Kruskal–Szekeres coordinates

E11652

coordinate system maximal analytic extension spacetime coordinate chart

Kruskal–Szekeres coordinates are a maximal extension coordinate system used in general relativity to smoothly describe the entire spacetime of a Schwarzschild black hole, including regions across the event horizon.

Aliases (5)

Statements (49)

Predicate	Object
instanceOf	coordinate system → maximal analytic extension → spacetime coordinate chart →
appearsIn	literature on black hole physics → textbooks on general relativity →
appliesTo	Schwarzschild metric → spherically symmetric vacuum solution →
assumes	non-rotating black hole → uncharged black hole →
basedOn	Schwarzschild coordinates →
coordinateType	global coordinates → null-like coordinates → regular coordinates at the event horizon →
describes	regions inside the Schwarzschild event horizon → regions outside the Schwarzschild event horizon → second asymptotically flat region of Schwarzschild spacetime → white hole region of Schwarzschild spacetime →
domain	regions I, II, III, and IV of Schwarzschild spacetime →
enables	analysis of geodesic completeness of Schwarzschild spacetime → study of causal connections between different regions → visualization of black hole and white hole regions →
feature	light cones appear at 45 degrees in Kruskal diagrams → metric is finite at the event horizon → timelike and spacelike character of coordinates changes across regions →
field	general relativity →
introducedBy	George Szekeres → Martin David Kruskal →
massParameter	M →
mathematicalNature	analytic coordinate transformation → conformal to part of Minkowski-like plane →
namedAfter	George Szekeres → Martin David Kruskal →
preserves	curvature singularity at r = 0 →
relatedConcept	Schwarzschild radius → causal structure → curvature singularity → event horizon → geodesic completeness →
relatedTo	Eddington–Finkelstein coordinates → Penrose–Carter diagrams → maximal analytic extension of black hole spacetimes →
removes	coordinate singularity at r = 2M →
usedFor	describing Schwarzschild spacetime → describing the full maximally extended Schwarzschild black hole → drawing Kruskal diagrams → extending Schwarzschild solution across the event horizon → removing coordinate singularity at the Schwarzschild radius → studying causal structure of Schwarzschild spacetime →
yearProposed	1960 →

Referenced by (11)

Subject (surface form when different)	Predicate
Eddington–Finkelstein coordinates → Painlevé–Gullstrand coordinates → Schwarzschild coordinates →	relatedTo
Einstein–Rosen bridge ("Region I of Kruskal–Szekeres diagram") → Einstein–Rosen bridge ("Region III of Kruskal–Szekeres diagram") →	hasRegion
George Szekeres ("Szekeres–Kruskal coordinates in general relativity") → Martin David Kruskal →	notableWork
Schwarzschild black hole →	alternativeCoordinates
Schwarzschild black hole ("maximally extended Kruskal–Szekeres spacetime") →	hasCausalStructure
Martin David Kruskal ("Kruskal–Szekeres extension of the Schwarzschild solution") →	knownFor
Einstein–Rosen bridge →	visualizedUsing