Lecture

Curved Space-Time

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In courses (2)

PHYS-427: Relativity and cosmology I

Introduce the students to general relativity and its classical tests. ...

PHYS-428: Relativity and cosmology II

This course is the basic introduction to modern cosmology. It introduces students to the main concepts and formalism of cosmology, the observational status of Hot Big Bang theory and discusses major physical processes in the early Universe. ...

Description

This lecture discusses the concept of curved space-time, providing examples and explaining the correspondence with Newton's theory. The instructor presents arguments against scalar gravity and explores the relativistic effects of motion in a curved space-time.

Instructor

Victor Gorbenko

Teaching & PhD PhD Students Jonas Dujava, Anders Wallberg, Mattia Varrone, Aleksandr Zhabin, Veronica Sacchi Courses Classical electrodynamics PHYS-324 The goal of this course is the study of the physical and conceptual consequences of Maxwell equations. Relativity and cosmology II PHYS-428 This course is the basic introduction to modern cosmology. It introduces students to the main concepts and formalism of cosmology, the observational status of Hot Big Bang theory and dis

Official source

Ontological neighbourhood

Mathematics

Geometry: Differential geometry

Related concepts (32)

Spacetime

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects such as how different observers perceive where and when events occur. Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its description in terms of locations, shapes, distances, and directions) was distinct from time (the measurement of when events occur within the universe).

General relativity

General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime.

Absolute space and time

Absolute space and time is a concept in physics and philosophy about the properties of the universe. In physics, absolute space and time may be a preferred frame. A version of the concept of absolute space (in the sense of a preferred frame) can be seen in Aristotelian physics. Robert S. Westman writes that a "whiff" of absolute space can be observed in Copernicus's De revolutionibus orbium coelestium, where Copernicus uses the concept of an immobile sphere of stars.

Gaussian curvature

In differential geometry, the Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, κ1 and κ2, at the given point: The Gaussian radius of curvature is the reciprocal of Κ. For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere, and a flat plane and a cylinder have Gaussian curvature zero everywhere. The Gaussian curvature can also be negative, as in the case of a hyperboloid or the inside of a torus.

Scalar curvature

In the mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the geometry of the metric near that point. It is defined by a complicated explicit formula in terms of partial derivatives of the metric components, although it is also characterized by the volume of infinitesimally small geodesic balls.

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