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"a first course in abstract algebra".
"a first course in abstract algebra".

geroch and jang, 1975 - 'motion of a body in general relativity', jmp, vol.
geroch and jang, 1975 - 'motion of a body in general relativity', jmp, vol.

however, in general relativity, it is found that derivatives which are also tensors must be used.
however, in general relativity, it is found that derivatives which are also tensors must be used.

* asplund edgar and bungart lutz, 1966 -"a first course in integration" - holt, rinehart and winston.
*asplund edgar and bungart lutz, 1966 -"a first course in integration" - holt, rinehart and winston.

another appealing feature of spinors in general relativity is the condensed way in which some tensor equations may be written using the spinor formalism.
another appealing feature of spinors in general relativity is the condensed way in which some tensor equations may be written using the spinor formalism.

one of the main uses of the lie derivative in general relativity is in the study of spacetime symmetries where tensors or other geometrical objects are preserved.
one of the main uses of the lie derivative in general relativity is in the study of spacetime symmetries where tensors or other geometrical objects are preserved.

== tensor fields in general relativity ==tensor fields on a manifold are maps which attach a tensor to each point of the manifold.
==tensor fields in general relativity==tensor fields on a manifold are maps which attach a tensor to each point of the manifold.

*"a first course in database systems" (con j. widom), prentice-hall, englewood cliffs, nj, 1997, 2002.
*"a first course in database systems" (with j. widom), prentice-hall, englewood cliffs, nj, 1997, 2002.

studying the cauchy problem allows one to formulate the concept of causality in general relativity, as well as 'parametrising' solutions of the field equations.
studying the cauchy problem allows one to formulate the concept of causality in general relativity, as well as 'parametrising' solutions of the field equations.

unlike the covariant derivative, the lie derivative is independent of the metric, although in general relativity one usually uses an expression that seemingly depends on the metric through the affine connection.
unlike the covariant derivative, the lie derivative is independent of the metric, although in general relativity one usually uses an expression that seemingly depends on the metric through the affine connection.

=== the metric tensor ===the metric tensor is a central object in general relativity that describes the local geometry of spacetime (as a result of solving the einstein field equations).
===the metric tensor===the metric tensor is a central object in general relativity that describes the local geometry of spacetime (as a result of solving the einstein field equations).

=== singularity theorems ===in general relativity, it was noted that, under fairly generic conditions, gravitational collapse will inevitably result in a so-called singularity.
===singularity theorems===in general relativity, it was noted that, under fairly generic conditions, gravitational collapse will inevitably result in a so-called singularity.

an important affine connection in general relativity is the levi-civita connection, which is a symmetric connection obtained from parallel transporting a tangent vector along a curve whilst keeping the inner product of that vector constant along the curve.
an important affine connection in general relativity is the levi-civita connection, which is a symmetric connection obtained from parallel transporting a tangent vector along a curve whilst keeping the inner product of that vector constant along the curve.

* frame fields in general relativity* general relativity resources* raychaudhuri equation* unruh effect== referencias ==useful background:* see "chapter 4" for background concerning vector fields on smooth manifolds.
* frame fields in general relativity* general relativity resources* milne model* raychaudhuri equation* unruh effect== notes ==== references ==useful background:* see "chapter 4" for background concerning vector fields on smooth manifolds.