Adjoint operators, gauge invariant perturbations, and covariant symplectic structure for black holes in string theory

Expressions for the general and complete perturbations in terms of Debye potentials of static charged black holes in string theory, valid for curvature below the Planck scale, are derived starting from a decoupled set of equations and using Wald's method of adjoint operators. Our results cover both extremal and nonextremal black holes and are valid for arbitrary values of the dilaton coupling parameter. The decoupled set is obtained using the Newman-Penrose formulation of the Einstein-Maxwell-dilaton theory and involves naturally field quantities invariant under both ordinary gauge transformations of the electromagnetic potential perturbations and infinitesimal rotations of the perturbed tetrad. Furthermore, using the recent pointed out relationship between adjoint operators and conserved currents, a local continuity law for the field perturbations in terms of the potentials is also obtained. It is shown that such continuity equation implies the existence of conserved quantities and of a covariant symplectic structure on the phase space. Future extensions of the present results are discussed.Comment: LaTeX, 36 pages, submitted to J. Math. Phys. (2002

On the symplectic structures for geometrical theories

We present a new approach for constructing covariant symplectic structures for geometrical theories, based on the concept of adjoint operators. Such geometric structures emerge by direct exterior derivation of underlying symplectic potentials. Differences and similarities with other approaches and future applications are discussed.Comment: LaTeX, 12 page

Identically closed two-form for covariant phase space quantization of Dirac-Nambu-Goto p-branes in a curved spacetime

Using a fully covariant formalism given by Carter for the deformation dynamics of p-branes governed by the Dirac-Nambu-Goto action in a curved background, it is proved that the corresponding Witten's phase space is endowed with a covariant symplectic structure, which can serve as a starting point for a phase space quantization of such objects. Some open questions for further research are outlined.Comment: LaTeX, 8 pages, to be published in Phys. Lett. B. (2002

Global symplectic potentials on the Witten covariant phase space for bosonic extendons

It is proved that the projections of the deformation vector field, normal and tangential to the worldsheet manifold swept out by Dirac-Nambu-Goto bosonic extendons propagating in a curved background, play the role of {\it global} symplectic potentials on the corresponding Witten covariant phase space. It is also proved that the {\it presymplectic} structure obtained from such potentials by direct exterior derivation, has not components tangent to the action of the relevant diffeomorphisms group of the theory.Comment: LaTeX, 8 pages, submitted to Phys. Lett. B. (2002

The Euler characteristic and the first Chern number in the covariant phase space formulation of string theory

Using a covariant description of the geometry of deformations for extendons, it is shown that the topological corrections for the string action associated with the Euler characteristic and the first Chern number of the normal bundle of the worldsheet, although do not give dynamics to the string, modify the symplectic properties of the covariant phase space of the theory. Future extensions of the present results are outlined.Comment: 12 page