We study the influence of the instantaneous appearance of a time-like Killing vector (TKV) in self-gravitating fluid spheres during their evolution. For doing so, we resort to the concept of the asymmetry factor, which allows the existence of any specific type of symmetry (e.g., a TKV), exclusively, for a given value of the time-like coordinate. We consider adiabatic and dissipative fluids. The analysis of different relevant physical variables in this process shows the imprints of the emergence of the TKV at some point of the evolution. Particular attention is paid to the relationship appearing between the TKV and the complexity factor describing the degree of complexity of the fluid, bringing out for the first time a link between complexity and symmetry.
Citation: Luis Herrera. Complexity and symmetry: the asymmetry factor approach[J]. AIMS Mathematics, 2026, 11(10): 35737-35755. doi: 10.3934/math.20261385
We study the influence of the instantaneous appearance of a time-like Killing vector (TKV) in self-gravitating fluid spheres during their evolution. For doing so, we resort to the concept of the asymmetry factor, which allows the existence of any specific type of symmetry (e.g., a TKV), exclusively, for a given value of the time-like coordinate. We consider adiabatic and dissipative fluids. The analysis of different relevant physical variables in this process shows the imprints of the emergence of the TKV at some point of the evolution. Particular attention is paid to the relationship appearing between the TKV and the complexity factor describing the degree of complexity of the fluid, bringing out for the first time a link between complexity and symmetry.
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Figures(4)
Luis Herrera. Complexity and symmetry: the asymmetry factor approach[J]. AIMS Mathematics, 2026, 11(10): 35737-35755. doi: 10.3934/math.20261385
$ Y_{TF}/\alpha^2 $ as a function of $ y $ and $ x $ in the interval $ (y, -10, 10) $, $ (x, .5, .7) $; $ \alpha R_\Sigma $ in the interval $ (y, -7, 7) $; $ P_{r\Sigma} $ in the interval $ (y, -2, 2) $ for the non-dissipative case
$ 8\pi(P_r-P_\bot)/\alpha^2 $ as a function of $ y $ and $ x $ in the interval $ (y, -7, 7) $, $ (x, .2, .9) $; $ \alpha m_\Sigma $ and $ z_\Sigma $ in the interval $ (y, -3, 3) $ and $ (y, -5, 3) $, respectively, for the non-dissipative case
$ Y_{TF}/\alpha^2 $ as a function of $ y $, and $ x $ in the interval $ (y, -10, 10) $, $ (x, .5, 1) $; $ L_\infty $ and $ z_\Sigma $ in the interval $ (y, -2, 2) $, and $ (y, -10, 10) $, respectively, for the dissipative case
$ T^\ast $ as a function of $ y $ and $ x $ in the interval $ (y, -10, 10) $, $ (x, .3, .6) $ for $ \tau^\ast = 1 $ and $ \tau^\ast = 0 $; $ 8\pi(P_r-P_\bot)/\alpha^2 $ as a function of $ y $ and $ x $ in the interval $ (y, -5, 5) $, $ (x, .2, .7) $; for the dissipative case
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