What is recorded here?
Finkelstein constructs a regular analytic continuation across the Schwarzschild surface and explains its one-way causal character in time-reversed branches, while the paper itself records that this continuation is not the complete Schwarzschild spacetime. The familiar Schwarzschild formula fails at a particular radius. Is that a physical catastrophe, or a failure of the coordinates used to describe it? Finkelstein showed how an analytic continuation connects the outer region with the region beyond that surface. His causal analysis made the surface understandable as a boundary that influences can cross in one direction. The displayed branch permits outward crossing; reversing its time orientation gives the inward-crossing version familiar from black-hole descriptions. This distinction matters: the paper is not a complete model of a collapsing star. Its note added in proof acknowledges a remaining incomplete geodesic and a larger, time-symmetric construction described by Kruskal. Earlier regular coordinate forms remain predecessor work. The recorded contribution is the scoped continuation and causal interpretation, with its correction intact.
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Scientific scope
The coordinates describe the stated classical Schwarzschild spacetime and make the horizon’s causal asymmetry explicit. Regularity at the horizon is not regularity at the central singularity. This is not a model of every rotating/charged collapse, a quantum resolution or the full later maximal extension. Other coordinate and causal contributions remain separate.
Read the original work
- David Finkelstein: Past-Future Asymmetry of the Gravitational Field of a Point Particle,1958 original965-967 reprint
- APS1958 original bibliographic identity and sole byline
- Anıl Zenginoğlu2025: selected history and mathematics of horizon-penetrating coordinates
This English explanation is an editorial reading view. It does not replace the complete original work or certify its science.
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People and systems
David Finkelstein
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English catalogue narrative
Finkelstein: the Schwarzschild surface as a one-way causal boundary
Finkelstein constructs a regular analytic continuation across the Schwarzschild surface and explains its one-way causal character in time-reversed branches, while the paper itself records that this continuation is not the complete Schwarzschild spacetime.
The familiar Schwarzschild formula fails at a particular radius. Is that a physical catastrophe, or a failure of the coordinates used to describe it? Finkelstein showed how an analytic continuation connects the outer region with the region beyond that surface. His causal analysis made the surface understandable as a boundary that influences can cross in one direction. The displayed branch permits outward crossing; reversing its time orientation gives the inward-crossing version familiar from black-hole descriptions. This distinction matters: the paper is not a complete model of a collapsing star. Its note added in proof acknowledges a remaining incomplete geodesic and a larger, time-symmetric construction described by Kruskal. Earlier regular coordinate forms remain predecessor work. The recorded contribution is the scoped continuation and causal interpretation, with its correction intact.
Scientific scope
The coordinates describe the stated classical Schwarzschild spacetime and make the horizon’s causal asymmetry explicit. Regularity at the horizon is not regularity at the central singularity. This is not a model of every rotating/charged collapse, a quantum resolution or the full later maximal extension. Other coordinate and causal contributions remain separate.
People and systems
David Finkelstein