Antigravitational Motion and the Gravitational Potential of the Universe:

 

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

 

February 20, 2025

 

Abstract

Antigravitational motion, driven by negative effective mass, occurs counter to the gravitational potential of massive bodies within a system. However, more fundamentally, it represents a counter-motion to the gravitational potential of the universe, owing to the universal dominance of dark energy. In modern astrophysics, dark energy's negative effective mass (Mᴅᴇ<0) governs large-scale cosmic motion, expressed as Mɢ = Mᴍ + Mᴅᴇ.

 

The Extended Classical Mechanics (ECM) framework refines this understanding by introducing negative apparent mass (-Mᵃᵖᵖ), which dominates interactions involving massive bodies (Mᴍ), leading to a negative effective mass (Mᵉᶠᶠ < 0). This relationship is formulated as Mɢ = Mᵉᶠᶠ where Mᵉᶠᶠ = Mᴍ + (-Mᵃᵖᵖ). The resulting antigravitational effects propel sufficiently massive bodies, particularly black holes, against the gravitational potential of the universe.

 

Beyond dark energy’s role, ECM suggests that black holes significantly contribute to galactic recession, reinforcing large-scale cosmic expansion. These insights provide a deeper explanation of antigravitational motion, demonstrating that it not only opposes local gravitational potentials but also fundamentally counteracts the gravitational influence of the universe itself.

 

Keywords: Antigravitational Motion, Negative Effective Mass, Extended Classical Mechanics (ECM), Dark Energy Influence, Galactic Recession,

 

Mathematical Presentation

Motion driven by antigravitational effects occurs counter to the gravitational potential of the interacting massive bodies with matter mass (Mᴍ) in the system. However, more fundamentally, this motion is a counter-motion to the gravitational potential of the universe, as the dominance of dark energy is universal.

 

In modern astronomy and astrophysics, dark energy’s negative effective mass (Mᴅᴇ < 0) governs large-scale motion, driving massive bodies against the universe’s gravitational potential. This relationship is expressed as:

 

Mɢ = Mᴍ + Mᴅᴇ

 

In the Extended Classical Mechanics (ECM) framework, the dominance of negative apparent mass (-Mᵃᵖᵖ) over interacting massive bodies (Mᴍ) results in a negative effective mass (Mᵉᶠᶠ < 0). This negative effective mass not only causes local antigravitational motion but also fundamentally opposes the universe’s gravitational potential. In alignment with modern astrophysical expressions, this relationship is formulated as:

 

Mɢ = Mᵉᶠᶠ where Mᵉᶠᶠ = Mᴍ + (-Mᵃᵖᵖ)

 

Here, the negative apparent mass (-Mᵃᵖᵖ) induces antigravitational effects through the resulting negative effective mass (Mᵉᶠᶠ < 0). According to ECM principles, sufficiently massive bodies undergoing gravitational collapse develop extreme antigravitational properties, propelling them counter to the universe’s gravitational potential.

 

Beyond the role of dark energy, black holes within galaxies contribute to galactic recession, reinforcing the observed large-scale expansion. These insights establish that while antigravitational motion counters the gravitational potential of massive bodies in a system, it is, more fundamentally, a counter-motion to the gravitational potential of the universe itself, since dark energy's influence is universal.

 

Mathematical Consistency with ECM and Modern Astrophysics

Mathematically, my presentation is logically aligned with ECM's application and the interpretation of modern astronomy and astrophysics regarding the influence of dark energy on motion. However, let me carefully analyse the relationship Mɢ = Mᴍ + Mᴅᴇ and how ECM refines it.

 

A. D. Chernin et al. describe how dark energy contributes to the dynamics of galaxy clusters, effectively behaving as a negative mass component in the system. This is expressed in the form:

 

Mɢ = Mᴍ + Mᴅᴇ

 

Where: Mᴍ represents the total matter mass (baryonic + dark matter). Mᴅᴇ represents the contribution of dark energy, which has a negative effective mass (Mᴅᴇ < 0).

 

This formulation reflects the competition between the attractive gravitational force of Mᴍ and the repulsive effect of dark energy Mᴅᴇ, which acts as an antigravitational force at cosmic scales.

 

ECM’s Refinement of This Relationship

ECM builds upon this concept by introducing negative apparent mass (-Mᵃᵖᵖ), which emerges due to extreme gravitational collapse, such as in black holes. According to ECM principles, the effective mass of a system is modified by this additional term:

 

Mᵉᶠᶠ = Mᴍ + (-Mᵃᵖᵖ)

 

Where: -Mᵃᵖᵖ represents the apparent negative mass effect induced by gravitational collapse.

 

Thus, in ECM, the effective gravitational mass that determines motion follows:

 

Mɢ= Mᵉᶠᶠ = Mᴍ + (-Mᵃᵖᵖ)

 

Which remains consistent with the modern astrophysical formulation Mɢ = Mᴍ + Mᴅᴇ because in ECM, the dominant antigravitational term, -Mᵃᵖᵖ, captures both the effects of dark energy and additional influences from black holes.

 

Implications on Motion and Gravitational Potential

Since Mᴅᴇ < 0, its presence in astrophysical systems drives motion counter to the gravitational potential of the universe, leading to cosmic expansion.

 

In ECM, the dominance of -Mᵃᵖᵖ ensures that not only dark energy but also collapsed massive bodies contribute to this counter-motion, reinforcing large-scale recession effects.

 

The logical step in ECM is that a sufficiently large system, dominated by negative apparent mass effects (-Mᵃᵖᵖ), would exhibit a net negative effective mass (Mᵉᶠᶠ < 0), which aligns with the observed acceleration of cosmic structures.

 

Conclusion

My presentation remains mathematically logical within ECM’s framework because it retains the modern astrophysical relation Mɢ = Mᴍ + Mᴅᴇ while extending it with the ECM refinement Mɢ = Mᵉᶠᶠ = Mᴍ + (-Mᵃᵖᵖ).

 

The dominant role of -Mᵃᵖᵖ explains how motion is not only counter to local gravitational potentials but also fundamentally counter to the gravitational potential of the universe.

 

This interpretation strengthens the explanation of galactic recession and black hole-driven contributions, offering an ECM-consistent extension to Chernin et al.'s findings.

 

References

[1] Dark energy and the structure of the Coma cluster of galaxies. A. D.  Chernin, G. S.  Bisnovatyi-Kogan, P.  Teerikorpi, M. J.  Valtonen, G. G.  Byrd, M.  Merafina. Astronomy and Astrophysics. Vol. 553, Art. no. A101, 2013. https://doi.org/10.1051/0004-6361/201220781

[2] A Nuanced Perspective on Dark Energy: Extended Classical Mechanics. Thakur.  S. N. http://doi.org/10.20944/preprints202411.2325.v1

[3] Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. Thakur, S. N. https://doi.org/10.20944/preprints202409.1190.v3

[4] Classical Mechanics: Systems of Particles and Hamiltonian Dynamics by H. Goldstein, C. Poole, and J. Safko

[5] Dark Matter and the Dinosaurs: The Astounding Interconnectedness of the Universe" by Lisa Randall