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We show that a class of solutions of minimal supergravity in five dimensions is given by lifts of three--dimensional Einstein--Weyl structures of hyper-CR type. We characterise this class as most general near--horizon limits of supersymmetric solutions to the five--dimensional theory. In particular, we deduce that a compact spatial section of a horizon can only be a Berger sphere, a product metric on $S^1times S^2$ or a flat three-torus. We then consider the problem of reconstructing all supersymmetric solutions from a given near--horizon geometry. By exploiting the ellipticity of the linearised field equations we demonstrate that the moduli space of transverse infinitesimal deformations of a near--horizon geometry is finite--dimensional.
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We construct N=1 supersymmetrisations of some recently-proposed theories of critical gravity, conformal gravity, and extensions of critical gravity in four dimensions. The total action consists of the sum of three separately off-shell supersymmetric actions containing Einstein gravity, a cosmological term and the square of the Weyl tensor. For generic choices of the coefficients for these terms, the excitations of the resulting theory around an AdS_4 background describe massive spin-2 and massless spin-2 modes coming from the metric; massive spin-1 modes coming from a vector field in the theory; and massless and massive spin-3/2 modes (with two unequal masses) coming from the gravitino. These assemble into a massless and a massive N=1 spin-2 multiplet. In critical supergravity, the coefficients are tuned so that the spin-2 mode in the massive multiplet becomes massless. In the supersymmetrised extensions of critical gravity, the coefficients are chosen so that the massive modes lie in a window of lowest energies E_0 such that these ghostlike fields can be truncated by imposing appropriate boundary conditions at infinity, thus leaving just positive-norm massless supergravity modes.
We show how Einstein-Cartan gravity can accommodate both global scale and local scale (Weyl) invariance. To this end, we construct a wide class of models with nonpropagaing torsion and a nonminimally coupled scalar field. In phenomenological applications the scalar field is associated with the Higgs boson. For global scale invariance, an additional field --- dilaton --- is needed to make the theory phenomenologically viable. In the case of the Weyl symmetry, the dilaton is spurious and the theory reduces to a sub-class of one-field models. In both scenarios of scale invariance, we derive an equivalent metric theory and discuss possible implications for phenomenology.
The membrane paradigm posits that black hole microstates are dynamical degrees of freedom associated with a physical membrane vanishingly close to the black holes event horizon. The soft hair paradigm postulates that black holes can be equipped with zero-energy charges associated with residual diffeomorphisms that label near horizon degrees of freedom. In this essay we argue that the latter paradigm implies the former. More specifically, we exploit suitable near horizon boundary conditions that lead to an algebra of `soft hair charges containing infinite copies of the Heisenberg algebra, associated with area-preserving shear deformations of black hole horizons. We employ the near horizon soft hair and its Heisenberg algebra to provide a formulation of the membrane paradigm and show how it accounts for black hole entropy.
Gerochs solution-generating method is extended to the case of Einstein spaces, which possess a Killing vector {{}and are thus asymptotically (locally) (anti-)de Sitter}. This includes the reduction to a three-dimensional coset space, the description of the dynamics in terms of a sigma-model and its transformation properties under the $SL(2,mathbb{R})$ group, and the reconstruction of new four-dimensional Einstein spaces. The detailed analysis of the space of solutions is performed using the Hamilton--Jacobi method in the instance where the three-dimensional coset space is conformal to $mathbb{R}times mathcal{S}_2$. The cosmological constant appears in this framework as a constant of motion and transforms under $SL(2,mathbb{R})$.
We show that the diffeomorphism anomaly together with the trace anomaly reveal a chiral Virasoro algebra near the event horizon of a black hole. This algebra is the same irrespective of whether the anomaly is covariant or consistent, thereby manifesting its universal character and the fact that only the outgoing modes are relevant near the horizon. Our analysis therefore clarifies the role of the trace anomaly in the diffeomorphism anomaly approach cite{wilczek, isowilczek, shailesh, shailesh2, sunandan, sunandan10, rabin10} to the Hawking radiation.
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