Einstein field equations extended to fractal manifolds: A fractal perspective

Khalili Golmankhaneh, Alireza; Jørgensen, Palle E.T.; Schlichtinger, Agnieszka Matylda

doi:10.1016/j.geomphys.2023.105081

Cited by 6 publications

(1 citation statement)

References 40 publications

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“…Fractal calculus arises through an extension of conventional calculus, encompassing differential equations whose solutions manifest as functions characterized by fractal support, including fractal sets and curves [21]. This type of calculus is algorithmic in nature and offers a more streamlined approach when compared to alternative methodologies [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Fractal Schrödinger equation: implications for fractal sets

Khalili Golmankhaneh,

Pellis,

Zingales

2024

J. Phys. A: Math. Theor.

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This paper delves into the world of fractal calculus, investigating its implications for fractal sets. It introduces the Fractal Schrödinger Equation and provides insights into its consequences. The study presents a General Solution for the Time-Dependent Schrödinger Equation, unveiling its core aspects. Exploring quantum mechanics in the context of fractals, the paper analyzes the Probability Density of the Radial Hydrogen Atom, unveiling its behavior within fractal dimensions. The investigation extends to deciphering the intricate Energy Levels of the Hydrogen Atom, uncovering the interplay of quantum mechanics and fractal geometry. Innovatively, the research applies the Fractal Schrödinger Equation to Simple Harmonic Motion, leading to the introduction of the Fractal Probability Density Function for the Harmonic Oscillator. The paper employs a series of illustrative ﬁgures that enhance the comprehension of the ﬁndings. By intertwining quantum mechanics and fractal mathematics, this research paves the way for deeper insights into their relationship.

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Section: Introductionmentioning

confidence: 99%

Fractal Schrödinger equation: implications for fractal sets

Khalili Golmankhaneh,

Pellis,

Zingales

2024

J. Phys. A: Math. Theor.

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Power series solution for fractal differential equations

Khalili Golmankhaneh,

Bongiorno,

Jebali

et al. 2024

Boll Unione Mat Ital

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Schwarzschild spacetime in fractal dimensions: Deflection of light, supermassive black holes and temperature effects

El-Nabulsi,

Anukool

2024

Mod. Phys. Lett. A

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In this paper, we construct a Schwarzschild metric in the fractal dimension based on fractal calculus, and we study the deflection of light near the sun. It was observed that the new fractal spherically symmetric spacetime metric may describe supermassive black holes, which have been detected through various astronomical observations such as SDSS. We have discussed the deflection of light by the gravitational field of the sun. It was observed that the total deflection of light is affected by the fractal dimension. To estimate the numerical value of the fractal dimension, we have used the 2004[Formula: see text]analysis of almost 2 million VLBI observations of 541 radio sources made by 87 VLBI sites, which estimates the factor [Formula: see text] based on PNN formalism. It was observed that the fractal dimension is roughly less than unity. However, our analysis showed that large bending gravity gives fractal dimensions lower than unity to some extent. We also gave a naïve idea about the emission thermal Unruh process in fractal dimension. It was observed that both the temperature and the entropy of black holes are affected by the fractal dimension, and that for low numerical values, the entropy of the black hole is enhanced.

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Einstein field equations extended to fractal manifolds: A fractal perspective

Cited by 6 publications

References 40 publications

Fractal Schrödinger equation: implications for fractal sets

Fractal Schrödinger equation: implications for fractal sets

Power series solution for fractal differential equations

Schwarzschild spacetime in fractal dimensions: Deflection of light, supermassive black holes and temperature effects

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