Physics

In the present work, we investigate the possibility of obtaining stellar interiors for static self-gravitating systems describing an anisotropic matter distribution in the framework of Rastall gravity through gravitational decoupling by means of minimal geometric deformation approach. Due to Rastall gravity breaks down the minimal coupling matter principle, we have provided an exhaustive explanation about how Israel-Darmois junction conditions work in this scenario. Furthermore, to obtain the deformed space-time, the mimic constraint procedure has been used. In order to check the viability of this proposal, we have applied it to the well known Tolman IV solution. A complete thermodynamic description of the effects introduced by the additional source is given. Additionally, the results have been compared with their similes in the picture of pure general relativity, pure Rastall gravity and within the framework of general relativity including gravitational decoupling. To perform the mathematical and graphical analysis we have taken the gravitational decoupling constant α and the Rastall's parameter λ as free parameters and the compactness factor describing the general relativity sector to be 0.2 . Besides, to provide a more realistic picture we have bounded both parameters α and λ by using real observational data to explore the limits of the theory under this particular model. Applications to study neutron or quark stars are suggested by using this methodology.

In this paper, we analyze deflection angle of photon from magnetized black hole within non-linear electrodynamics with parameter β . In doing so, we find the corresponding optical spacetime metric and then we calculate the Gaussian optical curvature. Using the Gauss-Bonnet theorem, we obtain the deflection angle of photon from magnetized black hole in weak field limits and show the effect of non-linear electrodynamics on weak gravitational lensing. We also analyzed that our results reduces into Maxwell's electrodynamics and Reissner-Nordström (RN) solution with the reduction of parameters. Moreover, we also investigate the graphical behavior of deflection angle w.r.t correction parameter, black hole charge and impact parameter.

In this paper, we define a new velocity having a dimension of (Length ) α /(Time) and a new acceleration having a dimension of (Length ) α /(Time ) 2 , based on the fractional addition rule. We then discuss the fractional mechanics in one dimension. We show the conservation of fractional energy, and formulate the Hamiltonian formalism for the fractional mechanics. As a matter of illustration, we exhibit some examples for the fractional mechanics.

We demonstrate how to make the coordinate transformation or change of variables from Cartesian coordinates to curvilinear coordinates by making use of a convolution of a function with Dirac delta functions whose arguments are determined by the transformation functions between the two coordinate systems. By integrating out an original coordinate with a Dirac delta function, we replace the original coordinate with a new coordinate in a systematic way. A recursive use of Dirac delta functions allows the coordinate transformation successively. After replacing every original coordinate into a new curvilinear coordinate, we find that the resultant Jacobian of the corresponding coordinate transformation is automatically obtained in a completely algebraic way. In order to provide insights on this method, we present a few examples of evaluating the Jacobian explicitly without resort to the known general formula.

Independent investigations of nuclear quadrupole resonance (NQR) and of stripes in high- T c cuprates find a small deviation of doped-hole density h from the doping level of L a 2−x S r x Cu O 4 . The value observed with NQR, x−h≈0.02 , agrees closely with the density of itinerant holes, p ~ , responsible for suppression of 3D-AFM, as obtained from stripe incommensurability. The stripe model's assumption that doped holes in L a 2−x S r x Cu O 4 reside at oxygen sites, and that doped electrons in L n 2−x C e x Cu O 4 ( Ln=Pr,Nd ) reside at copper sites, is (to a large degree) confirmed with NQR. The NQR finding of doped-hole probabilities in oxygen and copper orbitals of HgB a 2 Cu O 4+δ and other oxygen-enriched high- T c cuprates, P p ≃ P d ≃1/2 , as well as of oxygen-doped YB a 2 C u 3 O 6+y , P p ≃2 P d ≃2/3 , is interpreted with the stripe model in terms of excess oxygen atoms in the Cu O 2 planes and CuO chains.

