Ground state for a massive scalar field in BTZ spacetime with Robin boundary conditions
arXiv:1708.00271 · doi:10.1103/PhysRevD.96.105016
Abstract
We consider a real, massive scalar field in BTZ spacetime, a 2+1-dimensional black hole solution of the Einstein's field equations with a negative cosmological constant. First, we analyze the space of classical solutions in a mode decomposition and we characterize the collection of all admissible boundary conditions of Robin type which can be imposed at infinity. Secondly, we investigate whether, for a given boundary condition, there exists a ground state by constructing explicitly its two-point function. We demonstrate that for a subclass of the boundary conditions it is possible to construct a ground state that locally satisfies the Hadamard property. In all other cases, we show that bound state mode solutions exist and, therefore, such construction is not possible.
arXiv comment17 pages, 3 figures
References in corpus (22)
- The Black Hole in Three Dimensional Space Time
- Hawking Radiation as Tunneling
- Geometry of the 2+1 Black Hole
- Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime
- Scalar field quantization on the 2+1 dimensional black hole background
- Bulk and Boundary Dynamics in BTZ Black Holes
- Entropies of Scalar Fields on Three Dimensional Black Holes
- Dynamics in Non-Globally-Hyperbolic Static Spacetimes II: General Analysis of Prescriptions for Dynamics
- The renormalized stress tensor in Kerr space-time: general results
- Passivity and microlocal spectrum condition
- Pragmatic mode-sum regularization method for semiclassical black-hole spacetimes
- Quantum Field Theory on Curved Backgrounds -- A Primer
- Renormalized stress-energy tensor of an evaporating spinning black hole
- Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions
- The Renormalized Stress Tensor in Kerr Space-Time: Numerical Results for the Hartle-Hawking Vacuum
- Stationary scalar clouds around a BTZ black hole
- State independence for tunneling processes through black hole horizons and Hawking radiation
- Dynamics in Stationary, Non-Globally Hyperbolic Spacetimes
- Black Hole Vacua and Rotation
- Quantum Scalar Field on the Massless (2+1)-Dimensional Black Hole Background
- Renormalized vacuum polarization on rotating warped AdS3 black holes
- Brick Walls and AdS/CFT
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- Algebraic quantum field theory on spacetimes with timelike boundary
- Comments on the anti-Hawking effect on a BTZ black hole spacetime
- Covariant canonical formulations of classical field theories
- Ground and thermal states for the Klein-Gordon field on a massless hyperbolic black hole with applications to the anti-Hawking effect
- A Gutzwiller trace formula for stationary space-times
- Proof of the weak cosmic censorship conjecture for several extremal black holes
- Anti-Hawking Phenomena around a Rotating BTZ Black Hole
- Vacuum polarization on three-dimensional anti-de Sitter space-time with Robin boundary conditions
- Tunnelling processes for Hadamard states through a 2+1 dimensional black hole and Hawking radiation
- Hidden freedom in the mode expansion on static spacetimes