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Related Concept Videos

Gravitational Force01:16

Gravitational Force

In the years before Newton, a general belief prevailed that different laws governed objects in the sky than objects on Earth. When Kepler wrote down the three laws of planetary motion, explaining in detail the geometrical properties of the planetary orbits around the Sun, there was no immediate idea to discern their connection with more fundamental laws. It was Isaac Newton who, in 1665–66, figured out the connection between planetary motion, the motion of the moon around the Earth, and the...
Gravity between Spherical Bodies01:27

Gravity between Spherical Bodies

Newton's law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, the Moon, and other planets, the law holds with an assumption that masses of spherical objects are concentrated at their respective centers.
This assumption can be proved easily by showing that the expression for gravitational potential energy between a hollow sphere of mass (M) and a point mass (m) is the same as it would be for a pair of extended...
The Principle of Superposition and the Gravitational Field01:17

The Principle of Superposition and the Gravitational Field

The principle of superposition applies to gravitational forces of objects that are sufficiently far apart. It states that the net gravitational force on a point object is the vector sum of the gravitational forces on it due to various objects. The principle helps calculate the force by listing the individual forces and then vectorially summing them up. However, it should be noted that the principle of superposition is not always apparent. In the presence of a second force, the first force could...
Newton's Law of Gravitational Attraction01:24

Newton's Law of Gravitational Attraction

Sir Isaac Newton established the universality of the law of gravitational attraction based on empirical evidence and inductive reasoning. He published his work in Philosophiae Naturalis Principia Mathematica ("the Principia") on July 5, 1687.
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Tidal Forces01:06

Tidal Forces

The origin of Earth's ocean tides has been a subject of continuous investigation for over 2000 years. However, the work of Newton is considered to be the beginning of the proper understanding of the phenomenon. Ocean tides are the result of gravitational tidal forces. These same tidal forces are present in any astronomical body; they are responsible for the internal heat that creates the volcanic activity on Io, one of Jupiter's moons, and the breakup of stars that get too close to black holes.
Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...

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Updated: May 12, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
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Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Frozen-In Gravitational Fields.

Felipe A Asenjo1, Maricarmen A Winkler1, Luca Comisso2,3,4

  • 1Universidad Adolfo Ibáñez, Facultad de Ingeniería y Ciencias, Santiago 7491169, Chile.

Physical Review Letters
|May 11, 2026
PubMed
Summary
This summary is machine-generated.

General relativity allows for "frozen-in" gravitational fields and conserved magnetic flux, revealing topological constraints on spacetime evolution. This framework offers new insights into the nonlinear dynamics of spacetime.

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Area of Science:

  • * Physics
  • * General Relativity
  • * Nonlinear Dynamics

Background:

  • * Spacetime evolution is governed by complex nonlinear Einstein field equations.
  • * Understanding emergent geometric structures in evolving spacetime is a key challenge.
  • * Existing frameworks struggle to fully capture the dynamics of these structures.

Purpose of the Study:

  • * To explore a novel formulation of Einstein equations analogous to nonlinear electrodynamics.
  • * To investigate the existence and properties of gravitational field connections and field lines.
  • * To identify conserved quantities and topological constraints in dynamic spacetimes.

Main Methods:

  • * Employed a mathematical formulation of Einstein equations mirroring nonlinear electrodynamics.
  • * Analyzed the emergence of gravitational field connections and associated field lines.
  • * Investigated the conditions for gravitational field "frozen-in" behavior.
  • * Derived conserved quantities such as gravitational magnetic flux and helicity.

Main Results:

  • * Demonstrated that general relativity admits "frozen-in" gravitational field connections and field lines.
  • * Identified an ideal Ohm-type condition enabling this gravitational frozen-in behavior.
  • * Revealed a conserved "gravitational magnetic" flux within the framework.
  • * Discovered a conserved gravitational helicity with topological significance.

Conclusions:

  • * The proposed framework provides a new perspective on spacetime dynamics.
  • * Gravitational frozen-in behavior and conserved fluxes impose topological constraints on spacetime evolution.
  • * This work offers an organizing principle for understanding the nonlinear dynamics of spacetime.