Killing tensor of five dimensional Melvin’s spacetime

In this research, (3+1)D Melvin’s spacetime was extended into (4+1)D Melvin’s spacetime using hypersphere coordinates. Later, the method to compute Killing ten- sor as introduced by Garfinkle for (3+1)D spacetime was studied to compute Killing tensor in (4+1)D Melvin’s spacetime. The method introduced by Garfinkle needs the existence of commuting Killing vectors or Killing vectors in a particular coor- dinate direction. It is not well understood that the method introduced by Garfinkle worked well for extended (4+1)D Melvin’s metric because the fifth component of the metric canceled one of the commuting Killing vector in 3-dimension. Therefore, Killing tensors are obtained using the method introduced by Garfinkle and they are compared with the ones obtained by symmetrically multiplying the Killing vectors. For the later case, we found Killing vectors and Killing tensors for (4+1)D Melvin’s spacetime. At the end it is concluded that the Killing tensor found for (4+1)D con- sist of products of some noncommuting Killing vector. Killing tensor found in this research might be applicable in separability of Hamilton-Jacobi and Klein-Gordon equation.

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