Search Results (58)

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

The area law obeyed by the thermodynamic entropy of black holes is one of the fundamental results relating gravity to statistical mechanics. In this work, we provide a derivation of the area law for the quantum relative entropy of the Schwarzschild black hole for an arbitrary Schwarzschild radius. The quantum relative entropy between the metric of the manifold and the metric induced by the geometry and the matter field has been proposed in G. Bianconi as the action for entropic quantum gravity leading to modified Einstein equations. The quantum relative entropy generalizes Araki’s entropy and treats the metrics between zero-forms, one-forms, and two-forms as quantum operators. Although the Schwarzschild metric is not an exact solution of the modified Einstein equations of the entropic quantum gravity, it is an approximate solution valid in the low-coupling, small-curvature limit. Here, we show that the quantum relative entropy associated to the Schwarzschild metric obeys the area law for a large Schwarzschild radius. We provide a full statistical mechanics interpretation of the results. Full article

In the framework of the analogous Hawking effect, we significantly improve our previous analysis of the master equation that encompasses very relevant physical systems, like Bose–Einstein condensates (BECs), dielectric media, and water. In particular, we are able to provide two significant improvements to the analysis. As our main result, we provide a complete set of connection formulas for both the subluminal and superluminal cases without resorting to suitable boundary conditions, first introduced by Corley, but simply on the grounds of a rigorous mathematical setting. Moreover, we provide an extension to the four-dimensional case, showing explicitly that, apart from obvious changes, adding transverse dimensions does not substantially modify the Hawking temperature in the dispersive case. Furthermore, an important class of exact solutions of the so-called reduced equation that governs the behavior of non-dispersive modes is also provided. Full article

We first briefly review the adventure of scale invariance in physics, from Galileo Galilei, Weyl, Einstein, and Feynman to the revival by Dirac (1973) and Canuto et al. (1977). In the way that the geometry of space–time can be described by the coefficients $g_{\mu \nu }$, a gauging condition given by a scale factor $\lambda \left(x^{\mu }\right)$ is needed to express the scaling. In general relativity (GR), $\lambda =1$. The “Large Number Hypothesis” was taken by Dirac and by Canuto et al. to fix $\lambda$. The condition that the macroscopic empty space is scale-invariant was further preferred (Maeder 2017a), the resulting gauge is also supported by an action principle. Cosmological equations and a modified Newton equation were then derived. In short, except in extremely low density regions, the scale-invariant effects are largely dominated by Newtonian effects. However, their cumulative effects may still play a significant role in cosmic evolution. The theory contains no “adjustment parameter”. In this work, we gather concrete observational evidence that scale-invariant effects are present and measurable in astronomical objects spanning a vast range of masses (0.5 ${\mathrm{M}}_{\odot }<$ M $<{10}^{14}$${\mathrm{M}}_{\odot }$) and an equally impressive range of spatial scales (0.01 pc < r < 1 Gpc). Scale invariance accounts for the observed excess in velocity in galaxy clusters with respect to the visible mass, the relatively flat/small slope of rotation curves in local galaxies, the observed steep rotation curves of high-redshift galaxies, and the excess of velocity in wide binary stars with separations above 3000 kau found in Gaia DR3. Last but not least, we investigate the effect of scale invariance on gravitational lensing. We show that scale invariance does not affect the geodesics of light rays as they pass in the vicinity of a massive galaxy. However, scale-invariant effects do change the inferred mass-to-light ratio of lens galaxies as compared to GR. As a result, the discrepancies seen in GR between the total lensing mass of galaxies and their stellar mass from photometry may be accounted for. This holds true both for lenses at high redshift like JWST-ER1 and at low redshift like in the SLACS sample. Of note is that none of the above observational tests require dark matter or any adjustable parameter to tweak the theory at any given mass or spatial scale. Full article

Our paper introduces a new theoretical framework called the Fractional Einstein–Gauss–Bonnet scalar field cosmology, which has important physical implications. Using fractional calculus to modify the gravitational action integral, we derived a modified Friedmann equation and a modified Klein–Gordon equation. Our research reveals non-trivial solutions associated with exponential potential, exponential couplings to the Gauss–Bonnet term, and a logarithmic scalar field, which are dependent on two cosmological parameters, m and ${\alpha }_0=t_0{H}_0$ and the fractional derivative order $\mu$. By employing linear stability theory, we reveal the phase space structure and analyze the dynamic effects of the Gauss–Bonnet couplings. The scaling behavior at some equilibrium points reveals that the geometric corrections in the coupling to the Gauss–Bonnet scalar can mimic the behavior of the dark sector in modified gravity. Using data from cosmic chronometers, type Ia supernovae, supermassive Black Hole Shadows, and strong gravitational lensing, we estimated the values of m and ${\alpha }_0$, indicating that the solution is consistent with an accelerated expansion at late times with the values ${\alpha }_0=1.38\pm 0.05$, $m=1.44\pm 0.05$, and $\mu =1.48\pm 0.17$ (consistent with ${\mathrm{\Omega }}_{m,0}=0.311\pm 0.016$ and $h=0.712\pm 0.007$), resulting in an age of the Universe $t_0=19.0\pm 0.7$ [Gyr] at 1$\sigma$ CL. Ultimately, we obtained late-time accelerating power-law solutions supported by the most recent cosmological data, and we proposed an alternative explanation for the origin of cosmic acceleration other than $\mathrm{\Lambda }$CDM. Our results generalize and significantly improve previous achievements in the literature, highlighting the practical implications of fractional calculus in cosmology. Full article

