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We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial spacelike hypersurface with a timelike boundary, there exists a unique, local in time solution to the Einstein equations in a neighbourhood of the boundary. As an application, we consider a particular elastic fluid interior matched to a vacuum exterior.
In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed in a generalized sense. The applications included the harmonic versio
We show that the spherically symmetric Einstein-scalar-field equations for wave-like decaying initial data at null infinity have unique global solutions in (0, infty) and unique generalized solutions on [0, infty) in the sense of Christodoulou. We emphasize that this decaying condition is sharp.
The Einstein-Yang-Mills equations are the source of many interesting solutions within general relativity, including families of particle-like and black hole solutions, and critical phenomena of more than one type. These solutions, discovered in the l
We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a wel
Spherically gravitational collapse towards a black hole with non-zero tangential pressure is studied. Exact solutions corresponding to different equations of state are given. We find that when taking the tangential pressure into account, the exact so