The spacetime life of a non-BPS D-particle

We investigate the classical geometry generated by a stable non-BPS D-particle. We consider the boundary state of a stable non-BPS D-particle in the covariant formalism in the type IIB theory orbifolded by (-1)^FLI₄. We calculate the scattering amplitude between two D-particles in the non-compact and compact orbifold and analyse the short and long distance behaviour. At short distances we find no force at order v² for any radius, and at the critical radius we find a BPS-like behaviour up to v⁴ corrections for long and short distances. Projecting the boundary state on the massless states of the orbifold closed string spectrum we obtain the large distance behaviour of the classical solution describing this non-BPS D-particle in the non-compact and compact cases. By using the non-BPS D-particle as a probe of the background geometry of another non-BPS D-particle, we recover the no-force condition at the critical radius and the v² behaviour of the probe. Moreover, assuming that the no-force persists for the complete geometry we derive part of the classical solution for the non-BPS D-particle.