相关论文: Holographic Renormalization of Asymptotically Flat…

We show the existence of a complete, strictly locally convex hypersurface within $\mathbb{H}^{n+1}$ that adheres to a curvature equation applicable to a broad range of curvature functions. This hypersurface possesses a prescribed asymptotic…

This paper studies sharp and rigid isoperimetric comparison theorems and asymptotic isoperimetric properties for small and large volumes on $N$-dimensional ${\rm RCD}(K,N)$ spaces $(X,\mathsf{d},\mathscr{H}^N)$. Moreover, we obtain almost…

We define a notion of renormalized volume of an asymptotically hyperbolic manifold. Moreover, we prove a sharp volume comparison theorem for metrics with scalar curvature at least -6. Finally, we show that the inequality is strict unless…

We show that if an asymptotically flat manifold with horizon boundary admits a global static potential, then the static potential must be zero on the boundary. We also show that if an asymptotically flat manifold with horizon boundary…

We present a novel approach to the analysis of regularity and decay for solutions of wave equations in a neighborhood of null infinity in asymptotically flat spacetimes of any dimension. The classes of metrics and wave type operators we…

The condition for the vanishing of the Weyl tensor is integrated in the spherically symmetric case. Then, the resulting expression is used to find new, conformally flat, interior solutions to Einstein equations for locally anisotropic…

We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this…

An outstanding question lying at the core of the AdS/CFT correspondence in string theory is the holographic prescription problem for Einstein metrics, which asserts that one can slightly perturb the conformal geometry at infinity of the…

We develop a general framework for constructing charges associated with diffeomorphisms in gravitational theories using covariant phase space techniques. This framework encompasses both localized charges associated with spacetime…

We present a new set of asymptotic conditions for gravity at spatial infinity that includes gravitational magnetic-type solutions, allows for a non-trivial Hamiltonian action of the complete $BMS_4$ algebra, and leads to a non-divergent…

We formulate new boundary conditions that prove well defined variational principle and finite response functions for conformal gravity (CG). In the Anti--de Sitter/conformal field theory framework, gravity theory that is considered in the…

A notable example due to Heier, Lu, Wong, and Zheng shows that there exist compact complex K\"ahler manifolds with ample canonical line bundle such that the holomorphic sectional curvature is negative semi-definite and vanishes along…

The asymptotic analysis for the metric of a generic solution of Einstein-Gauss-Bonnet AdS theory is provided by solving the field equations in the Fefferman-Graham frame. Using standard holographic renormalization, the counterterms that…

The formalism of hypersurface data is a framework to study hypersurfaces of any causal character abstractly (i.e. without the need of viewing them as embedded in an ambient space). In this paper we exploit this formalism to study the…

We give a Hamiltonian definition of mass for spacelike hypersurfaces in space-times with metrics which are asymptotic to the anti-de Sitter one, or to a class of generalizations thereof. We show that our definition provides a geometric…

We construct a gravitational dual of the pseudo-conformal universe, a proposed alternative to inflation in which a conformal field theory in nearly flat space develops a time dependent vacuum expectation value. Constructing this dual…

It is common knowledge that the Einstein-Hilbert action does not furnish a well-posed variational principle. The usual solution to this problem is to add an extra boundary term to the action, called a counter-term, so that the variational…

In the first part of this work we show a uniqueness result for globally hyperbolic spacetimes with a spacelike conformal boundary satisfying the vacuum Einstein equations with positive cosmological constant. Then we present applications of…

We show that in a generic scalar-tensor theory of gravity, the ``referenced'' quasilocal mass of a spatially bounded region in a classical solution is invariant under conformal transformations of the spacetime metric. We first extend the…

This article concerns a natural generalization of the classical asymptotic Plateau problem in hyperbolic space. We prove the existence of a smooth complete hypersurface of constant scalar curvature with a prescribed asymptotic boundary at…