We present the general properties of dynamic dissipative fluid distribution endowed with hyperbolical symmetry. All the equations required for its analysis are exhibited and used to contrast the behavior of the system with the spherically symmetric case. Several exact solutions are exhibited and prospective applications to astrophysical and cosmological scenarios are discussed.Comment: 12 pages revtex 4. Based on the conferences delivered at Gravitex 2021 Conference, Durban, South Africa, and 4th PU International Conference of Gravitation and Cosmology, Lahore, Pakistan, in August 2021 and November 2021 respectively. To appear in Int. J. Mod. Phys. D. arXiv admin note: text overlap with arXiv:2109.07758, arXiv:2110.0188
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