Наредни састанак Семинара биће одржан у четвртак, 16. маја 2024, у сали 301ф Математичког института САНУ са почетком у 17.15.
Предавач: Зоран Ракић, Математички факултет, Универзитет у Београду
Наслов предавања: ON THE SCHWARZSCHILD TYPE METRIC IN THE NONLOCAL DE SITTER $\sqrt{dS}$ GRAVITY
Апстракт: The general theory of relativity is one of the most elegant and successful theories that predicted and explained many significant gravitational phenomena, but it is not a complete theory of gravity. One of actual approaches towards a more complete theory of gravity is its nonlocal modification. We consider nonlocal modification of the Einstein theory of gravity in framework of the pseudo-Riemannian geometry, with the nonlocal term of the form $\,\mathcal{H} R)\mathcal{F} (\Box)\mathcal{G}(R),$ where $\mathcal{H}$ and $\mathcal{G}$ are differentiable functions of the scalar curvature $R$, and $\mathcal{F} (\Box) = \sum_{n=0}^{\infty}\, f_n\Box^n$ is an analytic function of the d’Alambert operator $\Box$.
After consideration of several models of the above-mentioned type, we deal with nonlocality of the form $\mathcal{H}(R)=\mathcal{G}(R)= \displaystyle{\sqrt{R-2\,\Lambda}},$ where $\mathcal{F} (\Box)$ is an analytic function of the d’Alembert operator $\Box$ and also $\Box^{-1}$. Specially, we investigated several classes of caling factors for flat, open and closed Universe, and we find some new exact cosmological solutions. We are paid our attention to the scaling factor of the form $a(t)=At^{\frac{2}{3}}\,e^{\frac{\Lambda}{14}\,t^2}.$ This simple nonlocal de Sitter gravity model, which we denote by $\sqrt{dS}$ gravity, contains an exact vacuum cosmological solution which mimics dark energy and dark matter and is in very good agreement with the standard model of cosmology. This success of $\sqrt{dS}$ gravity motivated us to investigate how it works at lower than cosmic scale-galactic and the solar system.
Here we present our investigation of the corresponding Schwarzschild-de Sitter metric of the $\sqrt{dS}$ gravity model. To get exact solution, it is necessary to solve the corresponding nonlinear differential equation, what is very hard problem. We obtained a solution of the linearized equation, which is related to space metric far from the massive body, where gravitational field is weak. The obtained approximate solution is of particular interest for examining the possible role of non-local de Sitter gravity $\sqrt{dS}$ in describing the effects in galactic dynamics that are usually attributed to dark matter. The solution has been tested on the Milky Way and the spiral galaxy M33 and is in good agreement with observational measurements.
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