Kastor-Traschen Solution Research Articles

Binary black hole systems do not interact in the Kastor-Traschen spacetime

Binary black hole merger has been detected directly by LIGO. But the detail physics of binary black hole merger has not been completely revealed due to the lack of exact solution for the corresponding spacetime. Currently only numerical solutions based on some specific coordinate for binary black hole are available. If we allow to including a cosmological constant into the Einstein equation, there is a Kastor-Traschen (KT) solution describing dynamical multi black holes. Through investigation of the related Bondi-Scahs quantities we find that the corresponding gravitational radiation and electromagnetic radiation both vanish. In addition, we have done gravitational electromagnetic analysis. All these quantitative calculations indicate that KT solution does not admit gravitational radiation nor electromagnetic radiation. Based on this finding we argue that the KT solution only describes black holes touch instead of collision.

Geometric horizons in the Kastor-Traschen multi-black-hole solutions

We investigate the existence of invariantly defined quasi-local hypersurfaces in the Kastor-Traschen solution containing $N$ charge-equal-to-mass black holes. These hypersurfaces are characterized by the vanishing of particular curvature invariants, known as Cartan invariants, which are generated using the frame approach. The Cartan invariants of interest describe the expansion of the outgoing and ingoing null vectors belonging to the invariant null frame arising from the Cartan-Karlhede algorithm. We show that the evolution of the hypersurfaces surrounding the black holes depends on an upper-bound on the total mass for the case of two and three equal mass black holes. We discuss the results in the context of the geometric horizon conjectures.

Shadows of multi-black holes: Analytic exploration

Shadows of multi-black holes have structures distinct from the mere superposition of the shadow of a single black hole: the eyebrow-like structures outside the main shadows and the deformation of the shadows. We present analytic estimates of these structures using the static multi-black hole solution (Majumdar-Papapetrou solution). We show that the width of the eyebrow is related to the distance between the black holes and that the shadows are deformed into ellipses due to the presence of the second black holes. These results are helpful to understand qualitatively the features of the shadows of colliding black holes. We also present the shadows of colliding or coalescing black holes in the Kastor-Traschen solution.

Cosmological Einstein-Maxwell instantons and euclidean supersymmetry: beyond self-duality

We construct new supersymmetric solutions to the Euclidean Einstein-Maxwell theory with a non-vanishing cosmological constant, and for which the Maxwell field strength is neither self-dual or anti-self-dual. We find that there are three classes of solutions, depending on the sign of the Maxwell field strength and cosmological constant terms in the Einstein equations which arise from the integrability conditions of the Killing spinor equation. The first class is a Euclidean version of a Lorentzian supersymmetric solution found in [1, 2]. The second class is constructed from a three dimensional base space which admits a hyper-CR Einstein-Weyl structure. The third class is the Euclidean Kastor-Traschen solution.

On the Topology of Black Lenses

The topological structure of black holes in 5-dimensional space-times with a horizon diffeomorphic with lens spaces is discussed. It is shown that such black holes can emerge from the crease set, which is composed of the plumbings of several 2-spheres, of the event horizon. It is also shown that such configurations are realized in the Kastor-Traschen solution of the Einstein-Maxwell system.

Topology changing process of coalescing black holes on Eguchi-Hanson space

We numerically study the event horizons of two kinds of five-dimensional coalescing black hole solutions with different asymptotic structures: the five-dimensional Kastor-Traschen solution (5DKT) and the coalescing black hole solution on Eguchi-Hanson space (CBEH). Topologies of the spatial infinity are ${\rm S}^3$ and $L(2;1)={\rm S}^3/{\mathbb Z}_2$, respectively. We show that the crease sets of event horizons are topologically ${\rm R}^1$ in 5DKT and ${\rm R}^1\times {\rm S}^1$ in CBEH, respectively. If we choose the time slices which respect space-time symmetry, the first contact points of the coalescing process is a point in the 5DKT case but a ${\rm S}^1$ in the CBEH case. We also find that in CBEH, time slices can be chosen so that a black ring with ${\rm S}^1\times {\rm S}^2$ topology can be also formed during a certain intermediate period unlike the 5DKT.

Cosmological black holes on Taub–NUT space in five-dimensional Einstein–Maxwell theory

The cosmological black hole solution on the Gibbons–Hawking space has been constructed. We also investigate the properties of this solution in the case of a single-black hole. Unlike the Kastor–Traschen solution, which becomes a static solution in a single-black hole, this solution is not static even in a single-black hole case.

Adaptive event horizon tracking and critical phenomena in binary black hole coalescence

This work establishes critical phenomena in the topological transition of black hole coalescence. We describe and validate a computational front tracking event horizon solver, developed for generic studies of the black hole coalescence problem. We then apply this to the Kastor-Traschen axisymmetric analytic solution of the extremal Maxwell-Einstein black hole merger with a cosmological constant. The surprising result of this computational analysis is a power law scaling of the minimal throat proportional to time. The minimal throat connecting the two holes obeys this power law during a short time immediately at the beginning of merger. We also confirm the behavior analytically. Thus, at least in one axisymmetric situation a critical phenomenon exists. We give arguments for a broader universality class than the restricted requirements of the Kastor-Traschen solution.

Topological Appearance of Event Horizon: What Is the Topology of the Event Horizon That We Can See?

The topology of the event horizon (TOEH) is usually believed to be a sphere. Nevertheless, some numerical simulations of gravitational collapse with a toroidal event horizon or the collision of event horizons are reported. Considering the indifferentiability of the event horizon (EH), we see that such non-trivial TOEHs are caused by the set of endpoints (the crease set) of the EH. The two-dimensional (one-dimensional) crease set is related to the toroidal EH (the coalescence of the EH). Furthermore, examining the stability of the structure of the endpoints, it becomes clear that the spherical TOEH is unstable under linear perturbation. On the other hand, a discussion based on catastrophe theory reveals that the TOEH with handles is stable and generic. Also, the relation between the TOEH and the hoop conjecture is discussed. It is shown that the Kastor-Traschen solution is regarded as a good example of the hoop conjecture by the discussion of its TOEH. We further conjecture that a non-trivial TOEH can be smoothed out by rough observation in its mass scale.