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Uniform density static fluid sphere in Einstein-Gauss-Bonnet gravity and its universality

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In Newtonian theory, gravity inside a constant density static sphere is independent of spacetime dimension. Interestingly this general result is also carried over to Einsteinian as well as higher order Einstein-Gauss-Bonnet (Lovelock) gravity notwithstanding their nonlinearity. We prove that the necessary and sufficient condition for universality of the Schwarzschild interior solution describing a uniform density sphere for all n ≥ 4 is that its density is constant.

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DADHICH, N., MOLINA, Alfred and KHUGAEV, Avas. Uniform density static fluid sphere in Einstein-Gauss-Bonnet gravity and its universality. Physical Review D. 2010. Vol. 81, num. 10, pags. 104026-104026. ISSN 1550-7998. [consulted: 22 of May of 2026]. Available at: https://hdl.handle.net/2445/131684

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