Spacetime Exterior to a Star: Against Asymptotic Flatness

Abstract

Abstract:In many circumstances the perfect fluid conservation equations can be directly integrated to give a geometric-thermodynamic equation: typically that the lapse N is the reciprocal of the enthalphy h, (N = 1/h). This result is aesthetically appealing as it depends only on the fluid conservation equations and does not depend on specific field equations such as Einstein's. Here the form of the geometric-thermodynamic equation is derived subject to spherical symmetry and also for the shift-free ADM formalism. There at least three applications of the geometric-thermodynamic equation, the most important being to the notion of asymptotic flatness and hence to spacetime exterior to a star. For asymptotic flatness one wants h → 0 and N → 1 simultaneously, but this is incompatible with the geometric-thermodynamic equation. Observational data and asymptotic flatness are discussed. It is argued that a version of Mach's principle does not allow asymptotic flatness.

Convex Regions of Stationary Spacetimes and Randers Spaces. Applications to Lensing and Asymptotic Flatness

“…The list of useful solutions presently consists of the Neugebauer-Meinel dust (a rigidly rotating thin disk of dust with finite radius surrounded by an asymptotically flat vacuum region), and a few variants, see [43,44]. Moreover, as emphasized by Roberts [56], there is no known perfect fluid source which can be matched to a Kerr vacuum exterior, as one would expect in order to create the simplest possible model of a rotating star 7 -this contrasts with the plenitude of solutions which match to Schwarzschild. So, the true applicability of the results in this contexts requires accurate hypotheses, as the optimized fall-off hypotheses in our definition.…”