- #1
How Can Differential Equations Help Solve Homework Problems?
- Thread starter Sujanbasnet6
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- Homework
Hi,
I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem.
Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$
Where ##b=1## with an orbit only in the equatorial plane.
We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$
Ultimately, I was tasked to find the initial...
Boundary conditions:
The derived Dirichlet and Neumann boundary conditions
In terms of the magnetic scalar potential:
The value of H equals ## 10^{3}## in natural units,
According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##,
## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units.
So is this conversion correct?
Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?
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