Related papers: Static Ricci-flat 5-manifolds admitting the 2-sphe…
We present numerical evidence for the existence of new black hole solutions in $d\geq 6$ spacetime dimensions. They approach asymptotically the Minkowski background and have an event horizon topology $S^2\times S^{d-4}$. These static…
A five-dimensional Ricci-flat cosmological solution is studied by assuming that the induced 4D matter contains two components: the usual fluid for dark matter as well as baryons and a scalar field with an exponential potential for dark…
Up to overall harmonic factors, the D8-brane solution of the massive type IIA supergravity theory is the product of nine-dimensional Minkowski space (the worldvolume) with the real line (the transverse space). We show that the equations of…
Junction conditions for vacuum solutions in five-dimensional Einstein-Gauss-Bonnet gravity are studied. We focus on those cases where two spherically symmetric regions of space-time are joined in such a way that the induced stress tensor on…
We give an infinite number of exact solutions to the 5-dimensional static Einstein equation with axial symmetry by using the inverse scattering method. The solutions are characterized by two integers representing the soliton numbers. The…
We present a characterization of $2$-dimensional Lorentzian manifolds with constant Ricci scalar curvature. It is well known that every $2$-dimensional Lorentzian manifolds is conformally flat, so we rewrite the Ricci scalar curvature in…
In this paper we consider $4$-dimensional steady soliton singularity models, i.e., complete steady gradient Ricci solitons that arise as the rescaled limit of a finite time singular solution of the Ricci flow on a closed $4$-manifold. In…
We study the 5D static Einstein-Maxwell equations with a dilaton field. We construct an infinte number of solutions by using a soliton technique. We study the rod structure of 2-soliton solution and show the 5D dilatonic black ring and…
We construct a new static solution to the 5D Einstein-Maxwell equations describing a static black hole surrounded by a non-rotating dipole black ring. The configuration is kept in equilibrium by an external magnetic field interacting with…
Regarding Ricci flow as a dynamical system, we derive sufficient conditions for noncompact stationary (Ricci-flat) solutions to possess infinite-dimensional unstable manifolds, and provide examples satisfying those criteria that have…
In this paper, we extend the work of Cao-Chen [9] on Bach-flat gradient Ricci solitons to classify $n$-dimensional ($n\ge 5$) complete $D$-flat gradient steady Ricci solitons. More precisely, we prove that any $n$-dimensional complete…
We analyze the localization equations relevant to the quantum entropy of spinning supersymmetric black holes in five-dimensional asymptotically flat space. The precise problem is to classify all solutions to the off-shell supersymmetry…
Static spherically symmetric spacetimes with vanishing second Ricci invariant constitute an important class of solutions to Einstein's equations and more generally as archetypes of regular black holes. When studying completeness one is most…
We study five-dimensional black holes obtained by compactifying M theory on Calabi-Yau threefolds. Recent progress in solving topological string theory on compact, one-parameter models allows us to test numerically various conjectures about…
We survey some recent developments in the study of collapsing Riemannian manifolds with Ricci curvature bounded below, especially the locally bounded Ricci covering geometry and the Ricci flow smoothing techniques. We then prove that if a…
It is well known that vacuum equation of arbitrary Lovelock order for static spacetime ultimately reduces to a single algebraic equation, we show that the same continues to hold true for pure Lovelock gravity of arbitrary order $N$ for…
The renormalization group equations of two-dimensional sigma models describe geometric deformations of their target space when the world-sheet length changes scale from the ultra-violet to the infra-red. These equations, which are also…
Typical existence result on Ricci-flat metrics is in manifolds of finite geometry, that is, on $F=\bar F-D$ where $\bar F$ is a compact K\"ahler manifold and $D$ is a smooth divisor. We view this existence problem from a different…
We study Robinson-Trautman spacetimes in the presence of an aligned p-form Maxwell field and an arbitrary cosmological constant in n>=4 dimensions. As it turns out, the character of these exact solutions depends significantly on the…
We construct and investigate non conformal anisotropic Bianchi type VII solutions in 5 dimensions. The solutions are asymptotically flat, but they contain a naked singularity at the origin. We also construct solutions of Einstein-Maxwell…