On fractional and fractal Einstein's field equations
Modern Physics Letters A, vol.36, no.5, 2021 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 36 Issue: 5
- Publication Date: 2021
- Doi Number: 10.1142/s0217732321500309
- Journal Name: Modern Physics Letters A
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH
- Keywords: Fractional Einstein's field equations, Lorentz invariance violation, spatially-varying cosmological constant
- Van Yüzüncü Yıl University Affiliated: Yes
Abstract
In this study, Einstein's field equations are derived based on two dissimilar frameworks: the first is based on the concepts of "fractional velocity"and "fractal action"motivated by Calcagni's approach to fractional spacetime while the second is derived based on fractal calculus which is a generalization of ordinary calculus that include fractal sets and curves. The fractional theory displays a breakdown of Lorentz invariance. It was observed that a spatially dependent cosmological constant emerges in the fractional theory. A connection between the fractional order parameter and the dimensionless parameter γ arising in the parameterized post-Newtonian (PPN) formalism is observed. A confrontation with very long-baseline radio interferometry targeting quasars 3C273 and 3C279 is done which proves that the fractional order parameter is within the range 0.99980 < α < 1.00004. Moreover, emergence of quantum Hawking radiation is realized in the theory supporting Hawking's best calculations that black holes are not black. Nevertheless, based on the fractal calculus approach, there is a conservation of the Lorentz invariance and absence of spatially-dependent cosmological constant. The theory depends on the fractal order 0 < β < 1 and gives rise to a fractal Schwarzschild radius of the massive body greater than the conventional radius besides a fractal Hawking's temperature less than the standard one. However, the confrontation with radio interferometry targeting quasars 3C273 and 3C279 gives 0.999997444β < 1.0000128.