Related papers: Naked singularities in the Einstein-Euler system
We study the problem of asymptotically flat bi-axially symmetric stationary solutions of the vacuum Einstein equations in $5$-dimensional spacetime. In this setting, the cross section of any connected component of the event horizon is a…
In the present paper we prove a uniqueness theorem for the static and asymptotically flat solutions to the Einstein-scalar field equations which possess a photon sphere. We show that such solutions are uniquely specified by their mass $M$…
Quantum singularities considered in the 3D BTZ spacetime by Pitelli and Letelier (Phys. Rev. D77: 124030, 2008) is extended to charged BTZ and 3D Einstein-Maxwell-dilaton gravity spacetimes. The occurence of naked singularities in the…
We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is…
For all $\epsilon>0$, we prove the existence of finite-energy strong solutions to the axi-symmetric $3D$ Euler equations on the domains $ \{(x,y,z)\in\mathbb{R}^3: (1+\epsilon|z|)^2\leq x^2+y^2\}$ which become singular in finite time. We…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
By using of the Euler-Lagrange equations, we find a static spherically symmetric solution in the Einstein-aether theory with the coupling constants restricted. The solution is similar to the Reissner-Nordstrom solution in that it has an…
We discuss the corrected thermodynamics and naked singularity structure of the topological static spherically symmetric solution in $\mathcal{F}(R,\mathcal{G})$ - gravity coupled with Born-Infeld - like nonlinear electrodynamics. Solutions…
We construct the general spherically symmetric and self-similar solution of the Einstein-Vlasov system (collisionless matter coupled to general relativity) with massless particles, under certain regularity conditions. Such solutions have a…
Singular solutions of the harmonic Einstein evolution equation are constructed which are related to spatially global and time-local solutions for a certain class of quasilinear hyperbolic systems of second order. The constructed…
We characterize the local instability of pressureless Friedmann spacetimes to radial perturbation at the Big Bang. The analysis is based on a formulation of the Einstein-Euler equations in self-similar variables $(t,\xi)$, with $\xi=r/t$,…
A new mechanism for causing naked singularities is found in an effective superstring theory. We investigate the gravitational collapse in a spherically symmetric Einstein-Maxwell-dilaton system in the presence of a pure cosmological…
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…
We prove definitive results on the global stability of the flat space among solutions of the Einstein-Klein-Gordon system. Our main theorems in this monograph include: (1) A proof of global regularity (in wave coordinates) of solutions of…
It is shown that the vacuum Einstein equations for an arbitrary stationary axisymmetric space-time can be completely separated by re-formulating the Ernst equation and its associated linear system in terms of a non-autonomous…
In this paper, we elucidate the problem of gravitating Skyrmion governed by field equations of the Einstein-Skyrme system with no potential term in the Bondi coordinate. The spherical symmetry has to be assumed and both the metric functions…
A homothetic, static, spherically symmetric solution to the massless Einstein- Klein-Gordon equations is described. There is a curvature singularity which is central, null, bifurcate and marginally trapped. The space-time is therefore…
We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past…
Using numerical integration, in 1969 Penston [22] and Larson [17] independently discovered a self-similar solution describing the collapse of a self-gravitating asymptotically flat fluid with the isothermal equation of state $p=k\varrho$,…
The existence of stationary solutions to the Einstein-Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat…