We show that the asymptotic symmetries close to nonextremal black hole horizons are generated by an extension of supertranslations. This group is generated by a semidirect sum of Virasoro and Abelian currents. The charges associated with the asymptotic Killing symmetries satisfy the same algebra. When considering the special case of a stationary black hole, the zero mode charges correspond to the angular momentum and the entropy at the horizon.
We prove that non-extremal black holes in four-dimensional general relativity exhibit an infinite-dimensional symmetry in their near horizon region. By prescribing a physically sensible set of boundary conditions at the horizon, we derive the algebra of asymptotic Killing vectors, which is shown to be infinite-dimensional and includes, in particular, two sets of supertranslations and two mutually commuting copies of the Witt algebra. We define the surface charges associated to the asymptotic diffeomorphisms that preserve the boundary conditions and discuss the subtleties of this definition, such as the integrability conditions and the correct definition of the Dirac brackets. When evaluated on the stationary solutions, the only non-vanishing charges are the zero-modes. One of them reproduces the Bekenstein-Hawking entropy of Kerr black holes. We also study the extremal limit, recovering the NHEK geometry. In this singular case, where the algebra of charges and the integrability conditions get modified, we find that the computation of the zero-modes correctly reproduces the black hole entropy. Furthermore, we analyze the case of three spacetime dimensions, in which the integrability conditions notably simplify and the field equations can be solved analytically to produce a family of exact solutions that realize the boundary conditions explicitly. We examine other features, such as the form of the algebra in the extremal limit and the relation to other works in the literature.
A consistent set of asymptotic conditions for higher spin gravity in three dimensions is proposed in the case of vanishing cosmological constant. The asymptotic symmetries are found to be spanned by a higher spin extension of the BMS3 algebra with an appropriate central extension. It is also shown that our results can be recovered from the ones recently found for asymptotically AdS3 spacetimes by virtue of a suitable gauge choice that allows to perform the vanishing cosmological constant limit.
Massive gravity in three dimensions accepts several different formulations. Recently, the 3-dimensional bigravity dRGT model in first order form, Zwei-Dreibein gravity, was considered by Bergshoeff et al. and it was argued that the Boulware-Deser mode is killed by extra constraints. We revisit this assertion and conclude that there are sectors on the space of initial conditions, or subsets of the most general such model, where this mode is absent. But, generically, the theory does carry 3 degrees of freedom and thus the Boulware-Deser mode is still active. Our results also sheds light on the equivalence between metric and vierbein formulations of dRGT model.The search for a well-defined, unitary, stable, massive version of general relativity has seen huge interest in recent years (for a review see [17] A particularly simple and nice formulation of dRGT gravity was put forward in [18] (see also [11,12] for a discussion on the equivalence between metric and vielbein formulations). The action is built using vielbeins 1-forms and their corresponding 2-forms curvatures. A three dimensional version of this formulation, which can shed light on the four dimensional one, has recently been considered in [4]. The action iswhereê a andl a are two independent dreibeins. Here and henceforth wedge product are implicit. The connections are denoted byŵ a andπ a with curvatureŝAll hatted quantities are spacetime forms. The corresponding spatial forms will be denoted by the same letter without the hat. Latin indexes are raised and lowered with Minkowski metric η ab and η ab . For simplicity we do not incorporate cosmological constants at each sector. k 1 and k 2 are free parameters. It was argued in [4] that (1) does not carry a BoulwareDeser mode, in agreement with the 4-dimensional claims (mostly based on the metric formulation, see however [1,12,18]). The goal of this Letter is to critically analyze this issue. Our conclusion will be that the BoulwareDeser mode is generically still active in the formulation (1) even though there are indeed subcases where it is absent.The simplicity of working in three dimensions is seen by the fact that the action (1) is already in Hamiltonian form. One only needs to perform a 2+1 decomposition of forms,êand likewise forŵ a µ dx µ ,π a µ dx µ . The action in the 2+1 decomposition becomeswhere one can read the symplectic structure in a straightforward way. Here 'dot' stands for time derivative andNote that we still use form notation on the 2-dimensional spatial manifold. The spatial fields {e a i , w b j } and {ℓ a i , π b j } form 12 canonical pairs, while the temporal components e a 0 , ℓ a 0 , w a 0 , π a 0 are 12 Lagrange multipliers. This property is characteristic of generally covariant systems and, as we shall remark below, has important consequences on the consistency algorithm. Let us do a first counting of degrees of freedom based on the number of canonical variables and constraints (we shall argue below that there are no secondary constraints in the most generic case). There are 24 ca...
Astrophysical tests of the stability of fundamental couplings, such as the finestructure constant α, are becoming an increasingly powerful probe of new physics. Here we discuss how these measurements, combined with local atomic clock tests and Type Ia supernova and Hubble parameter data, constrain the simplest class of dynamical dark energy models where the same degree of freedom is assumed to provide both the dark energy and (through a dimensionless coupling, ζ, to the electromagnetic sector) the α variation. Specifically, current data tightly constrains a combination of ζ and the present dark energy equation of state w 0 . Moreover, in these models the new degree of freedom inevitably couples to nucleons (through the α dependence of their masses) and leads to violations of the Weak Equivalence Principle. We obtain indirect bounds on the Eötvös parameter η that are typically stronger than the current direct ones. We discuss the model-dependence of our results and briefly comment on how the forthcoming generation of high-resolution ultra-stable spectrographs will enable significantly tighter constraints.
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