time
flat Minkowski spacetime
fluid
spacetime
In the usual flatspace hydrodynamics, there is a unique split between Eulerian and Lagrangian observers. An Eulerian observer is one at rest in space, while the Lagrangian observer is one at rest in the fluid. We can define an observer at an event in spacetime by giving his 4-velocity at that event. The path through spacetime taken by the observer is called the timeline of that observer. In flat Minkowski spacetime (the spacetime of special relativity), the Eulerian observerâ€™s 4-velocity is exceedingly simple, because the time slices (3-spaces representing a given instant of time) are parallel flat 3-planes. Since the Eulerian observer is at rest, his 4-velocity is normal to the time slice. He is not shearing, converging, accelerating, or rotating relative to nearby Eulerian observers. In contrast, the Lagrangian observer at the same event is doing all these things, relative to nearby Lagrangian observers. While the timelines of the Lagrangian observers, following the fluid particles, are complicated curved trajectories through spacetime, the Eulerian observerâ€™s timelines are straight and parallel to each other.
Minkowski spacetime
same event
fluid particles
chapters
things
https://scigraph.springernature.com/explorer/license/
Eulerian observer
path
observer
rest
trajectories
false
chapter
hydrodynamics
events
gravitational collapse
1986
space
particles
curved trajectories
relativistic gravitational collapse
Lagrangian observer
https://doi.org/10.1007/978-94-009-4754-2_15
1986-01-01
split
slices
unique split
collapse
timeline
Numerical Relativistic Gravitational Collapse with Spatial Time Slices
contrast
2022-11-24T21:18
time slices
491-529
Astrophysical Radiation Hydrodynamics
978-94-009-4754-2
978-94-010-8612-7
10.1007/978-94-009-4754-2_15
doi
dimensions_id
pub.1018172973
Engineering
Springer Nature
Evans
Charles R.
Michael L.
Norman
Larry L.
Smarr
Departments of Astronomy and Physics, University of Illinois, 61801, Urbana, IL, USA
Departments of Astronomy and Physics, University of Illinois, 61801, Urbana, IL, USA
Interdisciplinary Engineering
James R.
Wilson
Lawrence Livermore National Laboratory, P.O. Box 808 L-35, 94550, Livermore, CA, USA
Department of Astronomy, University of Illinois, 61801, Urbana, IL, USA
Lawrence Livermore National Laboratory, P.O. Box 808 L-35, 94550, Livermore, CA, USA
Karl-Heiz A.
Winkler
Springer Nature - SN SciGraph project