Consider the minkowski space in spherical coordinates (t, r, θ, φ) and perform a transformation of coordinates to a system in rotation given by t '= t, r' = r, θ '= θ, φ' = φ + ωt.

(a) find the metric in the new coordinates and all christoffel symbols.

(b) take θ '= θ = π/2. write the equations of the geod'esica and compare with the equations d²xi'/dt'² = f^i , find the value of the "inertial forces" f ^ i. is it possible to have a particle at rest in these coordinates
(u^r' = u^φ' = 0) without applying an external force? if required, what is the external force that must be added to ensure that the particle remains at rest?