The Duality of Time Dilation and Velocity
| dc.creator | Monroe, Hunter | |
| dc.date | 2005-12-05 | |
| dc.date | 2006-03-24 | |
| dc.date.accessioned | 2026-07-07T06:53:55Z | |
| dc.date.available | 2026-07-07T06:53:55Z | |
| dc.description | Time dilation $\frac{1}{\sqrt{1-v^2}}$ and relative velocity $v$ are observationally indistinguishable in the special theory of relativity, a duality that carries over into the general theory under Fermi coordinates along a curve (in coordinate-independent language, in the tangent Minkowski space along the curve). For example, on a clock stationary at radius $r$, a distant observer sees time dilation of $\frac{1}{\sqrt{1-v^2}}=\frac{1}{\sqrt{1-2M/r}}$ under the Schwarzschild metric and sees the clock receding with a relative velocity of $v=\sqrt{2M/r}$ under the Painlev{é}-Gullstrand free fall metric. Duality implies that during gravitational collapse, the intensifying time dilation observed at the star's center from a fixed radius $r>0$ is indistinguishable (along a curve) from an increasing relative velocity at which the center recedes as seen from any direction, implying a local inflation. | |
| dc.description | 7 pages, Latex2e | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0512019 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0512019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/105759 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.subject | Astrophysics | |
| dc.subject | Differential Geometry | |
| dc.title | The Duality of Time Dilation and Velocity | |
| dc.type | text |