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The problem of a self-gravitating scalar field with positive cosmological constant
Costa, João; Alho, Artur; Natário, JoséWe study the Einstein-scalar field system with positive cosmological constant and spherically symmetric characteristic initial data given on a truncated null cone. We prove well-posedness, global existence and exponential decay in (Bondi) time, for small data. From this, it follows that initial data close enough to de Sitter data evolves to a causally geodesically complete spacetime (with boundary), which appro...
Mathisson's helical motions for a spinning particle: Are they unphysical?
Costa, L. Filipe; Herdeiro, Carlos; Natario, Jose; Zilhão, MiguelIt has been asserted in the literature that Mathisson's helical motions are unphysical, with the argument that their radius can be arbitrarily large. We revisit Mathisson's helical motions of a free spinning particle, and observe that such statement is unfounded. Their radius is finite and confined to the disk of centroids. We argue that the helical motions are perfectly valid and physically equivalent descript...
Spherical linear waves in de Sitter spacetime
Costa, João; Alho, Artur; Natário, JoséWe apply Christodoulou's framework, developed to study the Einstein-scalar eld equations in spherical symmetry, to the linear wave equation in de Sitter spacetime, as a rst step towards the Einstein-scalar eld equations with positive cosmological constant. We obtain an integro-di erential evolution equation which we solve by taking initial data on a null cone. As a corollary we obtain elementary derivations ...
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