Topological defects in contracting universes

P P Avelino1, C J A P Martins, C Santos

  • 1Centro de Fisica do Porto e Departamento de Fisica da Faculdade de Ciencias, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal. ppavelin@fc.up.pt

Physical Review Letters
|January 7, 2003
PubMed

Related Concept Videos

Schwarzschild Radius and Event Horizon01:21

Schwarzschild Radius and Event Horizon

No object with a finite mass can travel faster than the speed of light in a vacuum. This fact has an interesting consequence in the domain of extremely high gravitational fields.
The minimum speed required to launch a projectile from the surface of an object to which it is gravitationally bound so that it eventually escapes the object’s gravitational field is called the escape velocity. The escape velocity is independent of the mass of the object. Merging the idea of escape velocity with the...
Space-Time Curvature and the General Theory of Relativity01:17

Space-Time Curvature and the General Theory of Relativity

In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of motion,...
Imperfections in Crystal Structure: Point, Line and Plane Defects01:25

Imperfections in Crystal Structure: Point, Line and Plane Defects

A perfect crystal, in theory, has a uniform structure with the same unit cell and lattice points throughout. However, any deviation from this periodic arrangement is known as an imperfection or defect. These defects can be categorized into three types: point, line, and plane defects.Point defects occur when there is a deviation from the ideal due to missing atoms, displaced atoms, or additional atoms. These imperfections might occur due to imperfect packing during crystallization or because of...
Imperfections in Crystal Structure: Stoichiometric Point Defects01:26

Imperfections in Crystal Structure: Stoichiometric Point Defects

Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...
Torsion in Vector Calculus01:20

Torsion in Vector Calculus

A toy train ascending a winding track that curves and tilts offers an intuitive view of torsion, a key geometric concept in the study of space curves. While curvature measures how sharply a path bends, torsion captures how the path twists out of the plane of bending. This twisting behavior is crucial in understanding three-dimensional motion and is precisely described using the Frenet–Serret framework.At each point along a space curve, the Frenet–Serret frame consists of three orthogonal unit...
Divergence Theorem in 3D Space01:20

Divergence Theorem in 3D Space

In vector calculus, flux measures the total flow of a vector field through a surface. For a closed surface in three-dimensional space, this means measuring how much of the field passes outward through every point on the boundary. Directly calculating this flux can be difficult when the surface has a complicated or irregular shape. The Divergence Theorem provides a powerful alternative by relating surface flux to behavior inside the enclosed region.The Divergence Theorem states that the outward...