Quasilocal mass in general relativity is a notion defined for a closed spacelike 2-surface in spacetime. In this note, we explain the definition in [23] and [24] from a mathematical viewpoint, emphasizing the connection to differential geometry and nonlinear partial differential equations. We also discuss a minimax interpretation of the definition and compare with other notions of quasilocal ma...

After a review on asymptotic flatness, a general discussion of asymptotic weak and strong Poincaré charges in metric gravity is given with special emphasis on the boundary conditions needed to define the proper Hamiltonian gauge transformations and to get a differentiable Dirac Hamiltonian. Lapse and shift functions are parametrized in a way which allows to identify their asymptotic parts with ...

We consider a novel curvature flow for curves on the 2-dimensional light cone, contained in 3-dimensional Minkowski space. show that solutions to (CF) such are correspondence with inverse (ICF). prove ellipses and hyperbolas only evolve under homotheties. The closed ones they ancient solutions. spacelike curve cone is self-similar solution CF (resp. (ICF)) if, its of curvature) differs by const...

I argue that string theory compactified on a Riemann surface crosses over at small volume to a higher dimensional background of supercritical string theory. Several concrete measures of the count of degrees of freedom of the theory yield the consistent result that at finite volume, the effective dimensionality is increased by an amount of order 2h/V for a surface of genus h and volume V in stri...

We obtain necessary and sufficient conditions for an initial data set the vacuum conformal Einstein field equations to give rise a spacetime development in possession of Killing spinor. The fact that are used our derivation allows possibility hypersurface S intersecting non-trivially with (or even being subset of) null infinity I. For conciseness, these derived assuming is spacelike. Hence, par...

Recently there has been growing interest in asymptotically anti–de Sitter ~AdS! black holes, motivated by the discovery of the Bañados-Teitelboim-Zanelli ~BTZ! black hole @1# in general relativity ~for reviews see @2,3#! and by the so-called AdS-CFT ~conformal field theory! speculation in string theory @4#. Very recently, Pretorius and Choptuik presented results of fully nonlinear numerical sim...

We argue that any non-gravitational holographic dual to asymptotically flat string theory in d-dimensions naturally resides at spacelike infinity. Since spacelike infinity can be resovled as a (d − 1)-dimensional timelike hyperboloid (i.e., as a copy of de Sitter space in (d− 1) dimensions), the dual theory is defined on a Lorentz signature spacetime. Conceptual issues regarding such a duality ...

We study connected orientable spacelike hypersurfaces $x:M^{n}rightarrowM_q^{n+1}(c)$, isometrically immersed into the Riemannian or Lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~L_kx=Ax+b$,~ where $L_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $H_{k+1}$ of the hypersurface for a fixed integer $0leq k