What is recorded here?
Kruskal gives a simple global coordinate representation of the maximal singularity-free analytic Schwarzschild extension, displaying two exterior and two interior regions while retaining the intrinsic center singularity. A coordinate system can show only part of a spacetime, much as one map can omit a region of the Earth. The original Schwarzschild coordinates break down at a horizon; Finkelstein had continued through one horizon branch. Kruskal supplied a particularly clear global map: both horizon branches and a second exterior region fit into one regular representation. Radial light rays become straight diagonal lines, making the allowed causal connections easy to follow. The horizon is regular, but the center remains a genuine curvature singularity. The bridge pictured in the paper does not provide a traversable shortcut or a model of an actual collapsing star. Earlier extension work is acknowledged in the original, and Szekeres independently obtained the same extension. This record credits Kruskal’s explicit representation and scoped maximality argument, not every later black-hole result.
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Scientific scope
The extension is for the classical Schwarzschild vacuum solution with the stated mass/coordinate construction. Removing a horizon coordinate singularity does not remove the central curvature singularity. The complete idealized extension differs from the spacetime of a particular collapsing star. Rotating/charged and quantum geometries are outside this target.
Read the original work
- M. D. Kruskal: Maximal Extension of Schwarzschild Metric,1960original1743-1745
- APS1960originalbibliographicidentity/byline
- Cederbaum and Wolff2024 selected introduction andgeneralizedextensionconstruction
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People and systems
M. D. Kruskal
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English catalogue narrative
Kruskal: a global map of the extended Schwarzschild spacetime
Kruskal gives a simple global coordinate representation of the maximal singularity-free analytic Schwarzschild extension, displaying two exterior and two interior regions while retaining the intrinsic center singularity.
A coordinate system can show only part of a spacetime, much as one map can omit a region of the Earth. The original Schwarzschild coordinates break down at a horizon; Finkelstein had continued through one horizon branch. Kruskal supplied a particularly clear global map: both horizon branches and a second exterior region fit into one regular representation. Radial light rays become straight diagonal lines, making the allowed causal connections easy to follow. The horizon is regular, but the center remains a genuine curvature singularity. The bridge pictured in the paper does not provide a traversable shortcut or a model of an actual collapsing star. Earlier extension work is acknowledged in the original, and Szekeres independently obtained the same extension. This record credits Kruskal’s explicit representation and scoped maximality argument, not every later black-hole result.
Scientific scope
The extension is for the classical Schwarzschild vacuum solution with the stated mass/coordinate construction. Removing a horizon coordinate singularity does not remove the central curvature singularity. The complete idealized extension differs from the spacetime of a particular collapsing star. Rotating/charged and quantum geometries are outside this target.
People and systems
M. D. Kruskal