Scalar field dynamics in a BTZ background with generic boundary conditions

ALAN GARBARZ; JOAN LA MADRID; MAURICIO LESTON

EUROPEAN PHYSICAL JOURNAL C - PARTICLES AND FIELDS

SPRINGER

Año: 2017

1434-6044

We revisit the dynamics of a massive scalar field in a Banados, Teitelboim, and Zanelli background taking into account the lack of global hyperbolicity of the spacetime. We approach this issue using the strategy of Ishibashi and Wald which finds a unique smooth solution as the causal evolution of initial data, each possible evolution corresponding to a positive self-adjoint extension of certain operator in a Hilbert space on the initial surface. Moreover, solutions obtained this way are the most general ones satisfying a few physically sensible requirements. This procedure is intimately related to the choice of boundary conditions and the existence of bound states. We find that the scalar field dynamics in the (effective) mass window −3/4≤m2eℓ2