Palabras clave
momento de inercia
ecuación de Lane-Emden
diagramas masa-radio
índice politrópico
Cómo citar
Descargas
Societal impact
Resumen
Los politropos newtonianos son modelos fundamentales en astrofísica que pueden representar sistemas autogravitantes, como son las estrellas y ciertos objetos compactos. Sin embargo, llama la atención que, a pesar de su popularidad, muy poco se ha discutido en la literatura sobre su momento de inercia. Por ello, en este estudio nos propusimos analizar algunas propiedades integrales y de la estructura de los politropos newtonianos, prestando especial atención a su momento de inercia. Con ese fin estudiamos la ecuación de Lane-Emden y presentamos soluciones tanto analíticas como numéricas para diferentes valores del índice politrópico n. Asimismo, ofrecemos diagramas de masa-radio y calculamos el momento de inercia de varias configuraciones. Encontramos que el momento de inercia normalizado I/MR2, en función del índice politrópico n, se ajusta a una función polinómica de cuarto orden.
Referencias
Araujo, F. M., & Chirenti, C. B. M. H. (2011) Newtonian and relativistic polytropes. 4th School on Cosmic Rays and Astrophysics.
Beltracchi, P., & Posada, C. (2024a) Slowly rotating anisotropic relativistic stars. Phys. Rev. D, 110(2). https://doi.org/10.1103/physrevd.110.024052
Beltracchi, P., & Posada, C. (2024b) Slowly rotating ultra-compact Schwarzschild star in the gravastar limit. Class. Quantum Grav., 41(4), 045001. https://doi.org/10.1088/1361-6382/ad1a52
Beltracchi, P., & Posada, C. (2025) Slowly rotating covariant anisotropic objects. Phys. Rev. D, 112(8), 084046. https://doi.org/10.1103/71cv-lnzk
Bludman, S. A. (1973) Stability of general-relativistic polytropes. Astrophys. J, 183, 637–648. https://doi.org/10.1086/152253
Breu, C., & Rezzolla, L. (2016) Maximum mass, moment of inertia and compactness of relativistic stars. Mon. Not. Roy. Astron. Soc., 459(1), 646–656. https://doi.org/10.1093/mnras/stw575
Chandrasekhar, S. (1964) Dynamical Instability of Gaseous Masses Approaching the Schwarzschild Limit in General Relativity. Phys. Rev. Lett., 12, 114–116. https : //doi.org/10.1103/PhysRevLett.12.114
Chandrasekhar, S., & Miller, J. C. (1974) On slowly rotating homogeneous masses in general relativity. Mon. Not. Roy. Astron. Soc., 167, 63–80. https : / /doi.org/10.1093/mnras/167.1.63
Chandrasekhar, S. (1967) An introduction to the study of stellar structure. Dover Publications.
Eddington, A. S. (1920) The internal constitution of the stars. The Scientific Monthly, 11(4), 297–303. Retrieved May 4, 2025, from http://www.jstor.org/stable/6491
Emden, R. (1907) Gaskugeln: Anwendungen der mechanischen w¨armetheorie auf kosmologische und meteorologische probleme (gas spheres: Applications of the mechanical theory of heat to cosmological and meteorological problems). B.G. Teubner.
Epperson, J. F. (2013) An introduction to numerical methods and analysis (2nd ed.).Wiley.
Hartle, J. B. (1967) Slowly rotating relativistic stars. 1. Equations of structure. Astrophys. J., 150, 1005–1029. https://doi.org/10.1086/149400
Hartle, J. B., & Thorne, K. S. (1968) Slowly Rotating Relativistic Stars. II. Models for Neutron Stars and Supermassive Stars. Astrophys. J., 153, 807. https://doi.org/10.1086/149707
Hlad´ık, J., Posada, C., & Stuchl´ık, Z. (2020) Radial instability of trapping polytropic spheres. Int. J. Mod. Phys. D, 29(05), 2050030. https://doi.org/10.1142/s0218271820500303
Horedt, G. P. (2004) Polytropes : Applications in astrophysics and related fields. Kluwer Academic Publishers.
Horedt, G. P. (2013) Early Evolution of Prestellar Cores. Astrophys. J, 773(2), Article 131, 131. https://doi.org/10.1088/0004-637X/773/2/131
Jiang, N., & Yagi, K. (2020) Analytic I-Love-C relations for realistic neutron stars. Phys. Rev. D, 101(12), 124006. https://doi.org/10.1103/PhysRevD.101.124006
Kippenhahn, R.,Weigert, A.,&Weiss, A. (2012) Stellar structure and evolution. Springer.
Kiusalaas, J. (2013) Numerical methods in engineering with python 3 (3rd ed.). Cambridge University Press.
Lane, H. J. (1870) On the theoretical temperature of the sun, under the hypothesis of a gaseous mass maintaining its volume by its internal heat, and depending on the laws of gases as known to terrestrial experiment. American Journal of Science and Arts, s2-50, 57–74. https://api.semanticscholar.org/CorpusID:131102972
Lopes, I., & Panotopoulos, G. (2019) Mass-to-radius profiles of newtonian polytropic spheres: Low-mass main-sequence stars in palatini gravity versus dark-matteradmixed low-mass stars in general relativity. Phys. Rev. D, 99, 103013. https : //doi.org/10.1103/PhysRevD.99.103013
Posada, C., Hlad´ık, J., & Stuchl´ık, Z. (2020) Dynamical instability of polytropic spheres in spacetimes with a cosmological constant. Phys. Rev. D, 102, 024056. https : //doi.org/10.1103/PhysRevD.102.024056
Python Software Foundation. (2021) Python (versi´on 3.x). Retrieved November 11, 2025, from https://www.python.org/
Raposo, G., Pani, P., Bezares, M., Palenzuela, C., & Cardoso, V. (2019) Anisotropic stars as ultracompact objects in General Relativity. Phys. Rev. D, 99(10), 104072. https://doi.org/10.1103/PhysRevD.99.104072
Ravenhall, D. G., & Pethick, C. J. (1994) Neutron Star Moments of Inertia. Astrophys. J., 424, 846. https://doi.org/10.1086/173935
Schaffner-Bielich, J. (2020) Compact star physics. Cambridge University Press.
Shapiro, S. L., & Teukolsky, S. A. (1983) Black holes, white dwarfs and neutron stars. The physics of compact objects. Wiley, VCH. https://doi.org/10.1002/9783527617661
Shojai, F., Fazel, M. R., Stepanian, A.,&Kohandel, M. (2015) On the Newtonian Anisotropic Configurations. Eur. Phys. J. C, 75(6), 250. https://doi.org/10.1140/epjc/s10052-015-3478-6
Stuchl´ık, Z., Hled´ık, S., & Novotn´y, J. (2016) General relativistic polytropes with a repulsive cosmological constant. Phys. Rev. D, 94(10), 103513. https://doi.org/10.1103/PhysRevD.94.103513
Stuchl´ık, Z., Novotn´y, J., & Hlad´ık, J. (2025) Dark matter halos modeled by polytropic spheres influenced by the relict cosmological constant and trapping polytropes forming supermassive black holes. Astron. Astrophys., 702, A2. https://doi.org/10.1051/0004-6361/202554520
Tooper, R. F. (1964) General relativistic polytropic fluid spheres. Astrophys. J, 140, 434. https://doi.org/10.1086/147938
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