Роль эллиптических интегралов в расчете гравитационного линзирования заряженной черной дыры Вейля, окруженной плазмой

In this paper, we mainly aim at highlighting the importance of (hyper-)elliptic integrals in the study of gravitational effects caused by strongly gravitating systems. For this, we study the application of elliptic integrals in calculating the light deflection as it passes a plasmic medium, surrounding a charged Weyl black hole. To proceed with this, we consider two specific algebraic ansatzes for the plasmic refractive index, and we characterize the photon sphere for each of the cases. This will be used further to calculate the angular diameter of the corresponding black hole shadow. We show that the complexity of the refractive index expressions, can result in substantially different types of dependencies of the light behavior on the spacetime parameters. В этой статье мы в основном стремимся подчеркнуть важность (гипер) эллиптических интегралов в изучении гравитационных эффектов, вызванных сильно гравитирующими системами. Для этого мы изучаем применение эллиптических интегралов при вычислении отклонения света при его прохождении через плазменную среду, окружающую заряженную черную дыру Вейля. Чтобы продолжить это, мы рассмотрим два конкретных алгебраических анзаца для показателя преломления плазмы и охарактеризуем фотонную сферу для каждого из случаев. Это будет использоваться в дальнейшем для вычисления углового диаметра соответствующей тени черной дыры. Мы показываем, что сложность выражений показателя преломления может привести к существенно разным типам зависимостей поведения света от пространственно-временных параметров.

Demonstrating Gravitational Lensing Using Solar Eclipses

As encouraged by the interesting paper “Solar eclipses as a teaching opportunity in relativity” by Overduin et al.,awe made measurements of the angular deflections of neighboring stars during the 9 March 2016 total solar eclipse as imaged by National University of Singapore (NUS) students, to verify a result of general relativity. In this project, we used these images and measured the stars’ pixel positions and transformed them to equatorial coordinates using a similar approach to Overduin et al., with a few modifications. Instead of solving to determine the pixel scale and rotation, we performed a plate solution using the software AstroImageJ which enables accounting for the image’s higher order distortion. This data is found in the image’s Flexible Image Transport System (FITS) header. Image star pair separations were then compared to their database separations after determining how the individual deflections affect angular separation. Our experimental results have large uncertainties and were deemed imprecise to confirm the effects of gravitational light deflection. We include a detailed analysis and discussion on this educational project.

Field Approach for General Relativity

The general theory of relativity is based on expressing gravity by means of the metric tensor and its elements instead of some fields as in electrodynamics. This work starts with by defining some vector fields for metric or metric tensor. After metric and metric tensor are expressed in terms of these fields, the geodesic equations and Einstein equations are derived for these fields. Finally, perihelion precession and light deflection are recalculated, as two different applications of the introduced fields.

Light deflection angle through velocity profile of galaxies in f(R) model

We explore a new realisation of the galactic scale dynamics via gravitational lensing phenomenon in power-law f(R) gravity theory of the type $$f(R)\propto R^{1+\delta }$$ f ( R ) ∝ R 1 + δ with $$\delta<<1$$ δ < < 1 for interpreting the clustered dark matter effects. We utilize the single effective point like potential (Newtonian potential + f(R) background potential) obtained under the weak field limit to study the combined observations of galaxy rotation curve beyond the optical disk size and their lensing profile in f(R) frame work. We calculate the magnitude of light deflection angle with the characteristic length scale (because of Noether symmetry in f(R) theories) appearing in the effective f(R) rotational velocity profile of a typical galaxy with the model parameter $$\delta \approx O(10^{-6})$$ δ ≈ O ( 10 - 6 ) constrained in previous work. For instance, we work with the two nearby controversial galaxies NGC 5533 and NGC 4138 and explore their galactic features by analysing the lensing angle profiles in f(R) background. We also contrast the magnitudes of f(R) lensing angle profiles and the relevant parameters of such galaxies with the generalised pseudo-isothermal galaxy halo model and find consistency.