The Role of Dark Matter in Gravitational Dynamics:

Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
29-08-2024

Abstract: 

This study explores the interplay between dark matter and negative gravitating mass, investigating their combined influence on the accelerated expansion of the universe. Our analysis reveals that when the effective mass, including dark matter contributions, exceeds matter mass, negative gravitating mass becomes dominant, leading to repulsive gravitational effects.

Key Findings:

Negative Gravitating Mass: The dominance of negative effective mass over matter mass results in negative gravitating mass (Mɢ < 0).

Repulsive Gravity: Negative gravitating mass generates repulsive gravitational effects, contributing to the accelerated expansion of the universe.

Dark Matter's Role: While the nature of dark matter remains uncertain, its gravitational influence contributes to the overall effective mass, impacting the dominance of negative gravitating mass.

Limitations of General Relativity: The observed accelerated expansion challenges the predictions of general relativity, necessitating the introduction of concepts like dark energy and negative effective mass.

Conclusion: 

Our research demonstrates that dark matter plays a pivotal role in shaping the gravitational dynamics of the universe. By incorporating dark matter into the total matter mass (Mᴍ), and considering the influence of negative effective mass (Mᵉᶠᶠ), we observe that the negative gravitating mass Mɢ becomes dominant. This dominance leads to repulsive gravitational effects, significantly contributing to the accelerated expansion of the universe.

#DarkMatter, #NegativeGravitatingMass, #AcceleratedExpansion,

Generation of Dark Energy in the Universe: Dominance in Gravitational Dynamics

Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
29 August 2024

The Dark Energy is Generated When Mᵉᶠᶠ>Mᴍ, Gravitating Mass Mɢ<0 Dominates the Gravitational Universe!

Mɢ = Mᴍ + Mᵉᶠᶠ 

The relationship between different types of mass in the context of dark energy and gravitational dynamics in the universe.. 

The interpretation:

• Mɢ represents the gravitating mass. This is the mass that contributes to the gravitational effects we observe in the universe.

• Mᴍ represents the matter mass. This is the conventional mass associated with matter in the universe, such as stars, planets, and galaxies.

• Mᵉᶠᶠ represents the effective mass. This term could be associated with the influence of forces or energy, such as dark energy, on the system.

• The equation Mɢ = Mᴍ + Mᵉᶠᶠ suggests that the gravitating mass (Mɢ) is the sum of the matter mass (Mᴍ) and the effective mass (Mᵉᶠᶠ).

The second part of the statement asserts that dark energy is generated when the effective mass (Mᵉᶠᶠ) exceeds the matter mass (Mᴍ). This implies that the contribution of dark energy (or the forces and phenomena it represents) becomes significant when it dominates over the conventional matter mass.

Finally, gravitating mass (Mɢ) being less than zero (Mɢ < 0) indicates that this total mass (including both matter and effective mass) dominates the gravitational behavior of the universe. When the gravitating mass is negative, it suggests that gravity may exhibit repulsive characteristics, contributing to the structure and dynamics of the universe in a way influenced by dark energy.

In summary, the statement highlights a scenario where dark energy, represented by the effective mass, plays a dominant role in the gravitational dynamics of the universe when it exceeds the contribution from ordinary matter, especially under conditions where the gravitating mass is negative (Mɢ < 0), potentially leading to repulsive gravitational effects.

#DarkEnergy, #GravitationalDynamics, #EffectiveMass, #MatterMass, #GravitatingMass,

Summary of the Dark Energy Equation and Its Integration with Classical Mechanics:

Soumendra Nath Thakur

28-08-2024

The derived equation Mɢ = Mᴍ + Mᵉᶠᶠ builds upon the foundational equation Mɢ = Mᴍ + Mᴅᴇ, established through empirical research by A. D. Chernin et al. in 'Dark Energy and the Coma Cluster of Galaxies,' and its consistent application within classical mechanics. In this formulation, Mᵉᶠᶠ represents the effective mass associated with dark energy. This approach adheres to classical mechanics principles and the author's rigorous mathematical framework, particularly in converting potential energy (including dark energy) into kinetic energy. This conversion affects both local gravitational dynamics and cosmic expansion.

