Conceptual Alignment of Apparent Mass and Dark Energy Effective Mass in Gravitational Dynamics: Extended Classical Mechanics.

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

22-09-2024

This presentation explores the interconnected concepts of Negative Effective Mass, highlighting how both Apparent Mass (−Mᵃᵖᵖ) and Dark Energy Effective Mass (Mᴅᴇ) exert negative influences on gravitational dynamics. It emphasizes that these negative mass properties contribute to repulsive forces that counteract gravitational attraction. The relationship between Apparent Mass and total gravitating mass (Mɢ) is established, paralleling the framework proposed by Chernin et al., where Mɢ is derived from the sum of matter mass and dark energy effective mass. The significance of these concepts is particularly pronounced under extreme conditions, such as high velocities and strong gravitational fields, underscoring their importance in cosmic dynamics. Ultimately, the discussion illustrates how Apparent Mass and Dark Energy Effective Mass are conceptually aligned, both playing pivotal roles in shaping gravitational behaviours within galaxy clusters.

1. Negative Effective Mass: 

Both the Apparent Mass (−Mᵃᵖᵖ) and the Dark Energy Effective Mass (Mᴅᴇ) are characterized as having a negative influence on gravitational dynamics. This is central to both concepts, where negative mass contributes to repulsive forces that counteract gravitational attraction.

2. Influence on Gravitating Mass: 

The response emphasizes how Apparent Mass affects the total gravitating mass (Mɢ), showing that it can be expressed as Mɢ = Mᴍ + (−Mᵃᵖᵖ). This is similar to the framework from Chernin et al., where the total gravitating mass is also derived from the combination of matter mass and the dark energy effective mass: Mɢ = Mᴍ + Mᴅᴇ.

3. Context of High Velocities and Strong Fields: 

Both descriptions note that the effects of these negative mass concepts become significant under extreme conditions, such as high velocities or strong gravitational fields, reinforcing the idea that they are crucial for understanding cosmic dynamics.

4. Role in Gravitational Dynamics: 

The alignment is further supported by stating that dark energy’s negative mass plays a significant role in local gravitational dynamics within galaxy clusters, mirroring the implications of Apparent Mass in altering expected gravitational behaviours.

Overall, the presentation conveys that Apparent Mass and Dark Energy Effective Mass share a conceptual foundation, both influencing gravitational dynamics through their negative mass properties.

Keywords: Apparent Mass, Dark Energy, Gravitational Dynamics,

References:

1. Chernin, A. D., Bisnovatyi-Kogan, G. S., Teerikorpi, P., Valtonen, M. J., Byrd, G. G., & Merafina, M. (2013). Dark energy and the structure of the Coma cluster of galaxies. Astronomy and Astrophysics, 553, A101. https://doi.org/10.1051/0004-6361/201220781

2. Thakur, S. N. (2024). Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. Preprints.org (MDPI). https://doi.org/10.20944/preprints202409.1190.v2

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