Related papers: General Bounds on Holographic Complexity
In the AdS/CFT correspondence one encounters theories that are not invariant under diffeomorphisms. In the boundary theory this is a gravitational anomaly, and can arise in 4k+2 dimensions. In the bulk, there can be gravitational…
The recently suggested notion of total mass density for closed universes is extended to closed universes with a positive cosmological constant. Assuming that the matter fields satisfy the dominant energy condition, it is shown that the…
Motivated by the holographic principle, within the context of the AdS/CFT Correspondence in the large t'Hooft limit, we investigate how the geometry of certain highly symmetric bulk spacetimes can be recovered given information of physical…
We provide a background-independent formulation of the holographic principle. It permits the construction of embedded hypersurfaces (screens) on which the entire bulk information can be stored at a density of no more than one bit per Planck…
Due to quantum fluctuations, spacetime is foamy on small scales. For maximum spatial resolution of the geometry of spacetime, the holographic model of spacetime foam stipulates that the uncertainty or fluctuation of distance $l$ is given,…
We present explicit expressions of the thermodynamic volume inside and outside the cosmological horizon of Eguchi-Hanson solitons in general odd dimensions. These quantities are calculable and well-defined regardless of whether or not the…
We prove several global existence theorems for spacetimes with toroidal or hyperbolic symmetry with respect to a geometrically defined time. More specifically, we prove that generically, the maximal Cauchy development of $T^2$-symmetric…
Known solutions to three-dimensional gravity with negative cosmological constant so far consist of either AdS$_3$ or its orbifolds (or orientifolds). We geometrically derive a novel non-orientable AdS$_3$ spacetime that is an orientifold of…
We describe what can be called the "universal" phase space of AdS3 gravity, in which the moduli spaces of globally hyperbolic AdS spacetimes with compact spatial sections, as well as the moduli spaces of multi-black-hole spacetimes are…
A generic spacetime topology contains timelike boundaries. Making use of two such boundaries, we formulate a microscopic holographic dual that captures cosmological spacetime beyond the cosmic horizon patch, including the future wedge. We…
We study the dimensionality manifested in the AdS/CFT correspondence. We show that the dimensionality as expressed by the high temperature behavior of a system has a holographic nature also at the quantum level. The emergence of the AdS…
Say S is a compact three-manifold with non-positive Yamabe invariant. We prove that in any long time constant mean curvature Einstein flow over S, having bounded C^{\alpha} space-time curvature at the cosmological scale, the reduced volume…
We show that gravitational energy expression simplifies when a new set of coordinates that satisfies a certain asymptotic gauge condition is used. Compared to the ADM formula, positivity of the energy is more transparent in this new…
We extend standard results for vacuum asymptotically locally AdS (AlAdS) spacetimes, showing that such spacetimes can be constructed as foliations where the induced metric on each hypersurface satisfies Einstein's equation with…
We present several classes of exact solutions in the Einstein-Klein-Gordon system with a cosmological constant. The spacetime has spherical, plane, or hyperbolic symmetry and the higher-dimensional solutions are obtained in a closed form…
We consider solutions in Einstein-Maxwell theory with a negative cosmological constant that asymptote to global $AdS_{4}$ with conformal boundary $S^{2}\times\mathbb{R}_{t}$. At the sphere at infinity we turn on a space-dependent…
We review issues related to conservation laws for gravity with a negative cosmological constant subject to asymptotically (locally) anti-de Sitter boundary conditions. Beginning with the empty AdS spacetime, we introduce asymptotically…
It is argued that the role of infinite dimensional asymptotic symmetry groups in gravity theories are essential for a holographic description of gravity and possibly to a resolution of the black hole information paradox. I present a simple…
We study asymptotically Lifshitz spacetimes and the constraints on flows between Lifshitz fixed points imposed by the null energy condition. In contrast with the relativistic holographic c-theorem, where the effective AdS radius, L, is…
The fact that AdS black hole interior geometries are time-dependent presents two challenges: first, to holographic duality (the boundary matter tends to equilibrate, often very quickly), and, second, to the idea that wormholes can be…