Gravitation and Cosmology最新文献

This semi-review paper studies null geodesics which exist for black hole solutions in a gravitational 4D model with an anisotropic fluid. The equations of state for the fluid and the solutions depends on the integer parameter (q=1,2,...): (p_{r}=-rho c^{2}(2q-1)^{-1},quad p_{t}=-p_{r}), where (rho) is the mass density, (c) is the speed of light, (p_{r}) and (p_{t}) are pressures in the radial and transverse directions, respectively. Circular null geodesics are explored, and a master equation for the radius (r_{*}) of a photon sphere is found, as well as the proposition on the existence and uniqueness of a solution to the master equation, obeying (r_{*}>r_{h}), where (r_{h}) is the horizon radius. Relations for the spectrum of quasinormal modes for a test massless scalar field in the eikonal approximation are overviewed and compared with the cyclic frequencies of circular null geo desics. Shadow angles are explored.

As a possible realization of Einstein’s idea of representing particles as solitons, i.e., clots of some nonlinear universal field, the Brioschi 16-spinors are introduced, these complex projective coordinates in the 8-geometry being well suited for the role of that fundamental “unitary field.” Within the scope of the 16-spinor realization of the Skyrme–Faddeev chiral model (SFCM), it is suggested to describe the family of charged leptons, including the electron, the muon and the taon, as topological solitons endowed with the Hopf topological invariant (Q_{textrm{H}}), which can be interpreted, following Faddeev, as the lepton number (mathbb{L}). For constructing axially symmetric topological soliton configurations, group theoretical analysis based on the Coleman–Palais principle of symmetric criticality is applied. Taking into account that according to Faddeev’s suggestion, these soliton configurations should have a closed string structure, the corresponding approximation method is used, its effectiveness being proven. Finally, spins and masses of the soliton configurations are found.

The behavior of black hole horizons under extreme conditions—such as near collapse or phase transitions—remains less understood, particularly in the context of soft hair and Aretakis instabilities. We show that the breakdown of conformal symmetry during the balding phase induces a topological reorganization of the horizon, leading to divergent entropy corrections and emergent pressure terms. These corrections exhibit universal scaling laws, analogous to quantum phase transitions in condensed matter systems, with extremal limits functioning as quantum critical points. Interestingly, by employing quasi-equilibrium boundary conditions, one could stabilize horizon dynamics without explicitly introducing ad hoc higher-order corrections, further limiting the universal applicability of conformal invariance in black hole physics.

The gauge gravitation theory in the Riemann–Cartan space-time is investigated in order to solve the fundamental problems of the general relativity theory. The constraints on indefinite parameters of the theory, under which the solutions of isotropic cosmology describe a nonsingular accelerating Universe, are given. Numerical solutions of cosmological equations are obtained near the limiting energy density at a transition from gravitational compression to expansion, in dependence on the energy density, in the case of flat, closed and open models. Some physical and astrophysical consequences of the gauge gravitational theory in Riemann–Cartan space-time are discussed.

The mixmaster Hořava–Lifshitz model belongs to generalized Euclidean Toda chains with 28 vectors. The longest three vectors of the spectrum play a dominant role in studying its dynamics. The truncated cosmological model is presented as a periodic three-particle Toda chain. It is associated with an affine Kac–Moody Lie algebra (A_{2}^{+}). According to the Adler–van Moerbeke criterion, the truncated Hamiltonian system is algebraically completely integrable. The phase curves wrap a torus of genus 2. The Jacobi problem of inversion of ultraelliptic integrals is solved by using theta-functions of two variables. The solutions of the dynamical problem are expressed in rational functions of Rosenhain theta-functions. They are four-periodic functions.

We investigate the behavior of light rays in a rotating observer’s frame in the Schwarzschild background. We derive the null geodesic equations and effective potential for photons in this space-time and then use them to investigate the radial and circular motion of light and its coordinate velocity. Then, we investigate some phenomena related to the motion of light in this space-time, including the Sagnac effect, the radar echo experiment, the gravitational redshift, and the gravitational analog of the space-time index of refraction. In all cases, for the Earth-fixed rotating observer, we calculate the corrections due to the Earth’s rotation (which appear through the rotational coordinate transformation), and the general-relativistic corrections that are obtained by assuming the Schwarzschild background.

A comparison between classical, relativistic and Brans–Dicke gravitational effects related to planetary shape characterization is presented. The periastron shifts for orbits around the Earth and the giant planets which can be used as tools for determinations of their shape and density distribution, are the main object of our analysis. The conditions on the parameters improving the possibility to resolve mixed effects are studied. Differing from the approach in a previous work, we now include the observational errors for the classical expansion parameters (J_{n})—which are of particular relevance for the ice giants Uranus and Neptune—as well as the corrections to gravitomagnetic effects resulting from a slight inclination of the satellite orbits. Also, some non-orbital considerations are carried out for the coefficient (J_{3}) associated to the South-North asymmetry of the mass distribution of the other two giant planets and the Earth.

We consider an anisotropic space-time model and explore the universe evolution using analytical solutions of directional scale factors. In the Bianchi type V space-time framework, a new set of exact solutions of Einstein’s field equations with dynamical gravitational and cosmological constants have been obtained. The time-dependent expansion scalar is used to illustrate the observational compatibility with the Cosmic chronometer data. The cosmographic parameters are studied using the best-fit parameter values. The model yields a consistent evolution as compared to the (Lambda)–cold dark matter model at low redshift. Further, we study the existence of finite-time singularities in the anisotropic space-time. The universe evolution with the linear equation of state has been probed for different aspects, such as the behavior of physical parameters and dissipation of anisotropy. The model may explain the accelerating universe expansion with vanishing anisotropy at late times.

A cosmological scenario with dark energy (DE), rotation and hybrid inflation is proposed with the Bianchi type II metric. At the stage of early inflation, the decay of a double scalar field is considered, with a transition to the ultrarelativistic stage of the universe evolution. A solution to the Einstein equations and scalar field equations is found, together with the energy density and pressure components of an anisotropic fluid. A description of hybrid inflation with slow and fast rolling stages is obtained. The evolution of the rotation of DE, modeled by an anisotropic fluid, is investigated. We suppose that the anisotropic fluid does not transfer rotation to other types of matter, and at the Friedmann stages, it does not transfer rotation to produced matter particles. Then we obtain the result that if our scenario models the entire evolution of the Universe, assuming that the scale factor of the universe evolves as it inflates and then expands from the Planck value to the current size of the observable Universe, we can assume that in the modern era, the rotational velocity of the anisotropic fluid is of the order (omega_{c}=10^{-11})/year. Important observations have been made on the application of our work with Sbytov and the results from the James Webb telescope in order to detect the possible rotation of the Universe.

We carry out geometric attribution of perfect fluid space-time in terms of a Riemann soliton with a torse forming vector field. It is shown that a perfect fluid space-time becomes a dark fluid space-time when we represent the timelike velocity vector field to be a torse-forming vector field. Next, we have investigated the nature of a Riemann soliton in perfect fluid space-time under certain curvature conditions in terms of the cosmological constant, the gravitational constant, energy density and isotropic pressure. We have also constructed an example of Riemann soliton in perfect fluid space-time. Finally, we have classified the Riemann soliton in a perfect fluid space-time obeying (f(r,T))-gravity in terms of energy density and isotropic pressure.