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I have a metric for wormhole. Now if I want to find the closed trajectory for this metric how will I proceed from here?
Help me with detailed maths if possible.
How to Find a Closed Trajectory for a Wormhole Metric?
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I have a metric for wormhole. Now if I want to find the closed trajectory for this metric how will I proceed from here?
Help me with detailed maths if possible.
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The closed trajectory for a metric can be found using the Hamilton-Jacobi equation. This equation states that the Hamiltonian of the system is equal to the partial derivative with respect to the action of the Hamilton-Jacobi function. The Hamilton-Jacobi equation can be written as follows
(x,p) = ∂S/∂t where x represents the coordinates of the system and p represents the momentum of the system. By solving this equation we can find the equation of motion of the system which will give us the closed trajectory of the system.
(x,p) = ∂S/∂t where x represents the coordinates of the system and p represents the momentum of the system. By solving this equation we can find the equation of motion of the system which will give us the closed trajectory of the system.