[Paper Review] Energy Conservation at the Gravitational Collapse

Vladim ́ õr Majern ́ õk|arXiv (Cornell University)|Jan 1, 2008

Relativity and Gravitational Theory1 references5 citations

TL;DR

This paper proposes a modified classical gravitational field theory where energy conservation requires a test particle's rest mass to decrease as it gains gravitational energy, leading to a revised force law. The resulting theory ensures all field quantities remain finite and positive for all r ≥ 0, yielding finite energy release during gravitational collapse and a horizon that shifts to the origin, contrasting with the Schwarzschild metric.

ABSTRACT

We apply the principle of energy conservation to the motion of the test particle in gravitational field by requiring that its energy, gained by gravitation, has to be balanced by decrease of its rest mass. Due to the change of mass in gravitational field Newton’s force law between gravitating bodies is modified, too. With this modified force law we build up the the classical field theory of gravitation in which all relevant field quantities are in the definition domain r ∈ [0, ∞) finite and positive. We show that under such circumstances, the energy release at any gravitational collapse is finite. On the other side, the energy conservation leads to an equation which relates the mass change of the test particle due to gravitation and the metric of the corresponding gravitational field. The mass change in Newton’s gravitational field lead to a remarkable simple metric which shifts, in contrast to the Schwarzschild metric, the horizon of events to the gravity center of the gravitational collapse.

Motivation & Objective

• To address the inconsistency in energy conservation during gravitational collapse by linking energy gain to rest mass decrease.
• To reformulate Newton’s gravitational force law by incorporating mass variation due to gravitational potential.
• To construct a classical field theory where all field quantities remain finite and positive across all radial distances r ∈ [0, ∞).
• To derive a metric that shifts the event horizon to the center of mass, differing from the Schwarzschild solution.
• To demonstrate that energy release during gravitational collapse remains finite under the proposed framework.

Proposed method

• Apply energy conservation by requiring that gravitational energy gain is balanced by a reduction in the test particle’s rest mass.
• Derive a modified Newtonian force law that accounts for the mass variation due to gravitational potential.
• Construct a classical field theory using the modified force law, ensuring all field quantities are finite and positive for all r ≥ 0.
• Derive a metric equation relating the mass change of the test particle to the gravitational field’s geometry.
• Use the mass change equation in Newtonian gravity to obtain a simple, finite metric that shifts the horizon to the origin.
• Compare the resulting metric with the Schwarzschild metric, highlighting the absence of a coordinate singularity at r = 0.

Experimental results

Research questions

• RQ1 How can energy conservation be consistently applied to test particles in gravitational fields when their rest mass changes?
• RQ2 What modifications to Newton’s force law arise from requiring energy conservation via mass-energy equivalence?
• RQ3 What is the resulting gravitational metric under the assumption of finite, positive field quantities for all r ≥ 0?
• RQ4 How does the horizon structure of the gravitational field differ from the Schwarzschild solution under this new framework?
• RQ5 Is the total energy released during gravitational collapse finite under this modified theory?

Key findings

• The energy released during gravitational collapse is finite under the proposed theory, avoiding infinite energy outputs seen in classical models.
• The modified force law leads to a gravitational field theory where all field quantities are finite and positive across the entire radial domain r ∈ [0, ∞).
• The derived metric, unlike the Schwarzschild metric, places the event horizon at the origin (r = 0), not at a finite radius.
• The mass change of the test particle due to gravity leads to a simple, finite metric that avoids singularities.
• The theory provides a classical alternative to general relativity that maintains energy conservation through variable rest mass.
• The horizon shift implies a fundamentally different causal structure compared to the Schwarzschild solution, with implications for black hole formation.