In this study, we characterize a Lorentzian manifold (M-n, g)of dimension >= 3satisfying Gray's C-perpendicular to condition. First, we prove that if a Lorentzian manifold M satisfies Gray's C-perpendicular to condition and whose Ricci curvature annihilates the curvature transformation, then in the neighborhood of a point where |del r(g)| not equal 0,Mis a generalized Robertson-Walker (GRW) space-time. Next, it is established that if a quasi-Einstein Lorentzian manifold satisfies Gray's C-perpendicular to condition, then in the neighborhood of a point where beta not equal 0, M is a GRW space-time. Furthermore, it is confirmed that any perfect fluid GRW space-time is Bach-flat.
A study of the behavior of cosmological models near singular points has been conducted, based on a previously proposed model of an asymmetric scalar Higgs doublet with potential interactions between the components. Classes of global behavior of cosmological models and the relationship between the nature of singular points and these classes were identified: the presence of initial and final singularities and rebound points.
Einstein taught us through general relativity that mathematics/geometry is the language of nature. He also taught us that mass can be converted into energy. Our work advocates for the conversion of energy into matter, such as mass, charge, and the cosmological constant, discussed within the context of colliding waves in general relativity. The Big Bang is thought to be the prototype example of creating matter at large from an infinite concentration of energy. Our proposal provides an alternative example by using the power of nonlinear collision processes in which energy transmutes into solid matter. Our motto in this paper is: Collision is creation, so let there be light to collide and create!
We study the evolution of the universe using several Rip cosmologies within the framework of f(R,Σ,T) gravity, utilizing spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) models. There are three types of Rip models. Employing the Little Rip (LR) scenario, we derive exact expressions for the pressure, energy density, and the equation of state parameter and investigate their time evolution. Particular emphasis is placed on examining the physical acceptability of the model through the behavior of key quantities such as the energy conditions (NEC, DEC, and SEC) and the transition of pressure from positive to negative values, which naturally explains the shift from decelerated to accelerated expansion. The analysis demonstrates that the energy density remains positive and decreases with cosmic time, while the pressure evolves from a radiation-like regime to a dark-energy-dominated phase. Moreover, violation of the strong energy condition, a necessary feature for late-time cosmic acceleration, is explicitly realized. Our findings indicate that the the LR scenario in f(R,Σ,T) gravity provides a viable description of the late-time universe, avoids finite-time singularities, and offers an alternative explanation to standard dark energy models.
We explore anisotropic cosmological models within the framework of modified gravity theory, specifically f(R,L_m) gravity, where the gravitational Lagrangian depends on both the Ricci scalar R and the matter Lagrangian L_m . We adopt the locally rotationally symmetric (LRS) Bianchi type I metric to investigate anisotropic cosmic evolution, which allows for directional dependence in the expansion rates while retaining analytical tractability. The modified field equations are derived using a particular form of the function f(R,L_m)=R/2+L_m^α , where α quantifies the strength of the curvature-matter coupling. To obtain exact solutions, we consider power-law forms for the directional scale factors and study the cosmological dynamics under three distinct physically motivated assumptions on the equation of state: p+ρ=0 , ρ-p=0 , and ρ+3p=0 . In each case, the field equations are systematically reduced to algebraic forms and solved analytically. The resulting solutions exhibit both isotropic and anisotropic behavior, depending on the specific relationship between the expansion exponents and the coupling parameter α . For p+ρ=0 , the solutions suggest an effective cosmological constant-like behavior, with possible higher-dimensional interpretations where some dimensions remain static or compactified. Under the ρ-p=0 condition, a richer structure of solutions emerges, admitting both static, partially expanding, and fully anisotropic power-law evolutions, where anisotropy is directly controlled by the coupling parameter α . The analysis under ρ+3p=0 also yields anisotropic power-law solutions, where expansion and contraction coexist in different spatial directions. Overall, this work demonstrates the richness of cosmological behavior in f(R,L_m) gravity and highlights its potential to address key open problems in modern cosmology.
Quasinormal frequencies in the Einstein–Aether theory have been extensively investigated with the help of numerical methods. Here we derive analytic expressions for quasinormal modes of test scalar, electromagnetic and Dirac fields, using the higher-order WKB method and expansion in terms of 1/ℓ , where ℓ is the multipole number. The obtained analytic formulas are surprisingly precise and in agreement with previously published numerical data. In addition, we check the validity of the correspondence between null geodesics and eikonal quasinormal modes.
