Analysis of Self-Gravitating Fluid Instabilities from the Post-Newtonian Boltzmann Equation
Self-gravitating fluid instabilities are analysed within the framework of a post-Newtonian Boltzmann equation coupled with the Poisson equations for the gravitational potentials of the post-Newtonian theory. The Poisson equations are determined from the knowledge of the energy–momentum tensor calcul...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/26/3/246 |
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| author | Gilberto M. Kremer |
| author_facet | Gilberto M. Kremer |
| author_sort | Gilberto M. Kremer |
| collection | DOAJ |
| description | Self-gravitating fluid instabilities are analysed within the framework of a post-Newtonian Boltzmann equation coupled with the Poisson equations for the gravitational potentials of the post-Newtonian theory. The Poisson equations are determined from the knowledge of the energy–momentum tensor calculated from a post-Newtonian Maxwell–Jüttner distribution function. The one-particle distribution function and the gravitational potentials are perturbed from their background states, and the perturbations are represented by plane waves characterised by a wave number vector and time-dependent small amplitudes. The time-dependent amplitude of the one-particle distribution function is supposed to be a linear combination of the summational invariants of the post-Newtonian kinetic theory. From the coupled system of differential equations for the time-dependent amplitudes of the one-particle distribution function and gravitational potentials, an evolution equation for the mass density contrast is obtained. It is shown that for perturbation wavelengths smaller than the Jeans wavelength, the mass density contrast propagates as harmonic waves in time. For perturbation wavelengths greater than the Jeans wavelength, the mass density contrast grows in time, and the instability growth in the post-Newtonian theory is more accentuated than the one of the Newtonian theory. |
| first_indexed | 2024-04-24T18:19:35Z |
| format | Article |
| id | doaj.art-d08a2814772449778c8a9c801184d21c |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-24T18:19:35Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-d08a2814772449778c8a9c801184d21c2024-03-27T13:36:57ZengMDPI AGEntropy1099-43002024-03-0126324610.3390/e26030246Analysis of Self-Gravitating Fluid Instabilities from the Post-Newtonian Boltzmann EquationGilberto M. Kremer0Departamento de Física, Universidade Federal do Paraná, Curitiba 81531-980, BrazilSelf-gravitating fluid instabilities are analysed within the framework of a post-Newtonian Boltzmann equation coupled with the Poisson equations for the gravitational potentials of the post-Newtonian theory. The Poisson equations are determined from the knowledge of the energy–momentum tensor calculated from a post-Newtonian Maxwell–Jüttner distribution function. The one-particle distribution function and the gravitational potentials are perturbed from their background states, and the perturbations are represented by plane waves characterised by a wave number vector and time-dependent small amplitudes. The time-dependent amplitude of the one-particle distribution function is supposed to be a linear combination of the summational invariants of the post-Newtonian kinetic theory. From the coupled system of differential equations for the time-dependent amplitudes of the one-particle distribution function and gravitational potentials, an evolution equation for the mass density contrast is obtained. It is shown that for perturbation wavelengths smaller than the Jeans wavelength, the mass density contrast propagates as harmonic waves in time. For perturbation wavelengths greater than the Jeans wavelength, the mass density contrast grows in time, and the instability growth in the post-Newtonian theory is more accentuated than the one of the Newtonian theory.https://www.mdpi.com/1099-4300/26/3/246self-gravitating fluid instabilityBoltzmann equationpost-Newtonian theory |
| spellingShingle | Gilberto M. Kremer Analysis of Self-Gravitating Fluid Instabilities from the Post-Newtonian Boltzmann Equation Entropy self-gravitating fluid instability Boltzmann equation post-Newtonian theory |
| title | Analysis of Self-Gravitating Fluid Instabilities from the Post-Newtonian Boltzmann Equation |
| title_full | Analysis of Self-Gravitating Fluid Instabilities from the Post-Newtonian Boltzmann Equation |
| title_fullStr | Analysis of Self-Gravitating Fluid Instabilities from the Post-Newtonian Boltzmann Equation |
| title_full_unstemmed | Analysis of Self-Gravitating Fluid Instabilities from the Post-Newtonian Boltzmann Equation |
| title_short | Analysis of Self-Gravitating Fluid Instabilities from the Post-Newtonian Boltzmann Equation |
| title_sort | analysis of self gravitating fluid instabilities from the post newtonian boltzmann equation |
| topic | self-gravitating fluid instability Boltzmann equation post-Newtonian theory |
| url | https://www.mdpi.com/1099-4300/26/3/246 |
| work_keys_str_mv | AT gilbertomkremer analysisofselfgravitatingfluidinstabilitiesfromthepostnewtonianboltzmannequation |