I deduce an exact and analytic Bianchi type I solution of Einstein’s field equations, which generalizes the isotropic ΛCDM universe model to a corresponding model with anisotropic expansion. The main point of the article is to present the anisotropic generalization of the ΛCDM universe model in a way suitable for investigating how anisotropic expansion modifies observable properties of the ΛCDM universe model. Although such generalizations of the isotropic ΛCDM universe model have been considered earlier, they have never been presented in this form before. Several physical properties of the model are pointed out and compared with properties of special cases, such as the isotropic ΛCDM universe model. The solution is then used to investigate the Hubble tension. It has recently been suggested that the cosmic large-scale anisotropy may solve the Hubble tension. I consider those earlier suggestions and find that the formulae of these papers lead to the result that the anisotropy of the cosmic expansion is too small to solve the Hubble tension. Then, I investigate the problem in a new way, using the exact solution of the field equations. This gives the result that the cosmic expansion anisotropy is still too small to solve the Hubble tension in the general Bianchi type I universe with dust and LIVE (Lorentz Invariant Vacuum Energy with a constant energy density, which is represented by the cosmological constant) and anisotropic expansion in all three directions—even if one neglects the constraints coming from the requirement that the anisotropy should be sufficiently small so that it does not have any significant effect upon the results coming from the calculations of the comic nucleosynthesis during the first ten minutes of the universe. If this constraint is taken into account, the cosmic expansion anisotropy is much too small to solve the Hubble tension. Full article

Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered “anomalous”. It is often used when traditional integer derivatives models fail to represent cases where the power law is observed accurately. Fractional calculus must reflect non-local, frequency- and history-dependent properties of power-law phenomena. This tool has various important applications, such as fractional mass conservation, electrochemical analysis, groundwater flow problems, and fractional spatiotemporal diffusion equations. It can also be used in cosmology to explain late-time cosmic acceleration without the need for dark energy. We review some models using fractional differential equations. We look at the Einstein–Hilbert action, which is based on a fractional derivative action, and add a scalar field, $\varphi$, to create a non-minimal interaction theory with the coupling, $\xi R{\varphi }^2$, between gravity and the scalar field, where $\xi$ is the interaction constant. By employing various mathematical approaches, we can offer precise schemes to find analytical and numerical approximations of the solutions. Moreover, we comprehensively study the modified cosmological equations and analyze the solution space using the theory of dynamical systems and asymptotic expansion methods. This enables us to provide a qualitative description of cosmologies with a scalar field based on fractional calculus formalism. Full article

In order to more accurately characterize the effects of nanoparticles on lubricant viscosity, the effects of copper dialkyl dithiophosphate (HDDP)-modified (CuDDP) nanoparticles on the dynamic viscosity of mineral oils 150N, alkylated naphthalene (AN5), diisooctyl sebacate (DIOS), and polyalphaolefins (PAO4, PAO6, PAO10, PAO40, and PAO100) were investigated at an experimental temperature of 40 °C and additive mass fraction ranging from 0.5% to 2.5%. CuDDP exhibits a viscosity-reducing effect on higher-viscosity base oils, such as PAO40 and PAO100, and a viscosity-increasing effect on lower-viscosity base oils, namely, 150N, AN5, DIOS, PAO4, PAO6, and PAO10. These effects can be attributed to the interfacial slip effect and the shear resistance of the nanoparticles. The experimental dynamic viscosity of the eight base oils containing CuDDP was compared with that calculated by the three classical formulae of nanofluid viscosity, The predicted viscosity values of the formulae deviated greatly from the experimental viscosity values, with the maximum deviation being 7.9%. On this basis, the interface slip effect was introduced into Einstein’s formula, the interface effect was quantified with the aniline point of the base oil, and a new equation was established to reflect the influence of CuDDP nanoparticles on lubricating oil viscosity. It can better reflect the influence of CuDDP on the viscosity of various base oils, and the deviation from the experimental data is less than 1.7%. Full article

Within the framework of the extended Einstein–aether–axion theory, we studied the model of a two-level aetheric control over the evolution of a spatially isotropic homogeneous Universe filled with axionic dark matter. Two guiding functions are introduced, which depend on the expansion scalar of the aether flow being equal to the tripled Hubble function. The guiding function of the first type enters the aetheric effective metric, which modifies the kinetic term of the axionic system; the guiding function of the second type predetermines the structure of the potential axion field. We obtained new exact solutions to the total set of master equations in the model (with and without cosmological constant), and studied four analytically solvable submodels in detail, for which both guiding functions are reconstructed and illustrations of their behavior are presented. Full article

