Generalized off-shell ADT conserved charges in the presence of matter Chern–Simons term

Abstract

In this paper we elevate the formalism for off-shell Abbott-Deser-Tekin (ADT) conserved charges in the presence of arbitrary matter fields to including the internal gauge transformation, when the gauge fields are present. For this purpose, we resort to exact symmetry, and the symmetry generator is combined by diffeomorphism and gauge transformation. For universality, we consider an apparently non-covariant Lagrangian, which contains a matter Chern-Simons term. We show that the elevated off-shell ADT formalism is equivalent to the covariant phase space method and the Barnich-Brandt-Compère (BBC) formalism. To check the validity of our method, we explicitly compute the conserved charges of general non-extremal rotating charged Gödel black holes in minimal five-dimensional gauged supergravity, reproducing the previously known results.

Surface charges toolkit for gravity

“…(J. 14) and we directly recover (J.12). This short calculation shows the power of the contracting homotopy operator approach.…”

“…In the present notes we extensively explore the first 2 See for instance a recent review about the equivalence among the Iyer-Wald and Barnich-Brandt procedure [13]. Analogously, in [14] was shown that the of-shell Abbot-Deser-Tekin formalism is related to the Iyer-Wald and Barnich-Brandt-Compére formalism. 3 It is worth to note here that the quasi-local treatment for the charge conservation ensures, given a spacetime with exact symmetries, the independence of the radius.…”

“…Coming back to the Cartan formulation of gravity, though less preferred in the literature 14 , it has undoubtedly advantages to provide an explicit coordinate-invariant description, to describe the coupling with fermionic matter fields, and to study dynamical and nondynamical torsion.…”

“…This formula should be compared with the results in[17],(4.22) in[18],(4.13) in[19], or recently(51) in[14]. In the explicit formulas of[18] and[19], an extra term 2F µρ δgρσg σν appears, due to their different definition of the variation of the field strength with the indices up: δF µν ≡ g µσ g νρ δFσρ.…”

Off-shell ADT conserved quantities in Palatini gravity

“…Along another line, general theory of conserved charges based on the cohomology principles was developed by Barnich-Brandt-Compère (BBC) [17][18][19][20]. Recently, an off-shell ADT formalism was proposed by Bouchareb, Clément [21] and Kim-Kulkami-Yi in [22], and subsequently was generalized to including the matter fields [23,24].…”