Related papers: Spherically symmetric Einstein-scalar-field equati…
We show that the spherically symmetric Einstein-scalar-field equations for wave-like decaying initial data at null infinity have unique local solutions and unique global solutions for small initial data. We also generalize Christodoulou's…
We prove the global existence and uniqueness of classical solutions with small initial data and with wake-like decaying null infinity for the spherically symmetric Einstein-scalar-field equations with potential, where the scalar potential V…
It is well-known that small, regular, spherically symmetric characteristic initial data to the Einstein-scalar-field system which are decaying towards (future null) infinity give rise to solutions which are foward-in-time global (in the…
We consider a characteristic initial value problem, with initial data given on a future null cone, for the Einstein (massless) scalar field system with a positive cosmological constant, in Bondi coordinates. We prove that, for small data,…
According to Birkhoff's theorem the only spherically symmetric solution of the vacuum Einstein field equations is the Schwarzschild solution. Inspite of imposing asymptotically flatness and staticness as initial conditions we obtain that…
We investigate the asymptotic stability of solutions to the characteristic initial value problem for the Einstein (massless) scalar field system with a positive cosmological constant. We prescribe spherically symmetric initial data on a…
Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are…
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…
We consider the Cauchy problem with smooth and compactly supported initial data for the wave equation in a general class of spherically symmetric geometries which are globally smooth and asymptotically flat. Under certain mild conditions on…
The time independent spherically symmetric solutions of General Relativity (GR) coupled to a dynamical unit timelike vector are studied. We find there is a three-parameter family of solutions with this symmetry. Imposing asymptotic flatness…
We critically examine the Roberts homothetic solution for the spherically symmetric Einstein-scalar field equations in double null coordinates, and show that the Roberts solution indeed solves the field equations only for one non-trivial…
Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on…
The present article considers time symmetric initial data sets for the vacuum Einstein field equations which in a neighbourhood of infinity have the same massless part as that of some static initial data set. It is shown that the solutions…
We review recent results concerning the spherically symmetric Einstein-scalar field system with positive cosmological constant. We do so by comparing with the classical results of Christodoulou concerning the asymptotically flat case…
We obtain an exact solution for the Einstein's equations with cosmological constant coupled to a scalar, static particle in static, "spherically" symmetric background in 2+1 dimensions.
Recent works by the second author and Maxwell et al. have shown that the Einstein-scalar field conformal constraint equations are highly complex and generally intractable, even in the vacuum case. In this article, to gain a clearer…
Numerical evidence is presented for the existence of a new family of static, globally regular `cosmological' solutions of the spherically symmetric Einstein-Yang-Mills-Higgs equations. These solutions are characterized by two natural…
Solutions to the wave equation on de Sitter-Schwarzschild space with smooth initial data on a Cauchy surface are shown to decay exponentially to a constant at temporal infinity, with corresponding uniform decay on the appropriately…
Spherically symmetric static empty space solutions are studied in f(R) theories of gravity. We reduce the set of modified Einstein's equations to a single equation and show how one can construct exact solutions in different f(R) models. In…
Einstein's field equations for timelike self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are…