arXiv subjects

Gloria Odak

Publications and source records attributed to Gloria Odak.

6 recordsLinked to original sources

arXiv2026

Weyl-transverse gravity with boundaries

We develop the covariant phase space formulation of Weyl-transverse gravity (WTG) in the presence of general timelike and spacelike boundaries. WTG is classically equivalent to General Relativity (GR) but possesses a reduced gauge symmetry consisting of Weyl transformations and transverse diffeomorphisms, together with a fixed background volume form. This structure modifies the variational principle and the definition of conserved quantities relative to GR. We derive the symplectic potential, presymplectic current, and Hamiltonian generators associated with transverse diffeomorphisms, and we identify a set of boundary conditions under which the WTG action is differentiable. These include Dirichlet and Neumann conditions for both the auxiliary Weyl-invariant metric and the dynamical metric, as well as a natural implementation of York boundary conditions, for which WTG exhibits a particularly transparent geometric formulation. We obtain the Noether current and surface charge, clarify the role of the Lagrangian ambiguity related to the cosmological constant, and evaluate the Hamiltonian identity on spacetimes containing a bifurcate Killing horizon. The resulting first-law relation shows that variations of the cosmological constant can contribute nontrivially unless additional physical restrictions are imposed.

gr-qc↗

arXiv2025

On a lower-dimensional Killing vector origin of irreducible Killing tensors

Considering a spacetime foliated by co-dimension-2 hypersurfaces, we find the conditions under which lower-dimensional symmetries of a base space can be lifted up to irreducible Killing tensors of the full spacetime. In this construction, the key ingredient for irreducibility is the non-commutativity of the underlying Killing vectors. It gives rise to a tower of growing rank Killing tensors determined by the structure constants of the corresponding Lie algebra. A canonical example of a metric with such emergent non-trivial hidden symmetries in all dimensions is provided by rotating (off-shell) generalized Lense-Thirring spacetimes, where the irreducible Killing tensors arise from the underlying spherical symmetry of the base space. A physical on-shell realization of this construction in four dimensions is embodied by a rotating black hole in the Einstein-Maxwell-Dilaton-Axion theory. Further examples of equal spinning Myers-Perry spacetimes and spacetimes built on planar and Taub-NUT base metrics are also discussed.

gr-qc↗

arXiv2023

General gravitational charges on null hypersurfaces

We perform a detailed study of the covariance properties of the symplectic potential of general relativity on a null hypersurface, and of the different polarizations that can be used to study conservative as well as leaky boundary conditions. This allows us to identify a one-parameter family of covariant symplectic potentials. We compute the charges and fluxes for the most general phase space with arbitrary variations. We study five symmetry groups that arise when different restrictions on the variations are included. Requiring stationarity as in the original Wald-Zoupas prescription selects a unique member of the family of symplectic potentials, the one of Chandrasekaran, Flanagan and Prabhu. The associated charges are all conserved on non-expanding horizons, but not on flat spacetime. We show that it is possible to require a weaker notion of stationarity which selects another symplectic potential, again in a unique way, and whose charges are conserved on both non-expanding horizons and flat light-cones. Furthermore, the flux of future-pointing diffeomorphisms at leading-order around an outgoing flat light-cone is positive and reproduces a tidal heating plus a memory term. We also study the conformal conservative boundary conditions suggested by the alternative polarization and identify under which conditions they define a non-ambiguous variational principle. Our results have applications for dynamical notions of entropy, and are useful to clarify the interplay between different boundary conditions, charge prescriptions, and symmetry groups that can be associated with a null boundary.

gr-qc↗

arXiv2023

Wald-Zoupas prescription with (soft) anomalies

We show that the Wald-Zoupas prescription for gravitational charges is valid in the presence of anomalies and field-dependent diffeomorphism, but only if these are related to one another in a specific way. The geometric interpretation of the allowed anomalies is exposed looking at the example of BMS symmetries: They correspond to soft terms in the charges. We determine if the Wald-Zoupas prescription coincides with an improved Noether charge. The necessary condition is a certain differential equation, and when it is satisfied, the boundary Lagrangian of the resulting improved Noether charge contains in general a non-trivial corner term that can be identified a priori from a condition of anomaly-freeness. Our results explain why the Wald-Zoupas prescription works in spite of the anomalous behaviour of BMS transformations, and should be helpful to relate different branches of the literature on surface charges.

hep-th↗

arXiv2021

Brown-York charges with mixed boundary conditions

We compute the Hamiltonian surface charges of gravity for a family of conservative boundary conditions, that include Dirichlet, Neumann, and York's mixed boundary conditions defined by holding fixed the conformal induced metric and the trace of the extrinsic curvature. We show that for all boundary conditions considered, canonical methods give the same answer as covariant phase space methods improved by a boundary Lagrangian, a prescription recently developed in the literature and thus supported by our results. The procedure also suggests a new integrable charge for the Einstein-Hilbert Lagrangian, different from the Komar charge for non-Killing and non-tangential diffeomorphisms. We study how the energy depends on the choice of boundary conditions, showing that both the quasi-local and the asymptotic expressions are affected. Finally, we generalize the analysis to non-orthogonal corners, confirm the matching between the covariant and canonical results without any change in the prescription, and discuss the subtleties associated with this case.

hep-th↗

arXiv2020

Conformally Coupled Scalar in Rotating Black Hole Spacetimes

We demonstrate separability of conformally coupled scalar field equation in general (off-shell) Kerr-NUT-AdS spacetimes in all dimensions. The separability is intrinsically characterized by the existence of a complete set of mutually commuting conformal wave operators that can be constructed from a hidden symmetry of the principal Killing-Yano tensor. By token of conformal symmetry, the separability also works for any Weyl rescaled (off-shell) metrics. This is especially interesting in four dimensions where it guarantees separability of a conformally coupled scalar field in the general Plebanski-Demianski spacetime.

hep-th↗