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Multidimensional Gravity with Einstein Internal Spaces
High Energy Physics - Theory · Submitted 5 Dec 1996
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It is proved that for a non-Euclidean signature the Riemann tensor squared of the solutions diverges on certain hypersurfaces in $R^{N_0}$.
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The abstract, sentence by sentence
A multidimensional gravitational model on the manifold $M = M_0 \times \prod_{i=1}^{n} M_i$, where M_i are Einstein spaces ($i \geq 1$), is studied. For $N_0 = dim M_0 > 2$ the $\sigma$ model representation is considered and it is shown that the corresponding Euclidean Toda-like system does not satisfy the Adler-van-Moerbeke criterion. For $M_0 = R^{N_0}$, $N_0 = 3, 4, 6$ (and the total dimension $D = dim M = 11, 10, 11$, respectively) nonsingular spherically symmetric solutions to vacuum Einstein equations are obtained and their generalizations to arbitrary signatures are considered. It is proved that for a non-Euclidean signature the Riemann tensor squared of the solutions diverges on certain hypersurfaces in $R^{N_0}$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A multidimensional gravitational model on the manifold $M = M_0 \times \prod_{i=1}^{n} M_i$, where M_i are Einstein spaces ($i \geq 1$), is studied. | contribution 0.78 | 0.80 | 0.05 | asserted 0.98 |
| s1 | For $N_0 = dim M_0 > 2$ the $\sigma$ model representation is considered and it is shown that the corresponding Euclidean Toda-like system does not satisfy the Adler-van-Moerbeke criterion. | result 0.83 | 0.90 | 0.13 | asserted 1.00 |
| s2 | For $M_0 = R^{N_0}$, $N_0 = 3, 4, 6$ (and the total dimension $D = dim M = 11, 10, 11$, respectively) nonsingular spherically symmetric solutions to vacuum Einstein equations are obtained and their generalizations to arbitrary signatures are considered. | result 0.92 | 0.94 | 0.20 | asserted 1.00 |
| s3 | It is proved that for a non-Euclidean signature the Riemann tensor squared of the solutions diverges on certain hypersurfaces in $R^{N_0}$. | result 1.00 | 0.93 | 0.27 | asserted 1.00 |
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Original abstract
A multidimensional gravitational model on the manifold $M = M_0 \times \prod_{i=1}^{n} M_i$, where M_i are Einstein spaces ($i \geq 1$), is studied. For $N_0 = dim M_0 > 2$ the $\sigma$ model representation is considered and it is shown that the corresponding Euclidean Toda-like system does not satisfy the Adler-van-Moerbeke criterion. For $M_0 = R^{N_0}$, $N_0 = 3, 4, 6$ (and the total dimension $D = dim M = 11, 10, 11$, respectively) nonsingular spherically symmetric solutions to vacuum Einstein equations are obtained and their generalizations to arbitrary signatures are considered. It is proved that for a non-Euclidean signature the Riemann tensor squared of the solutions diverges on certain hypersurfaces in $R^{N_0}$.
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