The mathematical rigor underlying the equation Mɢ = Mᴍ + Mᵉᶠᶠ is evident from its derivation and application, as detailed in the research paper. It provides a robust theoretical framework by establishing the equivalence of negative effective mass with potential energy and its conversion into kinetic energy. This framework enhances our understanding of the interaction between classical potential energy, gravitational dynamics, motion, and cosmic structures, explaining galactic recession and the broader implications for cosmic expansion.

Conceptual Innovations in the Extension of Classical Mechanics:

Soumendra Nath Thakur

28-08-2024

The research paper titled "Extended Classical Mechanics: Effective Mass and Acceleration Boost in Motion and Gravitational Dynamics," authored by Soumendra Nath Thakur, is meticulously designed to naturally underscore the conceptual innovations inherent in this extension of classical mechanics. The work represents a significant advancement within classical science, introducing novel ideas that are crucial for readers to comprehend the ground breaking contributions to the field.

This extension not only deepens our understanding of classical mechanics but also provides a necessary framework for interpreting new physical phenomena. The structure of the paper is intentionally crafted to highlight these theoretical advancements, ensuring that the innovations are effectively communicated and appreciated within the broader scientific community.

The derived equation Mɢ = Mᴍ + Mᵉᶠᶠ builds upon the foundational equation Mɢ = Mᴍ + Mᴅᴇ, established through empirical research by A. D. Chernin et al. in 'Dark Energy and the Coma Cluster of Galaxies,' and its consistent application within classical mechanics. In this formulation, Mᵉᶠᶠ represents the effective mass associated with dark energy. This approach adheres to classical mechanics principles and the author's rigorous mathematical framework, particularly in converting potential energy (including dark energy) into kinetic energy. This conversion affects both local gravitational dynamics and cosmic expansion.

The mathematical rigor underlying the equation Mɢ = Mᴍ + Mᵉᶠᶠ is evident from its derivation and application, as detailed in the research paper. It provides a robust theoretical framework by establishing the equivalence of negative effective mass with potential energy and its conversion into kinetic energy. This framework enhances our understanding of the interaction between classical potential energy, gravitational dynamics, motion, and cosmic structures, explaining galactic recession and the broader implications for cosmic expansion.

#EffectiveMass, #ClassicalMechanics, #ConceptualInnovations, #GravitationalDynamics, #MathematicalRigour,

Calculation of Effective mass and Gravitating mass: Extension to Classical mechanics

Calculation file attached: Here

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

27-08-2024

This expression F = (Mᴍ + Mᵉᶠᶠ)aᵉᶠᶠ, reflects an extended classical mechanics approach where the total force F is associated with both the matter mass Mᴍ and the effective mass Mᵉᶠᶠ. Here, the effective mass Mᵉᶠᶠ is introduced as an additional term that modifies the system's dynamics in motion. The effective acceleration aᵉᶠᶠ represents the combined effect of traditional acceleration and the influence of effective mass.

F = (Mᴍ + Mᵉᶠᶠ)aᵉᶠᶠ, Mᵉᶠᶠ generated when F acting in motion (v)

• F is the total force applied to the object, measured in Newtons N.
• Mᴍ is the matter mass of the object, representing its traditional inertial mass, measured in kilograms (kg).
• Mᵉᶠᶠ is the effective mass, which arises due to the interaction of the object with the applied force during motion, measured in kilograms (kg).
• aᵉᶠᶠ is the effective acceleration experienced by the object, which accounts for both the matter mass and the effective mass in the system, measured in meters per second squared (m/s²).
Calculation in attached file.

#EffectiveMass #GravitatingMass #EffectiveMassCalculation #GravitatingMassCalculation