相关论文: Boundary Value Problem for Black Rings
We study the boundary value problem for the stationary rotating black hole solutions to the five-dimensional vacuum Einstein equation. Assuming the two commuting rotational symmetry and the sphericity of the horizon topology, we show that…
We study axisymmetric self-gravitating non-linear $\sigma$-model in five-dimensional spacetime admitting three commutating Killing vector fields. We show that the only asymptotically flat black ring solution with a regular event horizon is…
The vacuum Einstein equations in five dimensions are shown to admit a solution describing an asymptotically flat spacetime regular on and outside an event horizon of topology S^1 x S^2. It describes a rotating ``black ring''. This is the…
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…
All known five dimensional, asymptotically flat, static black rings possess conical singularities. However, there is no fundamental obstruction forbidding the existence of balanced configurations, and we show that the Einstein--Klein-Gordon…
We present a solution of the vacuum Einstein's equations in five dimensions corresponding to a black ring with horizon topology S^1 x S^2 and rotation in the azimuthal direction of the S^2. This solution has a regular horizon up to a…
We prove uniqueness theorems for asymptotically flat, stationary, extremal, vacuum black hole solutions, in four and five dimensions with one and two commuting rotational Killing fields respectively. As in the non-extremal case, these…
We construct balanced black ring solutions in $d\geq 6$ spacetime dimensions, by solving the Einstein field equations numerically with suitable boundary conditions. The black ring solutions have a regular event horizon with $S^1\times…
We solve a class of boundary value problems for the stationary axisymmetric Einstein equations corresponding to a disk of dust rotating uniformly around a central black hole. The solutions are given explicitly in terms of theta functions on…
We prove local existence and uniqueness of static spherically symmetric solutions of the Einstein-Yang-Mills equations for an arbitrary compact semisimple gauge group in the so-called regular case. By this we mean the equations obtained…
Axially symmetric, stationary solutions of the Einstein-Maxwell equations with disconnected event horizon are studied by developing a method of explicit integration of the corresponding boundary-value problem. This problem is reduced to…
The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical…
The Kerr-Newman black hole solution can be constructed straightforwardly as the unique solution to the boundary value problem of the Einstein-Maxwell equations corresponding to an asymptotically flat, stationary and axisymmetric…
We study a method to solve stationary axisymmetric vacuum Einstein equations numerically. As an illustration, the five-dimensional doubly spinning black rings that have two independent angular momenta are formulated in a way suitable for…
The Harmonic Einstein equation is the vacuum Einstein equation supplemented by a gauge fixing term which we take to be that of DeTurck. For static black holes analytically continued to Riemannian manifolds without boundary at the horizon…
Using the inverse scattering method to solve the five-dimensional vacuum Einstein equations, we construct an asymptotically flat four-soliton solution as a stationary and bi-axisymmetric solution. We impose certain boundary conditions on…
The stationary, axisymmetric reduction of the vacuum Einstein equations, the so-called Ernst equation, is an integrable nonlinear PDE in two dimensions. There now exists a general method for analyzing boundary value problems for integrable…
New axisymmetric stationary solutions of the vacuum Einstein equations in five-dimensional asymptotically flat spacetimes are obtained by using solitonic solution-generating techniques. The new solutions are shown to be equivalent to the…
An intriguing open problem in general relativity is whether a stationary equilibrium configuration of multiple, physically relevant black holes can exist. In such a hypothetical setup, the gravitational attraction would need to be balanced…
We present balanced black ring solutions of pure Einstein-Maxwell theory in five dimensions. The solutions are asymptotically flat, and their tension and gravitational self-attraction are balanced by the repulsion due to rotation and…