spacetime manifold
E57420
A spacetime manifold is a four-dimensional, smooth geometric framework in general relativity that models the combined fabric of space and time on which gravitational phenomena are described.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
differentiable manifold
→
geometric structure → mathematical concept → model in general relativity → |
| allows |
definition of proper distance
→
definition of proper time → geodesic motion → |
| canModel |
black hole spacetimes
→
cosmological spacetimes → gravitational waves → |
| contains |
events
→
light cones → worldlines → |
| curvatureDeterminedBy |
stress-energy tensor
→
|
| describes |
curved spacetime
→
gravitational phenomena → |
| formalizedBy |
differential geometry
→
tensor calculus → |
| generalizes |
Minkowski spacetime
→
|
| hasComponent |
space
→
time → |
| hasCoordinateSystem |
spacetime coordinates
→
|
| hasCurvature |
spacetime curvature
→
|
| hasDimension |
4
→
|
| hasLocalProperty |
locally Minkowskian
→
locally flat in small neighborhoods → |
| hasMetricSignature |
(+,-,-,-)
→
(-,+,+,+) → Lorentzian signature → |
| hasProperty |
differentiable
→
smooth → |
| hasStructure |
Lorentzian metric
→
causal structure → differentiable structure → topological structure → |
| hasSubset |
null curves
→
spacelike hypersurfaces → timelike curves → |
| hasTopology |
four-dimensional manifold topology
→
|
| introducedInContextOf |
Einstein's theory of general relativity
→
|
| obeys |
Einstein field equations
→
|
| relatedTo |
Lorentzian manifold
→
Riemannian manifold → |
| requires |
compatibility of charts
→
smooth atlas of coordinate charts → |
| usedFor |
describing motion of particles
→
describing propagation of light → modeling gravitational fields → |
| usedInTheory |
general relativity
→
|
Referenced by (1)
| Subject (surface form when different) | Predicate |
|---|---|
|
Einstein tensor
→
|
definedOn |