47 research outputs found
On the Curvature Invariants of the Massive Banados-Teitelboim-Zanelli Black Holes and Their Holographic Pictures
In this paper, the curvature structure of a (2+1)-dimensional black hole in
the massive-charged-Born-Infeld gravity is investigated. The metric that we
consider is characterized by four degrees of freedom which are the mass and
electric charge of the black hole, the mass of the graviton field, and a
cosmological constant. For the charged and neutral cases separately, we present
various constraints among scalar polynomial curvature invariants which could
invariantly characterize our desired spacetimes. Specially, an appropriate
scalar polynomial curvature invariant and a Cartan curvature invariant which
together could detect the black hole horizon would be explicitly constructed.
Using algorithms related to the focusing properties of a bundle of light rays
on the horizon which are accounted by the Raychaudhuri equation, a procedure
for isolating the black hole parameters, as the algebraic combinations
involving the curvature invariants, would be presented. It will be shown that
this technique could specially be applied for black holes with zero electric
charge, contrary to the cases of solutions of lower-dimensional non-massive
gravity. In addition, for the case of massive (2+1)-dimensional black hole, the
irreducible mass, which quantifies the maximum amount of energy which could be
extracted from a black hole through the Penrose process would be derived.
Therefore, we show that the Hawking temperatures of these black holes could be
reduced to the pure curvature properties of the spacetimes. Finally, we comment
on the relationship between our analysis and the novel roles it could play in
numerical quark-gluon plasma simulations and other QCD models and also black
hole information paradox where the holographic correspondence could be
exploited.Comment: v3; 25 pages; 11 figures; 105 reference
Joint Invariants of Linear Symplectic Actions
We review computations of joint invariants on a linear symplectic space,
discuss variations for an extension of group and space and relate this to other
equivalence problems and approaches, most importantly to differential
invariants.Comment: In this revision we added missing references, and essentially changed
the presentation into a review. We corrected small errors, reduced the
material on algebraic part, and extended it on geometric part. Thus we
elaborate on known results from the classical invariant theory, discuss some
extensions and draw relations to the differential invariants theory via
symplectic invariant discretization
Bounds for degrees of syzygies of polynomials defining a grade two ideal
We make explicit the exponential bound on the degrees of the polynomials appearing in the Effective Quillen-Suslin Theorem, and apply it jointly with the Hilbert-Burch Theorem to show that the syzygy module of a sequence of polynomials in variables defining a complete intersection ideal of grade two is free, and that a basis of it can be computed with bounded degrees. In the known cases, these bounds improve previous results
Polynomial Invariants of the Euclidean Group Action on Multiple Screws
In this work, we examine the polynomial invariants of the special Euclidean group in three dimensions, SE(3), in its action on multiple screw systems. We look at the problem of finding generating sets for these invariant subalgebras,
and also briefly describe the invariants for the standard actions on R^n of both SE(3) and SO(3). The problem of the screw system action is then
approached using SAGBI basis techniques, which are used to find invariants for the translational subaction of SE(3), including a full basis in the one and two-screw cases. These are then compared to the known invariants of the
rotational subaction. In the one and two-screw cases, we successfully derive a full basis for the SE(3) invariants, while in the three-screw case, we suggest some possible lines of approach
Affine equivalences of surfaces of translation and minimal surfaces, and applications to symmetry detection and design
We introduce a characterization for affine equivalence of two surfaces of translation defined by either rational or meromorphic generators. In turn, this induces a similar characterization for minimal surfaces. In the rational case, our results provide algorithms for detecting affine equivalence of these surfaces, and therefore, in particular, the symmetries of a surface of translation or a minimal surface of the considered types. Additionally, we apply our results to designing surfaces of translation and minimal surfaces with symmetries, and to computing the symmetries of the higher-order Enneper surfaces.publishedVersio
Geometric Analysis of Nonlinear Partial Differential Equations
This book contains a collection of twelve papers that reflect the state of the art of nonlinear differential equations in modern geometrical theory. It comprises miscellaneous topics of the local and nonlocal geometry of differential equations and the applications of the corresponding methods in hydrodynamics, symplectic geometry, optimal investment theory, etc. The contents will be useful for all the readers whose professional interests are related to nonlinear PDEs and differential geometry, both in theoretical and applied aspects