Thermodynamics of bosonic systems in anti–de Sitter spacetime

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 Pöschl-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.

Figure 1

Log-log graphs for $\ln Z^{\mathrm{sc}}$ with $D=4$. The continuous line is the full numerical evaluation. The dashed lines are the low-temperature and high-temperature formulas. Results for other values of $D$ are qualitatively similar.

Figure 2

Log-log graphs for $\ln Z^{\mathrm{el}}$ with $D=5$. The continuous line is the full numerical evaluation. The dashed lines are the low-temperature and high-temperature formulas. Results for other values of $D$ are qualitatively similar.

Figure 3

Log-log graphs for $\ln Z^{\mathrm{gr}}$ with $D=6$. The continuous line is the full numerical evaluation. The dashed lines are the low-temperature and high-temperature formulas. Results for other values of $D$ are qualitatively similar.

Figure 4

Log-log graphs for $\ln Z^{\mathrm{gr}}$ as a function of $LT$ with $D=4$, 5, 6. Results for other fields and dimensions are qualitatively similar.

Figure 5

Log-log graphs for ${\mathrm{\Delta }}^{\mathrm{sc}}$ in terms of $LT$, considering the scalar gas with $D=4$, 5, 6. The bullets are the numerical results, and the straight lines are the power-law fits. For $D=4$, 5, 6, the fits are ${\mathrm{\Delta }}^{\mathrm{sc}}=1.52\times (LT{)}^{-2.95}$, ${\mathrm{\Delta }}^{\mathrm{sc}}=1.78\times (LT{)}^{-4.01}$, and ${\mathrm{\Delta }}^{\mathrm{sc}}=2.08\times (LT{)}^{-5.08}$. respectively.

Figure 6

Log-log graphs for $U^{\mathrm{gr}}$ as a function of the temperature with $D=4$, 5, 6. In the graphs, $L=1$. The results are qualitatively similar for other fields and values of $D$ and $L$.

Figure 7

Log-log graphs for $S^{\mathrm{gr}}$ as a function of the temperature with $D=4$, 5, 6. In the graphs, $L=1$. The results are qualitatively similar for other fields and values of $D$ and $L$.

Figure 8

Log-Log graphs for $P^{\mathrm{gr}}$ as a function of $L$ with $D=4$, 5, 6. In the graphs, $T=1$. The results are qualitatively similar for other fields and values of $D$ and $L$.

Figure 9

Graphs for $C_V^{\mathrm{gr}}$ as a function of the temperature with $D=4$, 5, 6. In the graphs, $L=1$. The qualitative behavior is the same for other fields and dimensions.

Figure 10

Graphs for ${\beta }_T^{\mathrm{gr}}$ as a function of the $V_{\mathrm{eff}}$ with $D=4$, 5, 6. In the graphs, $T=1$. The qualitative behavior is the same for other fields and dimensions.