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.
Using the solution phase space method, we investigate the thermodynamics of black holes in Einstein-aether-Maxwell theory, for which the traditional Wald method (covariant phase space method) fails. We show the first laws of thermodynamics and definitive entropy expressions at both Killing and universal horizons for some examples of exact black hole solutions, including threedimensional static charged quasi-BTZ black hole, two four-dimensional static charged black holes and three-dimensional rotating solution. At Killing horizons the entropies are exactly one quarter of the horizon area, but at universal horizons of three-dimensional black holes, the entropies have a corrected term in addition to the one proportional to the horizon area.
In the framework of the new version of the gedanken experiments proposed by Sorce and Wald, we investigate the weak cosmic censorship conjecture (WCCC) for an Einstein–Maxwell–Dilaton–Axion (EMDA) black hole. Our result shows that no violations of WCCC can occur with the increase of the background solution parameters for this near-extremal EMDA black hole when the second-order correction of the perturbations is taken into account. Namely, the near-extremal EMDA black hole cannot be over-charged or over-spun.
In this paper we generalize the off-shell Abbott–Deser–Tekin (ADT) conserved charge formalism to Palatini theory of gravity with torsion and non-metricity. Our construction is based on the coordinate formalism and the independent dynamic fields are the metric and the affine connection. For a general Palatini theory of gravity, which is diffeomorphism invariant up to a boundary term, we obtain the most general expression for off-shell ADT potential. As explicit examples, we derive the off-shell ADT potentials for Einstein–Hilbert action, the most general theories and the teleparallel Palatini gravity.
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