Abstract
We investigate a quantum vacuum state for $1 + 1$ dimensional de Sitter space, corresponding to a region within a perfectly reflecting symmetric box of fixed physical size. We find that a particle detector inside the box registers zero response, implying that the walls of the box screen out the thermal effects of the de Sitter horizon. The box thus creates a `quiescent oasis' with a temperature below the de Sitter horizon temperature, an unexpected feature that opens the way to an analysis of heat and entropy exchange between the box and the horizon in the context of the generalized second law of thermodynamics. We also calculate the stress-energy-momentum tensor of the region within the box, showing that the total energy in the box is less than the same volume of de Sitter space in the presence of thermal fluctuations.
Highlights
A landmark advance in theoretical physics was Hawking’s discovery that black holes possess a welldefined temperature and entropy, establishing a link among gravitation, quantum mechanics, and thermodynamics [1,2]
We investigated the properties of the vacuum state associated with a scalar field confined within a region of fixed size in de Sitter space, with Dirichlet boundary conditions
The thermal properties of this state, as opposed to that of the surrounding de Sitter spacetime, show that the effect of the cavity is to create an oasis that screens out the thermal properties of the horizon
Summary
A landmark advance in theoretical physics was Hawking’s discovery that black holes possess a welldefined temperature and entropy, establishing a link among gravitation, quantum mechanics, and thermodynamics [1,2]. The stress tensor in a thermal vacuum at temperature TdS yields hT μν iT dS Regardless of this observation, the thermodynamic properties of the quantum vacua of de Sitter space have been at the forefront of recent advances in cosmology. Many detailed analyses have demonstrated that these results are robust under a wide range of circumstances (see, for example, [21] and the references contained therein) This lends weight to the idea that the thermodynamic properties of de Sitter space bear close resemblance to those of black hole spacetimes. Outside the box one may choose the Boulware vacuum state in which a static particle detector registers a zero temperature [23] This effectively screens the exterior from the thermal effects of the black hole.
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