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From vacuum field equations on principal bundles to Einstein equations with fluids

M. Montesinos-Velasquez·T. Matos
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Abstract

In the present work we show that the Einstein equations on $M$ without cosmological constant and with perfect fluid as source, can be obtained from the field equations for vacuum with cosmological constant on the principal fibre bundle $P(\frac{1}{I} M,U(1))$, $M$ being the space-time and $I$ the radius of the internal space $U(1)$.

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M. Montesinos-Velasquez, T. Matos. 1996-01-10. From vacuum field equations on principal bundles to Einstein equations with fluids. https://arxiv.org/abs/gr-qc/9601013

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