spiral galaxy M33 and is in good agreement with observational measurements. Full article

We study the Schrödinger equation in quantum field theory (QFT) in its functional formulation. In this approach, quantum correlation functions can be expressed as classical expectation values over (complex) stochastic processes. We obtain a stochastic representation of the Schrödinger time evolution on Wentzel–Kramers–Brillouin (WKB) states by means of the Wiener integral. We discuss QFT in a flat expanding metric and in de Sitter space-time. We calculate the evolution kernel in an expanding flat metric in the real-time formulation. We discuss a field interaction in pseudoRiemannian and Riemannian metrics showing that an inversion of the signature leads to some substantial simplifications of the singularity problems in QFT. Full article

The main feature of elliptical space—the topological identification of its antipodal points—could be fundamental for understanding the nature of the cosmological redshift. The physical interpretation of the mathematical (topological) structure of elliptical space is made by using physical connections in the form of Einstein-Rosen bridges (also called “wormholes”). The Schwarzschild metric of these structures embedded into a dynamic (expanding) spacetime corresponds to McVittie’s solution of Einstein’s field equations. The cosmological redshift of spectral lines of remote sources in this metric is a combination of gravitational redshift and the time-dependent scale factor of the Friedmann-Lemaitre-Robertson-Walker metric. I compare calculated distance moduli of type-Ia supernovae, which are commonly regarded as “standard candles” in cosmology, with the observational data published in the catalogue “Pantheon+”. The constraint based on these accurate data gives a much smaller expansion rate of the Universe than is currently assumed by modern cosmology, the major part of the cosmological redshift being gravitational by its nature. The estimated age of the Universe within the discussed model is $1.48·{10}^{12}$ yr, which is more than two orders of magnitude larger than the age assumed by using the standard cosmological model parameters. Full article

We analyze the transformation of a very broad class of metrics that can be expressed in terms of static coordinates. Starting from a general ansatz, we obtain a relation for the parameters in which one can impose further symmetries or restrictions. One of the simplest restrictions leads to FLRW cases, while transforming from the initial static to other static-type coordinates can lead to near horizon coordinates, Wheeler–Regge, and isotropic coordinates, among others. As less restrictive cases, we show an indirect route for obtaining Kruskal–Szekeres within this approach, as well as Lemaître coordinates. We use Schwarzschild spacetime as a prototype for testing the procedure in individual cases. However, application to other spacetimes, such as de-Sitter, Reissner–Nordström, and Schwarzschild de Sitter, can be readily generalized. Full article

We study Einstein’s gravity coupled to nonlinear electrodynamics with two parameters in anti-de Sitter spacetime. Magnetically charged black holes in an extended phase space are investigated. We obtain the mass and metric functions and the asymptotic and corrections to the Reissner–Nordström metric function when the cosmological constant vanishes. The first law of black hole thermodynamics in an extended phase space is formulated and the magnetic potential and the thermodynamic conjugate to the coupling are obtained. We prove the generalized Smarr relation. The heat capacity and the Gibbs free energy are computed and the phase transitions are studied. It is shown that the electric fields of charged objects at the origin and the electrostatic self-energy are finite within the nonlinear electrodynamics proposed. Full article

We solve the particle-antiparticle and cosmological constant problems proceeding from quantum theory, which postulates that: various states of the system under consideration are elements of a Hilbert space $\mathcal{H}$ with a positive definite metric; each physical quantity is defined by a self-adjoint operator in $\mathcal{H}$; symmetry at the quantum level is defined by a representation of a real Lie algebra A in $\mathcal{H}$ such that the representation operator of any basis element of A is self-adjoint. These conditions guarantee the probabilistic interpretation of quantum theory. We explain that in the approaches to solving these problems that are described in the literature, not all of these conditions have been met. We argue that fundamental objects in particle theory are not elementary particles and antiparticles but objects described by irreducible representations (IRs) of the de Sitter (dS) algebra. One might ask why, then, experimental data give the impression that particles and antiparticles are fundamental and there are conserved additive quantum numbers (electric charge, baryon quantum number and others). The reason is that, at the present stage of the universe, the contraction parameter R from the dS to the Poincare algebra is very large and, in the formal limit $R\to \infty$, one IR of the dS algebra splits into two IRs of the Poincare algebra corresponding to a particle and its antiparticle with the same masses. The problem of why the quantities $(c,\hslash ,R)$ are as are does not arise because they are contraction parameters for transitions from more general Lie algebras to less general ones. Then the baryon asymmetry of the universe problem does not arise. At the present stage of the universe, the phenomenon of cosmological acceleration (PCA) is described without uncertainties as an inevitable kinematical consequence of quantum theory in semiclassical approximation. In particular, it is not necessary to involve dark energy the physical meaning of which is a mystery. In our approach, background space and its geometry are not used and R has nothing to do with the radius of dS space. In semiclassical approximation, the results for the PCA are the same as in General Relativity if $\mathsf{\Lambda }=3/R^2$, i.e., $\mathsf{\Lambda }>0$ and there is no freedom for choosing the value of $\mathsf{\Lambda }$. Full article

Quantum de Sitter geometry is discussed using elementary field operator algebras in Krein space quantization from an observer-independent point of view, i.e., ambient space formalism. In quantum geometry, the conformal sector of the metric becomes a dynamical degree of freedom, which can be written in terms of a massless minimally coupled scalar field. The elementary fields necessary for the construction of quantum geometry are introduced and classified. A complete Krein–Fock space structure for elementary fields is presented using field operator algebras. We conclude that since quantum de Sitter geometry can be constructed by elementary fields operators, the geometry quantum state is immersed in the Krein–Fock space and evolves in it. The total number of accessible quantum states in the universe is chosen as a parameter of quantum state evolution, which has a relationship with the universe’s entropy. Inspired by the Wheeler–DeWitt constraint equation in cosmology, the evolution equation of the geometry quantum state is formulated in terms of the Lagrangian density of interaction fields in ambient space formalism. Full article

The topic of gravitational lensing in the Mannheim–Kazanas solution of Weyl conformal gravity and the Schwarzschild–de Sitter solution in general relativity has featured in numerous publications. These two solutions represent a spherical massive object (lens) embedded in a cosmological background. In both cases, the interest lies in the possible effect of the background non-asymptotically flat spacetime on the geometry of the local light curves, particularly the observed deflection angle of light near the massive object. The main discussion involves possible contributions to the bending angle formula from the cosmological constant $\mathsf{\Lambda }$ in the Schwarzschild–de Sitter solution and the linear term $\gamma r$ in the Mannheim–Kazanas metric. These effects from the background geometry, and whether they are significant enough to be important for gravitational lensing, seem to depend on the methodology used to calculate the bending angle. In this paper, we review these techniques and comment on some of the obtained results, particularly those cases that contain unphysical terms in the bending angle formula. Full article