2006
DOI: 10.1070/sm2006v197n07abeh003784
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Projective geometry of systems of second-order differential equations

Abstract: We show that the 3D charged Banados-Teitelboim-Zanelli (BTZ) black hole solution interpolates between two different 2D AdS spacetimes: a near-extremal, nearhorizon AdS 2 geometry with constant dilaton and U(1) field and an asymptotic AdS 2 geometry with a linear dilaton. Thus, the charged BTZ black hole can be considered as interpolating between the two different formulations proposed until now for AdS 2 quantum gravity. In both cases the theory is the chiral half of a 2D CFT and describes, respectively, Brown… Show more

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Cited by 53 publications
(83 citation statements)
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“…In this paper a review has been provided of the geometric approach to symmetry analysis using the connection between symmetries of geometry and of differential equations provided by the system of geodesic equations, noted by Aminova and Aminov [13] and separately by Feroze et al [15]. This leads to a new approach to investigate the linearizability of ODEs.…”
Section: Resultsmentioning
confidence: 99%
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“…In this paper a review has been provided of the geometric approach to symmetry analysis using the connection between symmetries of geometry and of differential equations provided by the system of geodesic equations, noted by Aminova and Aminov [13] and separately by Feroze et al [15]. This leads to a new approach to investigate the linearizability of ODEs.…”
Section: Resultsmentioning
confidence: 99%
“…A bonus of this approach is that the solution of the linearized equations is obtainable by constructing the transformation of coordinates from Cartesian to the metric tensor given by the geodesic equations [16]. Using this approach and the projection procedure of Aminova and Aminov [13] one can re-derive the Lie criteria for a scalar equation and extend them to a system of equations [17]. One can also extend to the third and higher order scalar equations [19] and to the third order system of equations [21].…”
Section: Resultsmentioning
confidence: 99%
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“…The above matters have been discussed extensively in a series of interesting papers by Aminova [5], [2], [3], [4] who has given an answer. Furthermore in a recent work [6] they have considered the KVs of the metric and their relation to the Lie symmetries of the system of affinely parameterized geodesics of maximally symmetric spaces of low dimension.…”
Section: Motivationmentioning
confidence: 99%