Geodesic
Bose gas modeling of the Schwarzschild black hole
Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 2, pp. 223-237 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Black holes violate the third law of thermodynamics, and this gives rise to difficulties with the microscopic description of their entropy. Recently, it has been shown that the microscopic description of the Schwarzschild black hole thermodynamics in $D = 4$ space–time dimensions is provided by the analytic continuation of the entropy of Bose gas with a nonrelativistic one-particle energy to $d =-4$ negative spatial dimensions. In this paper, we show that the $D=5$ and $D=6$ Schwarzschild black holes thermodynamics can be modeled by the $d$-dimensional Bose gas, $d=1,2,3,\dots\,$, with the one-particle energy $\varepsilon(k)=k^\alpha$ under the respective conditions $\alpha=-d/3$ and $\alpha=-d/4$. In these cases, the free energy of the Bose gas has divergences, and we introduce a cut-off and perform the minimal renormalizations. We also perform renormalizations using analytic regularization and prove that the minimal cut-off renormalization gives the same answer as the analytic regularization by the Riemann zeta-function.
Keywords: black holes, Bose gas, third law of thermodynamics. 
@article{TMF_2024_218_2_a1,
     author = {I. Ya. Aref'eva and I. V. Volovich},
     title = {Bose gas modeling of {the~Schwarzschild} black hole},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {223--237},
     year = {2024},
     volume = {218},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2024_218_2_a1/}
}
TY  - JOUR
AU  - I. Ya. Aref'eva
AU  - I. V. Volovich
TI  - Bose gas modeling of the Schwarzschild black hole
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2024
SP  - 223
EP  - 237
VL  - 218
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2024_218_2_a1/
LA  - ru
ID  - TMF_2024_218_2_a1
ER  - 
%0 Journal Article
%A I. Ya. Aref'eva
%A I. V. Volovich
%T Bose gas modeling of the Schwarzschild black hole
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2024
%P 223-237
%V 218
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2024_218_2_a1/
%G ru
%F TMF_2024_218_2_a1
I. Ya. Aref'eva; I. V. Volovich. Bose gas modeling of the Schwarzschild black hole. Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 2, pp. 223-237. http://geodesic.mathdoc.fr/item/TMF_2024_218_2_a1/

[1] J. M. Bardeen, B. Carter, S. W. Hawking, “The four laws of black hole mechanics”, Commun. Math. Phys., 31:2 (1973), 161–170 | DOI | MR

[2] J. D. Bekenstein, “Black holes and entropy”, Phys. Rev. D, 7:8 (1973), 2333–2346 | DOI | MR

[3] I. Aref'eva, I. Volovich, Violation of the third law of thermodynamics by black holes, Riemann zeta function and Bose gas in negative dimensions, arXiv: 2304.04695

[4] V. S. Vladimirov, Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1976 | MR

[5] L. D. Landau, E. M. Lifshits, Kurs teoreticheskoi fiziki, v. 5, Statisticheskaya fizika, Nauka, M., 1976 | MR | Zbl

[6] V. A. Zagrebnov, J.-B. Bru, “The Bogoliubov model of weakly imperfect Bose gas”, Phys. Rep., 350:5–6 (2001), 291–434 | DOI | MR | Zbl

[7] P. L. Chebyshev, “Ob opredelenii chisla prostykh chisel, ne prevoskhodyaschikh dannoi velichiny”, Polnoe sobranie sochinenii, v. 1, Teoriya chisel, AN SSSR, M.–L., 1944, 173–190

[8] E. Bombieri, Problems of the Millennium: The Riemann Hypothesis, Clay Mathematics Institute, Cambridge, MA, 2000

[9] S. M. Voronin, A. A. Karatsuba, Dzeta-funktsiya Rimana, Fizmatlit, M., 1994 | DOI | MR | MR | Zbl | Zbl