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Register a new userFive dimensional Chern-Simons Gravity for the expanded (anti)-de Sitter gauge group C$_5$
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We study the Hamiltonian dynamics of a five-dimensional Chern-Simons theory for the gauge algebra $C_5$ of Izaurieta, Rodriguez and Salgado, the so-called S$_H$-expansion of the 5D (anti-)de Sitter algebra (a)ds, based on the cyclic group $mathbb{Z}_4$. The theory consists of a 1-form field containing the (a)ds gravitation variables and 1-form field transforming in the adjoint representation of (a)ds. The gravitational part of the action necessarily contains a term quadratic in the curvature, beyond the Einstein-Hilbert and cosmological terms, for any choice of the two independent coupling constants. The total action is also invariant under a new local symmetry, called crossed diffeomorphisms, beyond the usual space-time diffeomorphisms. The number of physical degrees of freedom is computed. The theory is shown to be generic in the sense of Ba~nados, Garay and Henneaux, i.e., the constraint associated to the time diffeomorphisms is not independent from the other constraints.
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We consider a five-dimensional Einstein-Chern-Simons action which is composed of a gravitational sector and a sector of matter, where the gravitational sector is given by a Chern-Simons gravity action instead of the Einstein-Hilbert action, and where the matter sector is given by a perfect fluid. The gravitational lagrangian is obtained gauging some Lie-algebras, which in turn, were obtained by S-expansion procedure of Anti-de Sitter and de Sitter algebras. On the cosmological plane, we discuss the field equations resulting from the Anti-de Sitter and de Sitter frameworks and we show analogies with four-dimensional cosmological schemes.
The equation of motion of an extended object in spacetime reduces to an ordinary differential equation in the presence of symmetry. By properly defining of the symmetry with notion of cohomogeneity, we discuss the method for classifying all these extended objects. We carry out the classification for the strings in the five-dimensional anti-de Sitter space by the effective use of the local isomorphism between $SO(4,2)$ and $SU(2,2)$. We present a general method for solving the trajectory of the Nambu-Goto string and apply to a case obtained by the classification, thereby find a new solution which has properties unique to odd-dimensional anti-de Sitter spaces. The geometry of the solution is analized and found to be a timelike helicoid-like surface.
We study the dynamics of a spherically symmetric thin shell of perfect fluid embedded in d-dimensional Anti-de Sitter space-time. In global coordinates, besides collapsing solutions, oscillating solutions are found where the shell bounces back and forth between two radii. The parameter space where these oscillating solutions exist is scanned in arbitrary number of dimensions. As expected AdS3 appears to be singled out.
We discuss dynamics of massive Klein-Gordon fields in two-dimensional Anti-de Sitter spacetimes ($AdS_2$), in particular conserved quantities and non-modal instability on the future Poincare horizon called, respectively, the Aretakis constants and the Aretakis instability. We find out the geometrical meaning of the Aretakis constants and instability in a parallel-transported frame along a null geodesic, i.e., some components of the higher-order covariant derivatives of the field in the parallel-transported frame are constant or unbounded at the late time, respectively. Because $AdS_2$ is maximally symmetric, any null hypersurfaces have the same geometrical properties. Thus, if we prepare parallel-transported frames along any null hypersurfaces, we can show that the same instability emerges not only on the future Poincare horizon but also on any null hypersurfaces. This implies that the Aretakis instability in $AdS_2$ is the result of singular behaviors of the higher-order covariant derivatives of the fields on the whole $AdS$ infinity, rather than a blow-up on a specific null hypersurface. It is also discussed that the Aretakis constants and instability are related to the conformal Killing tensors. We further explicitly demonstrate that the Aretakis constants can be derived from ladder operators constructed from the spacetime conformal symmetry.
Understanding black hole microstructure via the thermodynamic geometry can provide us with more deeper insight into black hole thermodynamics in modified gravities. In this paper, we study the black hole phase transition and Ruppeiner geometry for the $d$-dimensional charged Gauss-Bonnet anti-de Sitter black holes. The results show that the small-large black hole phase transition is universal in this gravity. By reducing the thermodynamic quantities with the black hole charge, we clearly exhibit the phase diagrams in different parameter spaces. Of particular interest is that the radius of the black hole horizon can act as the order parameter to characterize the black hole phase transition. We also disclose that different from the five-dimensional neutral black holes, the charged ones allow the repulsive interaction among its microstructure for small black hole of higher temperature. Another significant difference between them is that the microscopic interaction changes during the small-large black hole phase transition for the charged case, where the black hole microstructure undergoes a sudden change. These results are helpful for peeking into the microstructure of charged black holes in the Gauss-Bonnet gravity.
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