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Mathematical methods in general relativity

Table of contents

Coordinate charts in general relativity

Tensors in general relativity

Theorems in general relativity

ADM formalism

Apparent horizon

BTZ black hole

Canonical quantum gravity

Cartan–Karlhede algorithm

Construction of a complex null tetrad

Energy condition

Fermi–Walker transport

Frame fields in general relativity

Globally hyperbolic manifold

Linearized gravity

Mathematics of general relativity

Penrose–Hawking singularity theorems

Positive energy theorem

Scalar–vector–tensor decomposition

Solving the geodesic equations

Test particle

Trapped surface

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