Scalar field dynamics in a BTZ background with generic boundary conditions
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 in...
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_14346044_v77_n11_p_Garbarz |
| Aporte de: |
| id |
todo:paper_14346044_v77_n11_p_Garbarz |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_14346044_v77_n11_p_Garbarz2023-10-03T16:15:22Z Scalar field dynamics in a BTZ background with generic boundary conditions Garbarz, A. La Madrid, J. Leston, M. 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≤me2ℓ2<0 can be well defined within a one-parametric family of distinct boundary conditions (- 3 / 4 being the conformally coupled case), while for me2ℓ2≥0 the boundary condition is unique (only one self-adjoint extension is possible). It is argued that there is no sensible evolution possible for me2ℓ2<-1, and also it is shown that in the range me2ℓ2∈[-1,-3/4) there is a U(1) family of allowed boundary conditions, however, the positivity of the self-adjoint extensions is only motivated but not proven. We focus mainly on describing the dynamics of such evolutions given the initial data and all possible boundary conditions, and in particular we show the energy is always positive and conserved. © 2017, The Author(s). JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_14346044_v77_n11_p_Garbarz |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
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≤me2ℓ2<0 can be well defined within a one-parametric family of distinct boundary conditions (- 3 / 4 being the conformally coupled case), while for me2ℓ2≥0 the boundary condition is unique (only one self-adjoint extension is possible). It is argued that there is no sensible evolution possible for me2ℓ2<-1, and also it is shown that in the range me2ℓ2∈[-1,-3/4) there is a U(1) family of allowed boundary conditions, however, the positivity of the self-adjoint extensions is only motivated but not proven. We focus mainly on describing the dynamics of such evolutions given the initial data and all possible boundary conditions, and in particular we show the energy is always positive and conserved. © 2017, The Author(s). |
| format |
JOUR |
| author |
Garbarz, A. La Madrid, J. Leston, M. |
| spellingShingle |
Garbarz, A. La Madrid, J. Leston, M. Scalar field dynamics in a BTZ background with generic boundary conditions |
| author_facet |
Garbarz, A. La Madrid, J. Leston, M. |
| author_sort |
Garbarz, A. |
| title |
Scalar field dynamics in a BTZ background with generic boundary conditions |
| title_short |
Scalar field dynamics in a BTZ background with generic boundary conditions |
| title_full |
Scalar field dynamics in a BTZ background with generic boundary conditions |
| title_fullStr |
Scalar field dynamics in a BTZ background with generic boundary conditions |
| title_full_unstemmed |
Scalar field dynamics in a BTZ background with generic boundary conditions |
| title_sort |
scalar field dynamics in a btz background with generic boundary conditions |
| url |
http://hdl.handle.net/20.500.12110/paper_14346044_v77_n11_p_Garbarz |
| work_keys_str_mv |
AT garbarza scalarfielddynamicsinabtzbackgroundwithgenericboundaryconditions AT lamadridj scalarfielddynamicsinabtzbackgroundwithgenericboundaryconditions AT lestonm scalarfielddynamicsinabtzbackgroundwithgenericboundaryconditions |
| _version_ |
1782023746963374080 |