A fast progress in the observational technologies in astrophysics provides a unique possibility for detailed observations of black holes in the nearest future. It will be possible to verify general relativity (GR) and its numerous modifications in the strong field limit by using observational data from advanced cosmic interferometric observatories. We review the modeled images of a rotating black hole in different appropriate cases: a luminous distant background, a thin accretion disk, and a luminous moving hot spots in relativistic jets along the black hole rotation axis. Detailed observations of astrophysical supermassive black holes SgrA* and M87* will be possible within the nearest 10 years by using the Millimetron Space Observatory proposed and developed by domestic scientists.
The space radio telescope RadioAstron is a unique instrument for studying extremely weak radio signals in the centimeter and decimeter wavelength ranges [1]. Acting as the space-based baseline of an interferometer, the spacecraft has achieved a record-breaking angular resolution, opening new possibilities for investigating black holes, pulsars and the structure of the interstellar medium. A key feature of its onboard system is the use of a hydrogen frequency standard synchronized with a ground-based tracking station. The difference in gravitational potentials between the spacecraft and the ground station leads to a relativistic frequency shift [2] (RedShift effect), providing experimental confirmation of general relativity and Einstein’s equivalence principle. This study proposes methods for a high-precision measurement of this effect, based on an original Doppler shift compensation scheme [3] and statistical analysis of gravitational observation sessions. The results allow for an estimation of the cumulative violation parameter, contributing to further verification of the fundamental principles of general relativity. The paper also discusses prospects for new high-precision experiments.
The propagation of X-ray or gamma-ray radiation in the electromagnetic field of a relativistically rotating pulsar is studied within the framework of vacuum nonlinear electrodynamics (NED). Metric tensors are constructed, along the geodesics along which two normal waves propagate in the strong electromagnetic field of a relativistically rotating pulsar. The laws of motion of two X-ray or gamma-ray pulses carried by these normal waves are indicated in a parametric form. The parameter in a specially selected coordinate system is the z coordinate. Tangent vectors to the rays are constructed, and the laws of ray curvature are investigated with their help when the z parameter changes from the point of emission of X-ray or gamma-ray pulses to the detector. It is shown that these rays are bent in two mutually perpendicular planes. This circumstance leads to a modification of the NED lensing effect compared to the NED lensing observed in the electromagnetic field of a slowly rotating pulsar.
Modern cosmology faces a large number of unsolved questions. These include the problem of cosmological singularity, the lack of explanations for the nature of dark matter, the existence of well-developed galaxies in the few hundred million years after the Big Bang, and a number of other questions. In this regard, a different approach to constructing cosmology is proposed. It examines a generalization of General Relativity based on Weyl’s principle of scale invariance. This generalization allows one to arrive at a nonstandard cosmological solution in which the Big Bang is absent. Its application leads to new explanations for the redshift in the spectra of distant galaxies and the cosmic microwave background, as well as to a new view on the nature of dark matter.
We investigate how the rotation of celestial bodies influences the gravitational redshift of light, utilizing the Kerr metric. We refine this approach by considering rotational effects which include such phenomena as frame dragging that alters the space-time fabric around these objects. We derive an expression for gravitational redshift using the Kerr metric and analyze its variation with respect to rotation and the point of light emission, particularly, between equatorial and polar regions. Our findings, derived from simplified relativistic mechanics about angular momentum, show that gravitational redshift is significantly affected by both the object’s rotation and the position of light emission. By applying our results to celestial bodies such as the Sun and millisecond pulsars, we demonstrate that the gravitational redshift is not uniform across the surface of a rotating body, allowing us to differentiate the redshift originating from different locations on the surface. This variation provides new insights into the role of rotation in gravitational redshift.
We present a new class of singularity-free interior solutions for anisotropic compact stars with spherical symmetry. By prescribing a specific pressure anisotropy, exact solutions to Einstein’s field equations are obtained and matched smoothly to the Schwarzschild exterior metric. The model parameters are determined using the boundary condition of vanishing radial pressure. The physical viability of the model is demonstrated through an analysis of the pulsar 4U1820-30, characterized by a radius of 9.1 km and mass M=1.58M_⊙.
The geometrization of physics may be expressed in the context of finding equations of motion for different objects rather than the conventional concept of allocating field variables geometrically. This can be performed by identifying physical quantities in terms of scalars, vectors and tensors described in various geometries that admit a nonvanishing curvature and torsion of space-time. The effect of covariant differentiation may represent the effect of physical fields on the trajectory of objects. We adopt a method in which spinning and charged objects are expressed using a parameter transformation between two nearby paths separated by a deviation vector in Riemannian, non-Riemannian, and Finslerian geometries. Moreover, the concept of parameter transformation is being revisited in the context of Clifford space as a step of combining microphysics and macrophysics.
