Maximally Symmetric Boost-Invariant Solutions of the Boltzmann Equation in Foliated Geometries
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| Format: | Preprint |
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2025
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| _version_ | 1866911663693758464 |
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| author | Martinez, Mauricio Plumberg, Christopher |
| author_facet | Martinez, Mauricio Plumberg, Christopher |
| contents | In this work we study the relativistic kinetic theory of a boost-invariant conformal gas on a static, maximally symmetric background $dS_3\times \mathbb{R}$, considering all constant-curvature slicings of $dS_3$ - flat, spherical, or hyperbolic- and their associated symmetry groups. Using a symmetry-driven cotangent-bundle approach, we show that the isometry group of each slicing acts on phase space in such a way that only its Casimir invariants and the time-like coordinate unconstrained, so the distribution function depends solely on these quantities. This yields a unified boost-invariant exact solution of the Boltzmann equation valid for each constant-curvature foliation of $dS_3\times \mathbb{R}$. Specializing this general solution to the flat and spherical foliations reproduces the Bjorken and Gubser flows, respectively, while its restriction to the hyperbolic foliation produces a genuinely new analytic solution (`Grozdanov flow'). Hydrodynamics and free streaming emerge naturally as limiting regimes of this novel exact solution. We further comment on several relevant aspects of the new boost-invariant solution on the hyperbolic slicing and on their interpretation once mapped back to Minkowski space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_06257 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximally Symmetric Boost-Invariant Solutions of the Boltzmann Equation in Foliated Geometries Martinez, Mauricio Plumberg, Christopher High Energy Physics - Theory Statistical Mechanics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Nuclear Theory In this work we study the relativistic kinetic theory of a boost-invariant conformal gas on a static, maximally symmetric background $dS_3\times \mathbb{R}$, considering all constant-curvature slicings of $dS_3$ - flat, spherical, or hyperbolic- and their associated symmetry groups. Using a symmetry-driven cotangent-bundle approach, we show that the isometry group of each slicing acts on phase space in such a way that only its Casimir invariants and the time-like coordinate unconstrained, so the distribution function depends solely on these quantities. This yields a unified boost-invariant exact solution of the Boltzmann equation valid for each constant-curvature foliation of $dS_3\times \mathbb{R}$. Specializing this general solution to the flat and spherical foliations reproduces the Bjorken and Gubser flows, respectively, while its restriction to the hyperbolic foliation produces a genuinely new analytic solution (`Grozdanov flow'). Hydrodynamics and free streaming emerge naturally as limiting regimes of this novel exact solution. We further comment on several relevant aspects of the new boost-invariant solution on the hyperbolic slicing and on their interpretation once mapped back to Minkowski space. |
| title | Maximally Symmetric Boost-Invariant Solutions of the Boltzmann Equation in Foliated Geometries |
| topic | High Energy Physics - Theory Statistical Mechanics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2512.06257 |