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ds² = dt² – dz² – (1 + 2h(t − z))dx² − (1 – 2h(t – z))dy² - - how that this is a solution to the linearized empty space Einstein equations for n arbitrary function h. Show that the curve x=y=z=0 is a geodesic of the above metric.

ds² = dt² – dz² – (1 + 2h(t − z))dx² − (1 – 2h(t – z))dy² - - how that this is a solution to the linearized empty space Einstein equations for n arbitrary function h. Show that the curve x=y=z=0 is a geodesic of the above metric.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the metric ds² = = dt² − dz² − (1 + 2h(t − z))dx² − (1 – 2h(t – z))dy² Show that this is a solution to the linearized empty space Einstein equations for an arbitrary function h. Show that the curve x = y = z = 0 is a geodesic of the above metric.
Transcribed Image Text:Consider the metric ds² = = dt² − dz² − (1 + 2h(t − z))dx² − (1 – 2h(t – z))dy² Show that this is a solution to the linearized empty space Einstein equations for an arbitrary function h. Show that the curve x = y = z = 0 is a geodesic of the above metric.
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