Aichelberg/Sexl ultraboost

In general relativity, the Aichelburg/Sexl ultraboost is an exact solution which models the physical experience of an observer who whizzes by a Schwarzschild metric at nearly the speed of light. The metric tensor can be written, in terms of Brinkmann coordinates, as :

ds^2 = -8m \, \delta(u) \, \log r \, du^2 + 2 \, du \, dv + dr^2 + r^2 \, d\theta^2,

-\infty < u,r < 0, -\infty < v < \infty, \pi < \theta < \pi

The ultraboost can be obtained as the limit of various sequences smooth Lorentzian manifolds. For example, we can take ''Poor-man's Gaussian pulses'' :

ds^2 = -\frac{4 m a \, \log(r)}{\pi \, (1+a^2 u^2)} \, du^2
- 2 du \, dv + dr^2 + r^2 \, d\theta^2

In these plus-polarized ''axisymmetric vacuum pp-waves'', the curvature is concentrated along the axis of symmetry, falling off like O(m/r), and also near

u=0

. As

a \rightarrow \infty

, the wave profile turns into a Dirac delta, and we recover the ultraboost. == References == * ''See Section 7.6.12'' * See also * General relativity

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Words begining with Aichelberg/Sexl_ultraboost:

Aichelberg/Sexl_ultraboost