Time dilation near a horizon

Assembled from 19 blocks · 2 evidence · 16 related

1. Story
2. Clocks run slow in a gravitational potential, and near a black hole the effect becomes unbounded. A static clock at radius r ticks slower than a distant one by the square root of one minus the ratio of Schwarzschild radius to r, a factor that goes to zero at the horizon. The consequence is the sharpest asymmetry in the subject: an infalling observer crosses the horizon in finite proper time and notices nothing locally, while a distant observer never sees the crossing at all. What the distant observer sees instead is the infalling object slowing, reddening and fading, its light dimming exponentially on a timescale set by the light-crossing time of the hole - about a ten-thousandth of a second for a ten-solar-mass hole and a matter of hours for M87*. The object does not hover; it becomes unobservable. The two descriptions are not in conflict, because they are answers to different questions asked by observers who can no longer exchange signals. Not a place on Earth.
3. Knowledge
4. Schwarzschild radius
5. Time dilation near a horizon
6. Connections
7. Schwarzschild radius
8. Oppenheimer and Snyder compute continued gravitational contraction
9. S2 passes pericentre and its light is measurably redshifted
10. Karl Schwarzschild
11. The event horizon
12. The photon sphere and the shadow
13. Time dilation near a horizon
14. Tidal stretching near a black hole
15. Einstein presents the field equations of general relativity
16. Schwarzschild solves the field equations for a point mass
17. Evidence
18. Reports the combined gravitational and transverse Doppler shift in S2's spectrum at its 2018 pericentre passage, inconsistent with Newtonian prediction. V55 VERIFICATION BASIS: not consulted in session; no research tool was available. Volume and article number are from recall and must be checked.
19. The first exact solution of the Einstein field equations for the vacuum outside a spherical mass, containing the radius now named for its author. V55 VERIFICATION BASIS: the paper was NOT consulted in this session - WebFetch was refused by the network egress proxy for every host attempted and the WebSearch budget was exhausted before authoring began. Title, venue and page range are given from the author's recall of a canonical citation and must be checked.