Spectral Distance on Lorentzian Moyal Plane

We present here a completely operatorial approach, using Hilbert-Schmidt operators, to compute spectral distances between time-like separated "events ", associated with the pure states of the algebra describing the Lorentzian Moyal plane, using the axiomatic framework given by [13, 14]. The result shows no deformations of non-commutative origin, as in the Euclidean case.