Spacetime Structure near Generic Horizons and Soft Hair

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Expanding around null hypersurfaces, such as generic Kerr black hole horizons, using co-rotating Kruskal-Israel-like coordinates we study the associated surface charges, their symmetries and the corresponding phase space within Einstein gravity. Our surface charges are not integrable in general. Their integrable part generates an algebra including superrotations and a BMS 3 -type algebra that we dub "T-Witt algebra". The non-integrable part accounts for the flux passing through the null hypersurface. We put our results in the context of earlier constructions of near horizon symmetries, soft hair and of the program to semi-classically identify Kerr black hole microstates.

Section: Conserved Charges and Their Algebramentioning

confidence: 89%

Section: Generalized Charge Conservation Hamiltonian and Entropymentioning

confidence: 97%

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T-Witts from the horizon

Adami

Grumiller

Sadeghian

et al. 2020

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“…While we considered the specific example of two asymptotically anti-de Sitter regions, most of our considerations on holonomies and radial Wilson lines qualitatively apply whenever there are two boundaries, independently of the form that the boundary conditions explicitly take there. So, in particular, one boundary can describe an asymptotically anti-de Sitter region and the other can describe a black hole horizon, along the lines of [56,57] (see also [58,59]). Although we have not explored the problem, similar features are also expected to hold with more boundaries.…”

Section: Discussionmentioning

confidence: 99%

Asymptotic dynamics of AdS3 gravity with two asymptotic regions

Henneaux

Merbis

Ranjbar

2020

The asymptotic dynamics of AdS 3 gravity with two asymptotically anti-de Sitter regions is investigated, paying due attention to the zero modes, i.e., holonomies along non-contractible circles and their canonically conjugates. This situation covers the eternal black hole solution. We derive how the holonomies around the non-contractible circles couple the fields on the two different boundaries and show that their canonically conjugate variables, needed for a consistent dynamical description of the holonomies, can be related to Wilson lines joining the boundaries. The action reduces to the sum of four free chiral actions, one for each boundary and each chirality, with additional non-trivial couplings to the zero modes which are explicitly written. While the Gauss decomposition of the SL(2, R) group elements is useful in order to treat hyperbolic holonomies, the Iwasawa decomposition turns out to be more convenient in order to deal with elliptic and parabolic holonomies. The connection with the geometric action is also made explicit. Although our paper deals with the specific example of two asymptotically anti-de Sitter regions, most of our global considerations on holonomies and radial Wilson lines qualitatively apply whenever there are multiple boundaries, independently of the form that the boundary conditions explicitly take there.An interesting feature of the analysis is that the holonomy is dynamical and possesses a conjugate momentum. This conjugate momentum can be related to the radial Wilson lines connecting the boundaries. The phase space of the system is therefore not just two copies of the phase spaces of the boundary theories, but there is in addition the global dynamical zero modes described by the holonomy and the radial Wilson lines. In the quantum theory, the Hilbert space does not factorize into the mere tensor product of the boundary Hilbert spaces, but involves also the zero modes. The non-trivial link between the boundary Hilbert spaces does not need to be implemented by hand since it follows from the action, which is not given by mere multiple copies of one boundary action, but possesses an extra piece coupling the dynamical global zero modes to the boundary fields.It turns out that the resulting reduced boundary theory can be viewed as a dynamical theory of the boundary Virasoro charges, which, together with the zero modes, completely capture the physics of the system. These charges transform in the coadjoint representation of the Virasoro group and the boundary dynamics takes place on the coadjoint orbits.This leads to two different descriptions of the boundary dynamics. One is in terms of chiral bosons, which can be viewed as providing Darboux-like coordinates on the coadjoint orbits. Since there are two SL(2, R) factors and two boundaries, one ends up with four chiral bosons theories, one per SL(2, R) factor and boundary. We show that the chiral bosons corresponding to the same SL(2, R) at two different boundaries are linked by the fact that the conjugate momentum to the holonomy (which is ...

“…For instance, interpolating between asymptotically AdS D boundary conditions (see e.g. [56]) and near horizon boundary conditions [10] will be rewarding to better understand non-extremal black holes and their soft hairy counterparts.…”

Section: Discussionmentioning

confidence: 99%

Interpolating between asymptotic and near horizon symmetries

Grumiller

Sheikh-Jabbari

Troessaert

et al. 2020

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We develop basic tools and matching conditions to interpolate between asymptotic and near horizon symmetries. We focus on black holes in three dimensions. In particular, we match Brown-Henneaux boundary conditions at infinity, which yields two Virasoro algebras, to Heisenberg boundary conditions at the horizon yielding twô u(1) current algebras. Our construction allows to equip BTZ black holes with soft hair excitations at the horizon invisible to the asymptotic observer.