Extended classical mechanics offers an alternative
framework for understanding the behaviour of gravitational waves, particularly
in the context of binary black hole mergers, by focusing on the dynamic interactions
of mass and energy rather than relying on spacetime curvature as described by
general relativity.
Key Predictions and Insights:
Gravitational Waves as Momentum Exchange: Extended
classical mechanics views gravitational waves not as ripples in spacetime but
as manifestations of momentum and energy exchanges between massive bodies. In
binary black hole mergers, these waves represent the oscillatory exchange of
kinetic and potential energy between the interacting masses. This perspective
shifts the focus from spacetime distortion to direct interactions governed by
the dynamics of the merging bodies.
Effective Mass and Wave Generation:
The theory introduces the concept of effective mass,
including both ordinary and apparent (negative) mass components, which
influence the generation of gravitational waves. During a merger, the
fluctuating effective mass and associated energy dynamics produce waves that
propagate as energy disturbances. These waves encode information about the mass
distribution, energy exchange rates, and dynamic forces within the merging
system.
Amplitude and Frequency Characteristics:
Unlike general relativity, which ties gravitational wave
properties directly to spacetime curvature changes, extended classical
mechanics predicts that the amplitude and frequency of gravitational waves are
closely related to the variations in effective mass and momentum transfer
during the merger. As the black holes spiral inward, the increasing rate of
energy exchange intensifies the wave amplitude and frequency, culminating in a
peak at the point of coalescence.
Energy Conservation in Mergers:
The framework emphasizes conservation laws where the total
energy—kinetic and potential—remains consistent even as gravitational waves
carry energy away from the system. The merger does not violate energy
conservation principles but redistributes energy between the black holes and
the emitted gravitational waves, ensuring that total system energy, including
radiated waves, aligns with the mechanics of interaction rather than spacetime
deformation.
Avoidance of Singularities:
Extended classical mechanics inherently avoids singularity
issues by not requiring infinite densities or curvatures. The predicted
behaviour of gravitational waves during black hole mergers reflects continuous
energy dynamics without the need for spacetime to reach undefined states. This
smooth transition in wave production offers a more physically intuitive picture
of the merger process.
Implications for Detection:
Gravitational waves detected from binary black hole
mergers would still align with the observational data but would be interpreted
as energy flows rather than spacetime disturbances. The phase and amplitude
evolution of these waves, as observed by detectors like LIGO and Virgo, would
still provide insights into the mass, spin, and dynamics of the merging black
holes, but through the lens of direct force interactions.
Conclusion:
In the context of binary black hole mergers, extended
classical mechanics predicts that gravitational waves are the result of dynamic
energy exchanges between interacting masses rather than distortions of
spacetime. This approach provides a consistent and alternative interpretation
of wave generation, emphasizing momentum transfer and energy conservation, and
aligns well with observational evidence without requiring the complex
geometrical constructs of general relativity.
References:
1.
Thakur, S. N. (2024c). 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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