Tensors and Relativity: Chapter 6

Index

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basis, orthonormal
Bianchi identities
Bianchi identities, contracted
Christoffel symbols
Christoffel symbols, symmetry of
Christoffel symbols, from the metric
Christoffel symbols, in polar coordinates
comma goes to semicolon rule
covariant derivative, of a one- form
covariant derivative
covariant derivative, commutator of
covariant derivative, of a vector
curvature
curvature, extrinsic
curvature, intrinsic
curvature, of a cylinder
curvature, of a sphere or balloon
Einstein tensor, definition of
equivalence principle
equivalence principle
Euclidian space , gif
Euler- Lagrange equations
geodesic
geodesic, as equation of motion for a free particle
geodesic, calculating for a given metric
geodesic, definition of
geodesic, extremal length of
geodesic deviation
geodesic deviation, equation of
geodesic equation
geodesics
inertial frame, local
Lagrangian, for timelike curves
local flatness theorem
manifold
manifold, differentiable
manifold, dimension of
manifold, Riemannian
metric, as a mapping
metric, as gravitational potentials
metric, connection
metric, signature of
Newtonian gravity
one- form
one- form, basis in polar coordinates
parallel transport
parallel transport, around a loop, in flat space
parallel transport, definition of
parallel transport, around a loop, in curved space
polar coordinates, tensors in
polar coordinates, vector gradient in
proper time, for curved spacetime
proper time, for flat spacetime
Pseudo- Riemannian
Ricci scalar, definition of
Ricci tensor, definition of
Riemann tensor, definition of
Riemann tensor, in a local inertial frame
Riemann tensor, number of independent components of
Riemann tensor, symmetries of
Special Relativity
tensor
tensor, curvature
transformation, of Christoffel Symbols
vector
vector, basis in polar coordinates
worldlines