It is shown in Einstein gravity that the cosmological constant Lambda introduces a graviton mass m into the theory, a result that will be derived from the Regge-Wheeler-Zerilli problem for a particle falling onto a Kottler-Schwarzschild mass with Lambda. The value of m is precisely the Spin-2 gauge line appearing on the Lambda versus m2 phase diagram for Spin-2, the partially massless gauge lines introduced by Deser & Waldron and described as the Higuchi bound. Note that this graviton is unitary with only four polarization degrees of freedom (helicities plus & minus 2 and 1, but not 0 because a scalar gauge symmetry removes it). The conclusion is drawn that Einstein gravity (with Lambda) is a partially massless gravitation theory which has lost its helicity 0 due to a scalar gauge symmetry. That poses a challenge for gravitational wave antennas as to whether they can measure the loss of this gauge symmetry. Also, given the recent results measuring the Hubble constant Ho from LIGO-Virgo data, it is then shown that Lambda can be determined from the LIGO results for the graviton mass m and Ho. This is yet another multi-messenger source for determining the three parameters Lambda, m, and Ho in astrophysics and cosmology, at a time when there is much disparity in measurements of Ho.

The aim of the article is to develop a stochastic interpretation of the quantum mechanics by E. Nelson. Based on the consideration of the averaged states of a chaotically wandering particle, the stationary and time-dependent stochastic Schrodinger-Euler-Poisson equations (47) and (92) were obtained, which coincided with the corresponding Schrodinger equations up to coefficients. In this case, the ratio of the reduced Planck constant to the particle mass is expressed through the averaged characteristics of a three-dimensional random process in which the considered wandering particle participates. The obtained stochastic equations (39), (47), (88), (92) are suitable for describing quantum phenomena and averaged states of particles not only at atomic and subatomic scales, but also similar stochastic systems of the micro- and macroworld.

We discuss relations between Dirac and Majorana-like field operators with self/antiself charge-conjugate states. The connections with recent models of several authors were found. KEYWORDS: Dirac; field operators; Majorana; Neutral particles; QFT.

This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent relativistic quantum electrodynamics, the corresponding Feynman diagrams and S#-matrix elements are derived. In the special case of electron-electron scattering (Moller scattering), the explicit second order element <f|S#(2)|i> is deduced. Moreover, assuming the slow motions for two external electrons, the approximation of <f|S#(2)|i> yields a divergence-free Coulomb potential.

As a candidate of dark matter, and related to many fundamental physics issues, the primordial black hole (PBH) is a crucial topic. However, so far the existence of PBHs is still not confirmed, and currently running GW detectors are still not able to distinguish them from the normal astrophysical BHs. In this article, we propose that the GWs (of PBH binary mergers) could interact with the very widespread background galactic magnetic fields in the Milky way, to produce the perturbed electromagnetic waves (EMWs) with unique characteristics of frequencies, waveforms, spectra and polarizations. In order to be distinguished from astrophysical black holes, only the PBHs with masses less than the solarmass are considered here, and their binary mergers will radiate GWs in frequencies much higher above the plasma frequency of interstellar medium (ISM), so corresponding perturbed EMWs (in the same frequencies to such GWs) can propagate through the ISM until the Earth. Our estimations show that, for the sub-solar mass PBH binary mergers within the Milky way (disk or halo), the strengths of the perturbed EMWs turn into constant levels around 10^{-12} Tesla (for magnetic components) and around 10^{-10}Watt m^{-2} (for energy flux densities) at the Earth, generally for all cases of different PBH masses (and not dependent on the distance of sources), and the same mass ratio of the PBH binary gives the same strength (at the Earth) of perturbed EMWs despite different PBH masses (GW frequencies) or binary distances. Differently, for the PBH binary mergers outside the Milky way, the perturbed EMWs at Earth have lower strengths (and depend on the distance of sources), but for some part of distance range, they would also be detectable. If such EM signals and special EM counterpart of GWs from PBHs could be detected by space- or land-based EMWs detectors, it may provide direct evidence of the PBHs.