The balance problem for $n$ aligned black holes
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910127655747584 |
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| author | Hennig, Jörg |
| author_facet | Hennig, Jörg |
| contents | 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 by the repulsive spin-spin and electromagnetic interactions. This contribution reports on a method to address this problem for an arbitrary number of $n$ aligned, rotating and possibly charged black holes in an asymptotically flat spacetime. By employing soliton methods to study the underlying boundary value problem for the Einstein-Maxwell equations, we derive the most general form of the boundary data on the symmetry axis. The resulting axis potentials are necessarily rational functions of a specific form, depending on a finite number of parameters. This powerful result reduces the search for $n$-black-hole solutions from solving a highly nonlinear PDE system to analysing a well-defined, finite-parameter family of candidate solutions. We briefly review known results for special cases, such as the constructive uniqueness proofs for a single black hole in vacuum or electrovacuum, and the non-existence proof for two stationary black holes in vacuum, before stating the open problem for more general configurations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12134 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The balance problem for $n$ aligned black holes Hennig, Jörg General Relativity and Quantum Cosmology 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 by the repulsive spin-spin and electromagnetic interactions. This contribution reports on a method to address this problem for an arbitrary number of $n$ aligned, rotating and possibly charged black holes in an asymptotically flat spacetime. By employing soliton methods to study the underlying boundary value problem for the Einstein-Maxwell equations, we derive the most general form of the boundary data on the symmetry axis. The resulting axis potentials are necessarily rational functions of a specific form, depending on a finite number of parameters. This powerful result reduces the search for $n$-black-hole solutions from solving a highly nonlinear PDE system to analysing a well-defined, finite-parameter family of candidate solutions. We briefly review known results for special cases, such as the constructive uniqueness proofs for a single black hole in vacuum or electrovacuum, and the non-existence proof for two stationary black holes in vacuum, before stating the open problem for more general configurations. |
| title | The balance problem for $n$ aligned black holes |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2604.12134 |