On the shape of bodies in general relativistic regimes
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The analysis of axisymmetric spacetimes, dynamical or stationary, is usually made in the reduced space. We prove here a stability property of the quotient space and use it together with minimal surface techniques to constraint the shape of General Relativistic bodies in terms of their energy and rotation. These constraints are different in nature to the mechanical limitations that a particular material body can have and which can forbid, for instance, rotation faster than a certain rate, (after which the body falls apart). The relations we are describing instead are fundamental and hold for all bodies, albeit they are useful only in General Relativistic regimes. For Neutron stars they are close to be optimal, and, although precise models for these stars display tighter constraints, our results are significative in that they do not depend on the equation of state.
KeywordsGeneral relativity Radius Shape Angular momentum Rotating stars
I would like to thank Sergio Dain for important conversations and to the many colleagues of FaMAF (Argentina) where these results were first discussed.
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