We place further restriction on the possible topology of stationary asymptotically flat vacuum black holes in 5 spacetime dimensions. We prove that the horizon manifold can be either a connected sum of Lens spaces and "handles" $S^1 \times S^2$, or the quotient of $S^3$ by certain finite groups of isometries (with no "handles"). The resulting horizon topologies include Prism manifolds and quotients of the Poincare homology sphere. We also show that the topology of the domain of outer communication is a cartesian product of the time direction with a finite connected sum of $\mathbb R^4,S^2 \times S^2$'s and $CP^2$'s, minus the black hole itself. We do not assume the existence of any Killing vector beside the asymptotically timelike one required by definition for stationarity.
Extending recent work in 5 dimensions, we prove the existence and uniqueness of solutions to the reduced Einstein equations for vacuum black holes in $(n+3)$-dimensional spacetimes admitting the isometry group $\mathbb{R}\times U(1)^{n}$, with Kaluza-Klein asymptotics for $n\geq3$. This is equivalent to establishing existence and uniqueness for singular harmonic maps $φ: \mathbb{R}^3\setminusΓ\rightarrow SL(n+1,\mathbb{R})/SO(n+1)$ with prescribed blow-up along $Γ$, a subset of the $z$-axis in $\mathbb{R}^3$. We also analyze the topology of the domain of outer communication for these spacetime…
In this paper we investigate the thermodynamic properties of the stationary Lifshitz black hole solution of New Massive Gravity. We study the thermodynamic stability from local and global point of view. We also consider the space of equilibrium states for the solution within the framework of Thermodynamic Information Geometry. By investigating the proper thermodynamic metrics and their curvature invariants we find a set of restrictions on the parameter space and the critical points indicating phase transitions of the system. We confirm our findings by analytical analysis of the geodesics on th…
We produce new examples, both explicit and analytical, of bi-axisymmetric stationary vacuum black holes in 5 dimensions. A novel feature of these solutions is that they are asymptotically locally Euclidean in which spatial cross-sections at infinity have lens space $L(p,q)$ topology, or asymptotically Kaluza-Klein so that spatial cross-sections at infinity are topologically $S^1\times S^2$. These are nondegenerate black holes of cohomogeneity 2, with any number of horizon components, where the horizon cross-section topology is any one of the three admissible types: $S^3$, $S^1\times S^2$, or $…
A topological approach has been successfully used to study the properties of the light ring and the null circular orbit, in a generic black hole background. However, for the equatorial timelike circular orbit, quite different from the light ring case, its radius is closely dependent of the energy and angular momentum of a test particle. This fact seems to restrict the extension of the topological treatment to the timelike circular orbit. In this paper, we confirm that the angular momentum does not affect the asymptotic behavior of the constructed vector with its zero points denoting the equato…
We study the problem of stationary bi-axially symmetric solutions of the $5$-dimensional minimal supergravity equations. Essentially all possible solutions with nondegenerate horizons are produced, having the allowed horizon cross-sectional topologies of the sphere $S^3$, ring $S^1\times S^2$, and lens $L(p,q)$, as well as the three different types of asymptotics. The solutions are smooth apart from possible conical singularities at the fixed point sets of the axial symmetry. This analysis also includes the solutions known as solitons in which horizons are not present but are rather replaced b…
