Einstein metrics on group manifolds and cosets

Gibbons, G. W.; Lü, H.; Pope, C.N.

doi:10.1016/j.geomphys.2011.01.004

Cited by 23 publications

(29 citation statements)

References 16 publications

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“…Clearly p 1 , p 2 and p 3 are pairwise nonisomorphic for types A-II, E 6 -III and E 7 -II. We can prove 16 with the decomposition p = p 1 ⊕ p 2 ⊕ p 3 . Then p 1 , p 2 , p 3 are pairwise nonisomorphic with respect to the adjoint action of the Lie algebra h on p except types B-II for i = l and D-IV.…”

Section: Theorem 33 ([35]mentioning

confidence: 99%

Invariant Einstein metrics on three-locally-symmetric spaces

Chen

Kang

Liang

2016

Communications in Analysis and Geometry

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Section: Theorem 33 ([35]mentioning

confidence: 99%

Invariant Einstein metrics on three-locally-symmetric spaces

Chen

Kang

Liang

2016

Communications in Analysis and Geometry

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“…By properly fixing ξ = ξ (p), one can construct an invariant I that vanishes on the unperturbed black p-branes, but it is on-shell non-vanishing for the perturbed black p-branes (see also [16], [17] and [18]). The frequencies have been obtained by solving the master equation by power series.…”

Section: The Instabilitymentioning

confidence: 99%

Instability of black p-branes in Gauss-Bonnet theory in ten dimensions

Lagos¹,

Oliva²,

Vera³

2017

The Fourteenth Marcel Grossmann Meeting

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This work shows that the homogeneous black string and black p-branes of Gauss-Bonnet theory in ten dimensions are unstable. The perturbation that we consider is spherically symmetric and it is characterized by a total momentum k along the extended directions. There is a critical wavelength above which the instability is triggered, as it is the case for black strings and black p-branes in General Relativity. The master equation is solved by power series. We observe that the critical wavelength increases with the number of extended directions p, while the maximum exponential growth decreases as p increases.Keywords: Black strings and black p-branes; higher curvature gravity.It's by now well known that black strings and black p-branes in General Relativity (GR) are unstable under long wavelength perturbations travelling along the extended dimensions [1], [2]. For a given mass of the black hole on the brane such behaviour, known as the Gregory-Laflamme (GL) instability, can be avoided if one compactifies the extended directions on a scale smaller than the minimum characteristic wavelength that triggers the instability. This instability have lead to very interesting phenomenology. Concerned by the fact that, due to topological censorship, a naked singularity could be formed if the black string flows to a black hole, Horowitz and Maeda showed that such process could occur only on an infinite affine parameter at the horizon [3]. Non-homogeneous black strings were then constructed perturbatively [4] and numerically [5] in order to obtain stationary configurations that could provide us with a final stage of the instability of black strings. Nevertheless, it was shown that such configurations always have less entropy than the homogeneous black strings for dimensions lower than D = 13, and therefore the unstable black strings could not settle down at the final stage on these configurations [6] (such critical dimension changes for boosted black strings [7]). After a long standing numerical effort [8], [9], the full non-linear evolution of a perturbed unstable black string was achieved in D = 5 [10]. The result show that, as seen by an asymptotic observer, a null naked singularity is indeed formed at a finite time.Before the singularity appears, the black string evolves towards a configuration that can be interpreted as a set of black holes connected by black strings, on a kind of self-similar structure. The naked singularity appears when the transverse radii of such black strings reaches zero. This provides a non-fine tuned counterexample to cosmic censorship in an asymptotically M 4 × S 1 spacetime. A similar phenomenon has been recently reported for the asymptotically flat black ring in D = 5 [11], providing a counterexample of cosmic censorship in an asymptotically M 5 setup.

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“…A standard technique for evaluating this possibility is to calculate some dimensionless invariant quantity which is constructed from the metric and its curvature. We choose to use [1] [4] :…”

Section: Inequivalence Of Einstein Metricsmentioning

confidence: 99%

“…If the calculated values are equal the two metrics are likely equivalent but more investigation is required to prove it conclusively. [4].…”

Section: Inequivalence Of Einstein Metricsmentioning

confidence: 99%