See also
Cauchy Surface,
Globally Hyperbolic Spacetime,
Initial Data Set,
Kerr Metric,
Metric Signature,
Metric Tensor,
Metric
Tensor Index,
Positive Definite Tensor,
Pseudo-Euclidean Space,
Pseudo-Riemannian
Manifold,
Reissner-Nordstroem Metric,
Schwarzschild Metric,
Semi-Riemannian
Manifold,
Semi-Riemannian Metric,
Smooth Manifold,
Strong
Pseudo-Riemannian Metric,
Strong Riemannian
Metric,
Weak Pseudo-Riemannian Metric,
Weak Riemannian Metric
This entry contributed by Christopher
Stover
Explore with Wolfram|Alpha
References
Ratcliffe, J. G. Foundations of Hyperbolic Manifolds. New York: Springer-Verlag, 2006.Sachs,
R. K. and Wu, H. General
Relativity for Mathematicians. New York: Springer-Verlag, 1977.Snygg,
J. A
New Approach to Differential Geometry Using Clifford's Geometric Algebra.
New York: Springer Science+Business Media, 2012.Referenced on Wolfram|Alpha
Lorentzian Manifold
Cite this as:
Weisstein, Eric W., with contributions by Christopher Stover. "Lorentzian Manifold." From MathWorld--A
Wolfram Resource. https://mathworld.wolfram.com/LorentzianManifold.html
Subject classifications
such that 
and the index 
associated with the metric
tensor 
satisfies 
.
of dimension 
is Lorentzian if it comes equipped with a metric
tensor 
of metric signature 
when negative squares
are listed first, or 
when positive squares
are listed first.
