A p-Adic Matter in a Closed Universe

In this paper, we introduce a new type of matter that has origin in p-adic strings, i.e., strings with a p-adic worldsheet. We investigate some properties of this p-adic matter, in particular its cosmological aspects. We start with crossing symmetric scattering amplitudes for p-adic open strings and related effective nonlocal and nonlinear Lagrangian which describes tachyon dynamics at the tree level. Then, we make a slight modification of this Lagrangian and obtain a new Lagrangian for non-tachyonic scalar field. Using this new Lagrangian in the weak field approximation as a matter in Einstein gravity with the cosmological constant, one obtains an exponentially expanding FLRW closed universe. At the end, we discuss the obtained results, i.e., computed mass of the scalar p-adic particle, estimated radius of related closed universe and noted p-adic matter as a possible candidate for dark matter.

The Metric of Space-Time Curvature in a Weak Gravitational Field and it’s Consequence in Newtonian Approximation

In Newtonian mechanics, space and time are separate but in General, Relativity is unified. It is considered that the space in the weak-field approximation is quasi-static and it arises from a perfect field whose particles have very small velocity in comparison to light velocity in this coordinate system and the metric is a gravitational potential tensor of rank two which implies the field of empty space. If each point of an area in N-dimensional space there existed a corresponding definite tensor, where the components of the tensor are the function of space and space acts as the strong or weak gravitational field.

The Newtonian potential of a static Dirac spinor particle

The gravitational theory including spinor particle is formulated with the suggestion of tetrad fields [Formula: see text] by Utiyama, Kibble and Weinberg.[Formula: see text] We might take the metric [Formula: see text] as a constraint, that is used the method of Lagrange multiplier. In the weak-field approximation we calculate the metric of a static Dirac spinor particle proton and obtain that the metric is a diagonal [Formula: see text] which coincides with the anticipative result of Newtonian Gravitational potential.

Quasi-uniform gravitational field of a disk revisited

We calculate the quasi-uniform gravitational field of a disk in the weak-field approximation and demonstrate an inappropriateness of preceding results. The Riemann tensor of this field is determined. The nonexistence of the uniform gravitational field is proven without the use of the weak-field approximation. The previously found difference between equations of motion for the momentum and spin in the accelerated frame and in the quasi-uniform gravitational field also takes place for the disk. However, it does not violate the Einstein equivalence principle because of the nonexistence of the uniform gravitational field.

Boosted Kerr Black Hole in the Presence of Plasma

In this work, we obtain the deflection angle for a boosted Kerr black hole in the weak field approximation using the optics in a curved spacetime developed by J. L. Synge in 1960. We study the behavior of light in the presence of plasma by considering different distributions: uniform plasma, singular isothermal sphere, non-singular isothermal gas sphere, and plasma in a galaxy cluster. We found that the dragging of the inertial system along with the boosted parameter Λ affect the value of the deflection angle. As an application, we studied the magnification for both uniform and singular isothermal distributions.

The diagnostic potential of the weak field approximation for investigating the quiet Sun magnetism: the Si I 10 827 Å line

Aims. We aim to investigate the validity of the weak field approximation (WFA) for determining magnetic fields in quiet regions of the solar photosphere using the polarization caused by the Zeeman effect in the Si I10 827 Å line.Methods. We solved the NLTE line formation problem by means of multilevel radiative transfer calculations in a three-dimensional (3D) snapshot model taken from a state-of-the-art magneto-convection simulation of the small-scale magnetic activity in the quiet solar photosphere. The 3D model used is characterized by a surface mean magnetic field strength of about 170 G. The calculated Stokes profiles were degraded because of the atmospheric turbulence of Earth and light diffraction by the telescope aperture. We apply the WFA to the StokesI,Q,U,Vprofiles calculated for different seeing conditions and for the apertures of the VTT, GREGOR, EST and DKIST telescopes. We compare the inferred longitudinal and transverse components of the magnetic field with the original vertical and horizontal fields of the 3D model.Results. We find that with a spatial resolution significantly better than 0.5″ the surface maps of the magnetic field inferred from the Stokes profiles of the Si I10 827 Å line applying the WFA are close to the magnetic field of the model on the corrugated surface, corresponding to line optical depth unity at Δλ ≈ 0.1 Å for a disk-center line of sight. The correlation between them is relatively high, except that the inferred longitudinal and transverse components of the magnetic field turn out to be lower than in the 3D model.Conclusions. The use of the WFA for interpreting high-spatial-resolution spectropolarimetric observations of the Si I10 827 Å line obtained with telescopes like GREGOR, EST, and DKIST allows the longitudinal and transverse components of the magnetic field to be retrieved with reasonable precision over the whole quiet solar photosphere, the result being worse for telescopes of lower aperture.