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   

Negative Apparent Mass:

February 20, 2025

Extended Classical Mechanics (ECM) is also based on this idea of ​​introducing negative apparent mass (-Mᵃᵖᵖ), which arises due to extreme gravitational collapse, such as in black holes.

Mass Concepts in Classical, Relativistic, and Extended Classical Mechanics (ECM):

February 19, 2025

The book Concepts of Mass in Classical and Modern Physics by Max Jammer presents traditional mass concepts, primarily defining mass as either inertial mass or rest mass. However, these descriptions do not account for dynamic effective mass or apparent mass.

Extended Classical Mechanics (ECM) expands upon these conventional definitions by introducing negative apparent mass and negative effective mass, extending the concept of mass beyond ordinary matter to include the effects of dark matter. This distinction is crucial in understanding mass interactions at different cosmic scales.

Mass Equivalence in Different Frameworks

In classical mechanics, inertial mass is equivalent to gravitational mass: 

m = m𝑔 

​In relativistic mechanics, rest mass (invariant mass) is also equated to gravitational mass: 

m = m𝑔

​In Extended Classical Mechanics (ECM), gravitating mass (Mɢ) is equivalent to effective mass (Mᵉᶠᶠ), which includes both matter mass (Mᴍ) and negative apparent mass (−Mᵃᵖᵖ):

Mɢ = Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

where matter mass (Mᴍ) is the combined mass of ordinary matter (Mᴏʀᴅ) and dark matter mass (Mᴅᴍ):

Mᴍ = Mᴏʀᴅ + Mᴅᴍ 

Effective Mass at Celestial and Galactic Scales

At celestial or planetary scales within a galaxy, effective mass (Mᵉᶠᶠ) can be either positive or negative, depending on the balance between matter mass and negative apparent mass:

If matter mass dominates (Mᴍ > Mᵃᵖᵖ), then effective mass is positive:

Mᵉᶠᶠ > 0

If negative apparent mass dominates (Mᵃᵖᵖ > Mᴍ ), then effective mass becomes negative:

Mᵉᶠᶠ < 0

The ECM expression for gravitating mass can also be rewritten as:

Mɢ = Mᴍ + (−Mᵃᵖᵖ)

This formulation aligns conceptually with the expression discussed by A. D. Chernin et al. in Dark Energy and the Structure of the Coma Cluster of Galaxies:

Mɢ = Mᴍ + Mᴅᴇ, 

where Mᴅᴇ represents the effective mass of dark energy, which is always negative:

Mᴅᴇ < 0

While ECM extends this concept by incorporating negative apparent mass alongside dark energy effects, both frameworks recognize the role of negative mass contributions in gravitational dynamics.

This framework provides a more comprehensive approach to understanding mass interactions in the universe, bridging the gap between classical mechanics and modern astrophysical observations.

Author:

Soumendra Nath Thakur

Summary: Photon Energy Conservation and Gravitational Lensing in Extended Classical Mechanics:

February 18, 2025

Extended Classical Mechanics (ECM) establishes a conservation framework for photon energy interactions within the curvature of gravitational fields. By extending the energy-momentum relation p = hf/c to include apparent mass (Mᵃᵖᵖ) and negative inertia, ECM reveals that gravitational lensing involves a symmetric energy exchange. As a photon follows the curvature of a gravitational field, it undergoes a blueshift when approaching a gravitational well, gaining energy, and a redshift when receding, losing energy. This process maintains the photon's intrinsic energy (E) while offering a clear explanation for both light bending and its energy transformation in gravitational fields.

#ECMinterpretation #GravitationalLensing in #gravitationalfield not in #curvatureinspacetime #GravitationalLensingInECM

About Black Hole Motion, Negative Apparent Mass, and Galactic Recession in Extended Classical Mechanics (ECM):

Author: Soumendra Nath Thakur  

Date: February 18, 2025

Introduction

Extended Classical Mechanics (ECM) challenges the conventional view of black holes as stationary entities. Instead, they are dynamic, with motion exceeding the speed of light, dictated by the ratio of wavelength to time period surpassing the Planck scale limit.

Key Concepts

1. Black Holes and Motion:

   - Originating from gravitational collapse, black holes must exhibit rapid motion.

   - This motion is a result of their unique properties, going beyond the speed of light.

2. Transformation During Gravitational Collapse:

   - The baryonic mass of a massive body undergoes a transformation into negative apparent mass (-Mᵃᵖᵖ) during collapse.

   - This leads to a corresponding negative effective mass (Mᵉᶠᶠ < 0), altering the object's behavior.

3. Anti-Gravitational Properties:

   - The negative apparent mass gives black holes anti-gravitational properties.

   - This causes them to move away from gravitational wells, actively accelerating.

4. Galactic Interaction:

   - The interaction between a black hole's negative effective mass and the galaxy's positive effective mass creates a binding effect.

   - This keeps the black hole within the galaxy, rather than allowing it to escape.

5. Galactic Recession:

   - The entire galaxy undergoes recession, influenced by the interplay of effective masses.

   - This provides an alternative explanation to the large-scale recession of galaxies.

6. Local Scale Interactions:

   - Interactions between a black hole and nearby massive bodies are governed by their effective masses and force balance.

   - A black hole with a larger negative effective mass can attract nearby objects.

Conclusion

This refined interpretation offers deeper insights into black hole behavior and its impact on galactic recession and structure formation. Black holes are not just gravitational sinks but active drivers of cosmic motion, contributing to the universe's expansion. This framework provides a new perspective on the fundamental nature of black holes and their role in the universe.