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A pseudo-Riemannian manifold with Lorentzian signature.
wp-lorentzianlee-smooth-manifoldsEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require one time-like direction in the metric signature.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-lorentzianlee-smooth-manifoldsEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
General relativity treats a Lorentzian metric and related geometric fields as dynamical variables constrained by Einstein’s equations.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
einstein-general-relativityeinstein-equationwp-physics-general_relativitynlab-physics-general_relativitywp-lorentzianThis is an authored directed relation from the source endpoint to the target endpoint.
The Kerr solution is a Lorentzian manifold with a stationary, axisymmetric metric satisfying the vacuum Einstein equation.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
lee-smooth-manifoldseinstein-equationThis is an authored directed relation from the source endpoint to the target endpoint.
The Schwarzschild solution is a Lorentzian manifold with a metric satisfying the vacuum Einstein equation and spherical symmetry.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
lee-smooth-manifoldseinstein-equationThis is an authored directed relation from the source endpoint to the target endpoint.
A relativistic spacetime carries a Lorentzian metric encoding intervals, light cones, and causal structure.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
einstein-spacetimeeinstein-general-relativitywp-physics-spacetimenlab-physics-spacetimewp-lorentzianThis is an authored directed relation from the source endpoint to the target endpoint.
A spacetime metric is mathematically a Lorentzian metric on a manifold.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
wp-physics-spacetime_metriceinstein-general-relativitywp-lorentzianlee-smooth-manifolds