In this work, we perform a comparative study of the Kantowski–Sachs (KS) and Bianchi-I anisotropic universes with Modified Chaplygin gas (MCG) as matter source. We obtain the volume and scale factors as solutions to the Einstein Field Equations (EFEs) for the anisotropic universes, and check whether the initial anisotropy is washed out or not for different values of the MCG parameters present in the solution by obtaining the anisotropy parameters for each solution. The deceleration parameter is also obtained for each solution, the significance of which is discussed in the concluding section. Interestingly there are a number of notable results that appear from our study which help us to compare and contrast the two different anisotropic models along with proper understanding of the role of MCG as matter source in these models. Full article

A class of exact (non-perturbative) models of strong gravitational waves based on Shapovalov type III spacetimes and Einstein’s vacuum equations is obtained. Exact solutions are found for the trajectories of particles and radiation in a gravitational wave in privileged coordinate systems. Exact solutions are obtained for the equations of geodesic deviation and tidal acceleration of particles in a gravitational wave in privileged coordinate systems. An explicit analytical law of transition from a privileged coordinate system to a synchronous reference system associated with a freely falling observer with an explicit selection of time and spatial coordinates is obtained. An explicit form of the metric of a gravitational wave in a synchronous frame of reference is obtained. For a synchronous frame of reference, the trajectories of particles and radiation, the deviation of geodesics, and tidal accelerations in a gravitational wave are obtained. The presented methods and approaches are applicable both to Einstein’s general theory of relativity and to modified theories of gravity. Full article

We develop an action principle to construct the field equations for dissipative/resistive general relativistic two-temperature plasmas, including a neutrally charged component. The total action is a combination of four pieces: an action for a multifluid/plasma system with dissipation/resistivity and entrainment; the Maxwell action for the electromagnetic field; the Coulomb action with a minimal coupling of the four-potential to the charged fluxes; and the Einstein–Hilbert action for gravity (with the metric being minimally coupled to the other action pieces). We use a pull-back formalism from spacetime to abstract matter spaces to build unconstrained variations for the neutral, positively, and negatively charged fluid species and for three associated entropy flows. The full suite of field equations is recast in the so-called “$3+1$” form (suitable for numerical simulations), where spacetime is broken up into a foliation of spacelike hypersurfaces and a prescribed “flow-of-time”. A previously constructed phenomenological model for the resistivity is updated to include the modified heat flow and the presence of a neutrally charged species. We impose baryon number and charge conservation as well as the Second Law of Thermodynamics in order to constrain the number of free parameters in the resistivity. Finally, we take the Newtonian limit of the “$3+1$” form of the field equations, which can be compared to existing non-relativistic formulations. Applications include main sequence stars, neutron star interiors, accretion disks, and the early universe. Full article

We investigate the Chandrasekhar mass limit of white dwarfs in various models of $f\left(R\right)$ gravity. Two equations of state for stellar matter are used: the simple relativistic polytropic equation with polytropic index $n=3$ and the realistic Chandrasekhar equation of state. For calculations, it is convenient to use the equivalent scalar–tensor theory in the Einstein frame and then to return to the Jordan frame picture. For white dwarfs, we can neglect terms containing relativistic effects from General Relativity and we consider the reduced system of equations. Its solution for any model of $f\left(R\right)=R+\beta R^m$ ($m\ge 2$, $\beta >0$) gravity leads to the conclusion that the stellar mass decreases in comparison with standard General Relativity. For realistic equations of state, we find that there is a value of the central density for which the mass of a white dwarf peaks. Therefore, in frames of modified gravity, there is a lower limit on the radius of stable white dwarfs, and this minimal radius is greater than in General Relativity. We also investigate the behavior of the Chandrasekhar mass limit in $f\left(R\right)$ gravity. 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

Einstein–Newcomb–de Sitter (ENdS) space is de Sitter’s modification of spherical space used by Einstein in his first cosmological model paper published in 1917. The modification by de Sitter incorporated the topological identification of antipodal points in space previously proposed by Newcomb in 1877. De Sitter showed that space topologically modified in this way (called elliptical or projective space) satisfies Einstein’s field equations. De Sitter also found that in a space with constant positive curvature, spectral lines of remote galaxies would be red-shifted (called the de Sitter effect). However, de Sitter’s formulae relating distances to red shifts do not satisfy observational data. The likely reason for this mismatch is that de Sitter mainly focused on space curvature and ignored the identification of antipodal points. Herein, we demonstrate that it is this particular feature that allows an almost perfect fit of the ENdS-based cosmological model to observational data. We use 1701 sources from the type Ia supernovae data sample called Pantheon+, which was previously used to fit the $\mathrm{\Lambda }$CDM model. $\mathrm{\Lambda }$CDM and ENdS diverge in their predictions for red shifts exceeding $\mathrm{z}\sim 2.3$. Since there are no available type Ia supernovae (SNe) data for higher red shifts, both models can be validated by using an additional sample of 193 gamma-ray bursts (GRBs) spanning red shifts up to $\mathrm{z}\sim 8$. This validation shows that the minimum ${\chi }^2$ for the SNe+GRBs sample is about 2.7% smaller for the ENdS space model than for the $\mathrm{\Lambda }$CDM model. Full article