Noether symmetries of y´´ = f(x)yn with applications to non-static spherically symmetric perfect fluid solutions

Details Noether symmetries of y´´ = f(x)yn with applications to non-static spherically symmetric perfect fluid solutions Noether symmetries of y´´ = f(x)yn with applications to non-static spherically symmetric perfect fluid solutions

Nov 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999cqgra..16.3553w&link_type=abstract

Classical and Quantum Gravity, Volume 16, Issue 11, pp. 3553-3566 (1999).

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We study the Noether point symmetries and integrability of the second-order equation y´´ = f(x)yn, nicons/Journals/Common/ne" ALT="ne" ALIGN="TOP"/>-1,0,1. The case n = 2 is applied to shear-free spherically symmetric perfect fluid solutions. As a result we reobtain the Kustaanheimo and Qvist class and other known solutions in a systematic manner without resorting to ad hoc methods. Moreover, we show how one can construct new solutions as well. For the case n = -(1/3), it is shown that all existing solutions arise as a result of the equation admitting a Noether point symmetry. The Noether integral gives rise to a class of solutions which contains the existing solutions.

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