Concept

Metric tensor (general relativity)

Related lectures (32)

Implicit Surface Parametrizations

Explores implicit surface parametrizations and the use of metric tensors in surface parameterization.

Metric Tensor: Definition

Explores the definition and properties of the metric tensor, enabling control of geometric quantities and lengths.

Spherically Symmetric Metrics

Explores spherically symmetric metrics in flat space and their implications in gravity and spacetime.

Schwarzschild Metric: General Relativity

Explores the Schwarzschild metric in General Relativity, focusing on singularities and spherically symmetric solutions.

Intersection of Manifolds in Exercise 8.2

Covers the intersection of manifolds in exercise 8.2 and fiscal year 8.8.

Geodesics in Schwarzschild Spacetime

Explores geodesics in Schwarzschild spacetime, circular orbits, and the perihelion advance in General Relativity.

Static Isotropic Metric

Explores static isotropic metric properties and equations in physics, focusing on the behavior outside the gravitational field.

General Relativity: Energy-Momentum Tensor

Covers the Schwarzschild solution, the cosmological constant, and General Relativity as an Effective Field Theory.

Second Fundamental Tensor

Explores the second fundamental tensor and its role in calculating normal curvature on surfaces.

Penrose Diagrams: Spacetime Visualization

Explores Penrose diagrams for visualizing black hole spacetime, emphasizing the eternal nature of black holes formed by gravitational collapse.

Hodge Duality and Covariant Derivatives

Introduces Hodge duality, covariant derivatives, and key concepts in differential geometry.

Charged Particle in Minkowski Spacetime

Explores the worldline action of a charged particle in Minkowski spacetime, covering 4-vectors, intervals, Lorentz invariance, and charged particles in EM fields.

Stereographic Projection and Metric Tensors

Explores stereographic projection and metric tensors on hyperbolic planes, emphasizing isometry and conforming models.

Proper Time: Lorentz Transformations

Explores worldlines, Lorentz transformations, proper time intervals, and inertial reference frames in relativistic physics.

Lorentz-Minkowski Spacetime

Covers Lorentz-Minkowski spacetime, speed of light interpretation, isometries, and special relativity principles.

Holography in Classical Gravity

Explores hints of holography in classical black hole thermodynamics.

General Relativity: Predictions and Observations

Explores general relativity, focusing on predictions and observations, including gravitational lensing, black holes, and cosmology.

Einstein's Equations: Relativistic Mechanics

Covers Einstein's equations in non-relativistic limit and the Schwarzschild metric.

Einstein Equations

Covers the derivation of Einstein equations and the Schwarzschild metric.

Differential Geometry of Surfaces

Covers linear pressure vessels and the basics of differential geometry of surfaces, including covariant and contravariant base vectors.