Exact lambdavacuum solutions in higher dimensions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917363219169280 |
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| author | Sarmiento-Alvarado, I. A. Wiederhold, P. Matos, T. |
| author_facet | Sarmiento-Alvarado, I. A. Wiederhold, P. Matos, T. |
| contents | In this work, we obtain exact solutions to the $(n+2)$-dimensional Einstein Field Equations with a non-zero cosmological constant for $n > 1$.
These solutions depend on a set $\{ A_a, a=1,2,\ldots , m \}$ of pairwise commuting constant matrices in $\mathfrak{sl} ( n, \mathbb{R} )$ and on a constant matrix $g_0$ in $\mathcal{I} (\{ A_a, a=1,\ldots , m \})$, determined in previous work.
Different choices of $\{ A_a, a=1,\ldots , m \}$ and $g_0$ correspond to different solutions.
As examples, we show how to obtain the de Sitter metric, the Anti-de Sitter metric, the Birmingham metric, the Nariai metric and the Anti-Nariai metric in higher dimensions.
The generalized Nariai and Anti-Nariai solutions are direct topological products of $AdS_{\frac{n}{2} + 1} \times H^{\frac{n}{2} + 1}$, $dS_{\frac{n}{2} + 1} \times S^{\frac{n}{2} + 1}$, $AdS_2 \times H^n$, $AdS_n \times H^2$, $dS_2 \times S^n$ and $dS_n \times S^2$.
In addition, we study a solution in the context of cosmology. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_25651 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact lambdavacuum solutions in higher dimensions Sarmiento-Alvarado, I. A. Wiederhold, P. Matos, T. General Relativity and Quantum Cosmology In this work, we obtain exact solutions to the $(n+2)$-dimensional Einstein Field Equations with a non-zero cosmological constant for $n > 1$. These solutions depend on a set $\{ A_a, a=1,2,\ldots , m \}$ of pairwise commuting constant matrices in $\mathfrak{sl} ( n, \mathbb{R} )$ and on a constant matrix $g_0$ in $\mathcal{I} (\{ A_a, a=1,\ldots , m \})$, determined in previous work. Different choices of $\{ A_a, a=1,\ldots , m \}$ and $g_0$ correspond to different solutions. As examples, we show how to obtain the de Sitter metric, the Anti-de Sitter metric, the Birmingham metric, the Nariai metric and the Anti-Nariai metric in higher dimensions. The generalized Nariai and Anti-Nariai solutions are direct topological products of $AdS_{\frac{n}{2} + 1} \times H^{\frac{n}{2} + 1}$, $dS_{\frac{n}{2} + 1} \times S^{\frac{n}{2} + 1}$, $AdS_2 \times H^n$, $AdS_n \times H^2$, $dS_2 \times S^n$ and $dS_n \times S^2$. In addition, we study a solution in the context of cosmology. |
| title | Exact lambdavacuum solutions in higher dimensions |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.25651 |