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Isotropic coordinates
About: Isotropic coordinates is a research topic. Over the lifetime, 132 publications have been published within this topic receiving 4367 citations.
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TL;DR: In this article, a method is developed for treating Einstein's field equations, applied to static spheres of fluid, in such a manner as to provide explicit solutions in terms of known analytic functions.
Abstract: A method is developed for treating Einstein's field equations, applied to static spheres of fluid, in such a manner as to provide explicit solutions in terms of known analytic functions. A number of new solutions are thus obtained, and the properties of three of the new solutions are examined in detail. It is hoped that the investigation may be of some help in connection with studies of stellar structure. (See the accompanying article by Professor Oppenheimer and Mr. Volkoff.)
2,264 citations
TL;DR: In this paper, the exact solutions to Einstein's equations are compared to the field associated with an isolated static spherically symmetric perfect fluid source, and the candidate solutions are subjected to the following elementary tests: (i) isotropy of the pressure, (ii) regularity at the origin, (iii) positive definiteness of the energy density and pressure at the beginning, vanishing of pressure at some finite radius, and (iv) monotonic decrease of the EE with increasing radius.
474 citations
TL;DR: In this paper, an algorithm based on the choice of a single monotone function subject to boundary conditions is presented which generates all regular static spherically symmetric perfect-fluid solutions of Einstein's equations.
Abstract: An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect-fluid solutions of Einstein's equations. For physically relevant solutions the generating functions must be restricted by nontrivial integral-differential inequalities. Nonetheless, the algorithm is demonstrated here by the construction of an infinite number of previously unknown physically interesting exact solutions.
242 citations
TL;DR: In this article, the authors present a derivation of the family of analytic stationary $1+\mathrm{log} $ foliations of the Schwarzschild solution, and outline a transformation to isotropic coordinates.
Abstract: We expand upon our previous analysis of numerical moving-puncture simulations of the Schwarzschild spacetime. We present a derivation of the family of analytic stationary $1+\mathrm{log} $ foliations of the Schwarzschild solution, and outline a transformation to isotropic coordinates. We discuss in detail the numerical evolution of standard Schwarzschild puncture data, and the new time-independent $1+\mathrm{log} $ data. Finally, we demonstrate that the moving-puncture method can locate the appropriate stationary geometry in a robust manner when a numerical code alternates between two forms of $1+\mathrm{log} $ slicing during a simulation.
108 citations
TL;DR: In this paper, the motion of binary mass systems in gravity up to the sixth post-Newtonian order to the G N 3 terms ab initio using momentum expansions within an effective field theory approach based on Feynman amplitudes in harmonic coordinates.
102 citations