Abstract
We analyze the thermodynamics of massless bosonic systems in D-dimensional anti-de Sitter spacetime, considering scalar, electromagnetic, and gravitational fields. Their dynamics are described by Poschl-Teller effective potentials and quantized in a unified framework, with the determination of the associated energy spectra. From the microscopic description developed, a macroscopic thermodynamic treatment is proposed, where an effective volume in anti-de Sitter geometry is defined and a suitable thermodynamic limit is considered. Partition functions are constructed for the bosonic gases, allowing the determination of several thermodynamic quantities of interest. With the obtained results, general aspects of the thermodynamics are explored.
Highlights
Anti–de Sitter geometries gained a new relevance with the anti–de Sitter/conformal field theory (AdS=CFT) correspondences [1,2,3]
Hawking and Page, within a Euclidean path integral approach, considered the thermodynamics of thermal gases and black holes in AdS space [18]. They observed that the Schwarzschild-anti de Sitter (SAdS) and the thermal AdS geometries are different phases of a single physical system
The notion of an AdS effective volume will be important for the implementation of a thermodynamic limit on the field dynamics at the anti–de Sitter spacetime
Summary
Anti–de Sitter geometries gained a new relevance with the anti–de Sitter/conformal field theory (AdS=CFT) correspondences [1,2,3]. Hawking and Page, within a Euclidean path integral approach, considered the thermodynamics of thermal gases and black holes in AdS space [18]. They observed that the Schwarzschild-anti de Sitter (SAdS) and the thermal AdS geometries are different phases of a single physical system. We consider the thermal anti–de Sitter spacetime, that is, the setup treated by Hawking-Page in the no–black hole regime. To characterize the thermodynamics of a bosonic gas in AdS geometry, a unified framework for the quantization of the scalar, electromagnetic, and gravitational fields is introduced. We use signature (−; þ; Á Á Á ; þ) and natural units with G 1⁄4 ħ 1⁄4 c 1⁄4 kB 1⁄4 1 throughout this paper
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