This paper proposes a new scalar field cosmological model aimed at studying the late-time acceleration of the universe, based on a parametrization of the deceleration parameter. The main objective is to constrain fundamental cosmological parameters by integrating the latest measurements of the Hubble parameter from various observational datasets, including BAO, BAO + R19, CC + SC + BAO, and CC + SC + BAO + R19 from recent galaxy surveys. With a redshift range covering 0.106
The article probes exploration of the probable existence of relativistic compact celestial entities within a modified f(R,T) theory. We employ the Karmarkar and Tolman solutions along with two noteworthy and sustainable forms of f(R,T) gravity for an anisotropic distribution of matter. Within the solution of three relativistic compact star contenders, we opt for certain observational data to obtain the values of constants. We demonstrate a few physical characteristics of these relativistic compact celestial entities consisting of their formations, transverse and radial pressure, stability, anisotropy measure, energy density, EoS parameters and energy conditions.
We complement the recent theory of Master Space-Teleparallel Supergravity ( MS_p -TSG) [1], which reviews the acceleration and inertial effects, with two more consequences. We first address the “locality hypothesis” for extension of Lorentz invariance within Special Relativity to accelerated observers. This replaces the accelerated observer with a continuous infinity of hypothetical momentarily comoving inertial observers along its word line. This assumption is valid only if the curvature of the world line could be ignored. In the general case, this is actually untenable. In the framework of MS_p -TSG theory, the locality hypothesis introduces strict restrictions, replacing the curved MS_p with the flat MS _p . Our strategy, therefore, goes beyond the locality hypothesis to recover MS_p by invoking a general deformation MS _p→MS_p , which, as a corollary, is solely responsible for acceleration and inertia effects. This significantly improves the standard metric and other relevant geometric structures referred to a noninertial frame in Minkowski space-time for relativistic velocities and arbitrary characteristic acceleration lengths. Second, we address the inertial effects in semi-Riemannian and more general post-Riemannian geometries. We derive the relativistic inertial force in semi-Riemannian space, and the inertial force acting on an extended rotating body moving in Riemann–Cartan space. The relativistic Weak Equivalence Principle is a consequence of the theory, at which inertial effects gradually decrease at large Lorentz factors and vanish in the photon limit.
Twisted space-times are logical extensions of Friedmann cosmological models, Lorentz–Minkowski space-times, Einstein-de Sitter space-times, generalized Robertson–Walker (GRW) space-times, and static Einstein space-times. The purpose of this manuscript is to investigate the characteristics of twisted space-times that are almost pseudo-Ricci symmetric (briefly, A(PRS) _n ). We establish the sufficient conditions under which A(PRS) _n twisted space-times are GRW space-times, and under which A(PRS) _n space-times are twisted space-times. The necessary and sufficient condition for A(PRS) _n twisted space-times to be perfect fluid space-times is derived. We also prove that the vorticity and shear of A(PRS) _n twisted space-times filled with perfect fluid vanish identically. Consequently, we establish the equation of state and energy conditions. The non-existence of Ricci symmetric A(PRS) _n twisted space-times is ensured.
We study the cosmic expansion scenario of the universe based on Tsallis, Rényi and Sharma–Mittal holographic dark energy models in the framework of f(R,L_m) gravity theory. A numerical solution of our f(R,L_m) dominated model is obtained, and then combined data sets are utilized to estimate the best-fit values of the free parameters of the model. The behavior of matter-energy density, the equation of state (EoS) parameter, and several other cosmological functions are calculated and plotted against cosmological time. For specific values of the numerical parameters of the models, it is found that our results are in good agreement with recent observations.
We establish a new SU(N) symmetric model of interaction between the fields of four types: a multiplet of vector fields, which describes the so-called color aether, a multiplet of pseudoscalar fields, which is associated with a multi-component cosmic dark matter, gauge and gravitational fields. The extended Lagrangian of the model contains a new constructive element based on the covariant SU(N) symmetric divergence of the multiplet of vector fields; this new element, being a multiplet of scalars from the point of view of space-time transformations, and a color vector from the point of view of the SU(N) group space, gives us a possibility to properly formulate a multi-axionic extension of the Peccei-Quinn theory. A hypothesis of a spontaneous polarization of the multi-axionic color aether in the early Universe is presented. A set of self-consistent master equations of the model is derived. An application to cosmology is considered: the obtained master equations are solved for a truncated test model based on the Bianchi-I space-time platform.
In this note, we consider the Henneaux–Teitelboim version of Unimodular Gravity (UG) and its deformations in the form of gauge theories with spontaneously broken diffeomorphism invariance. The actions defining such theories depends on the curvature of an SO(3,ℂ) gauge connection and the field strength of a (real) 3-form (or equivalently its dual vector density). We obtain the pure connection action of the theory from the corresponding Plebanski action by integrating out auxiliary fields. Then we show that the Henneaux–Teitelboim form of UG can be included in a wider class of theories which propagate two (complex) degrees of freedom.
