Newtonian gravitation in Maxwell spacetime

Area of Science:

• Classical Mechanics
• General Relativity
• Mathematical Physics

Background:

• Newtonian gravity is typically formulated within a fixed spacetime background.
• The relationship between different gravitational theories and their underlying spacetime structures requires clarification.

Purpose of the Study:

• To establish Maxwell spacetime as the minimal structure for Newtonian gravity.
• To investigate the equivalence between Maxwell gravitation and Newton-Cartan theory.
• To explore the nature of curvature in classical spacetimes.

Main Methods:

• Intrinsic characterization of Maxwell gravitation using primitive structures.
• Comparison of Maxwell gravitation with Newton-Cartan theory, including vacuum cases.
• Analysis of the space of possible geometrizations for Maxwell gravitation.

Main Results:

• Maxwell spacetime is shown to be appropriate for Newtonian gravity.
• Maxwell gravitation and Newton-Cartan theory are demonstrated to be equivalent, except in the vacuum case.
• Curvature in classical spacetimes is argued to possess non-conventional aspects.

Conclusions:

• Maxwell spacetime provides a fundamental framework for Newtonian gravity.
• The equivalence between Maxwell gravitation and Newton-Cartan theory is robust.
• The geometric interpretation of classical gravity is further elucidated.