Agradecimentos: V. S. Barroso and J. P. M. Pitelli are grateful to Professor R. M. Wald and G. Satishchandran for enlightening discussions and also thank the Enrico Fermi Institute for the kind hospitality. J. P. M. Pitelli thanks Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) (Grant...

Agradecimentos: V. S. Barroso and J. P. M. Pitelli are grateful to Professor R. M. Wald and G. Satishchandran for enlightening discussions and also thank the Enrico Fermi Institute for the kind hospitality. J. P. M. Pitelli thanks Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) (Grant No. 2018/01558-9). V. S. Barroso thanks FAPESP (Grant No. 2018/09575-0). Finally, we all thank FAPESP (Grant No. 2013/09357-9)

Abstract: Initial conditions given on a spacelike, static slice of a non-globally hyperbolic spacetime may not define the fates of classical and quantum fields uniquely. Such lack of global hyperbolicity is a well-known property of the anti-de Sitter solution and led many authors to question how is...

Abstract: Initial conditions given on a spacelike, static slice of a non-globally hyperbolic spacetime may not define the fates of classical and quantum fields uniquely. Such lack of global hyperbolicity is a well-known property of the anti-de Sitter solution and led many authors to question how is it possible to develop a quantum field theory on this spacetime. Wald and Ishibashi took a step towards the healing of that causal issue when considering the propagation of scalar fields on AdS. They proposed a systematic procedure to obtain a physically consistent dynamical evolution. Their prescription relies on determining the self-adjoint extensions of the spatial component of the differential wave operator. Such a requirement leads to the imposition of a specific set of boundary conditions at infinity. We employ their scheme in the particular case of the four-dimensional AdS spacetime and compute the expectation values of the field squared and the energy-momentum tensor, which will then bear the effects of those boundary conditions. We are not aware of any laws of nature constraining us to prescribe the same boundary conditions to all modes of the wave equation. Thus, we formulate a physical setup in which one of those modes satisfy a Robin boundary condition, while all others satisfy the Dirichlet condition. Due to our unusual settings, the resulting contributions to the fluctuations of the expectation values will not respect AdS invariance. As a consequence, a back-reaction procedure would yield a non-maximally symmetric spacetime. Furthermore, we verify the violation of weak energy condition as a direct consequence of our prescription for dynamics

FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP

2013/09357-9; 2018/015589; 2018/09575-0

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