Related papers: Abstract Formulation of the Spacetime Matching Pro…
In order to produce a low energy effective field theory from a string model, it is necessary to specify a vacuum state. In order that this vacuum be supersymmetric, it is well known that all field expectation values must be along so-called…
In this paper we consider singular timelike spherical hypersurfaces embedded in a $D$-dimensional spherically symmetric bulk spacetime which is an electrovacuum solution of Einstein equations with cosmological constant. We analyse the…
The boundary at $\Cal I^+$, future null infinity, for a standard static, spherically symmetric spactime is examined for possible linear connections. Two independent methods are employed, one for treating $\Cal I^+$ as the future causal…
We study singular hypersurfaces in tensor multi-scalar theories of gravity. We derive in a distributional and then in an intrinsic way, the general equations of junction valid for all types of hypersurfaces, in particular for lightlike…
Given that observational and numerical climate data are being produced at ever more prodigious rates, increasingly sophisticated and automated analysis techniques have become essential. Deep learning is quickly becoming a standard approach…
We develop a framework based on the covariant phase space formalism that identifies gravitational edge modes as dynamical reference frames. They enable the identification of the associated spacetime region and the imposition of boundary…
In this paper, we consider vacuum asymptotically anti-de Sitter spacetimes $( \mathscr{M}, g )$ with conformal boundary $( \mathscr{I}, \mathfrak{g} )$. We establish a correspondence, near $\mathscr{I}$, between such spacetimes and their…
The first main result is a topological rigidity theorem for complete immersed hypersurfaces of spherical space forms which extends similar results due to do Carmo/Warner, Wang/Xia and Longa/Ripoll. Under certain sharp conditions on the…
One of the fundamental questions in physics concerns the relation between spacetime and quantum entanglement. The spacetime is usually considered as a fixed background physical space, and the quantum entanglement is usually manifested as a…
We study the geometry of a general class of vacuum asymptotically Anti-de Sitter spacetimes near the conformal boundary. In particular, the spacetime is only assumed to have finite regularity, and it is allowed to have arbitrary boundary…
The characteristic Cauchy problem of the Einstein field equations has been recently addressed from a completely abstract viewpoint by means of hypersurface data and, in particular, via the notion of double null data. However, this…
This article presents a comprehensive and rigorous overview of spacetime singularities within the framework of classical General Relativity. Singularities are defined through the failure of geodesic completeness, reflecting the limits of…
Modified theories of gravity that explicitly break diffeomorphism invariance have been used for over a decade to explore open issues related to quantum gravity, dark energy, and dark matter. At the same time, the Standard-Model Extension…
A candidate for a realistic relativistic quantum theory is the hypersurface Bohm-Dirac model. Its formulation uses a foliation of spacetime into space-like hypersurfaces. This structure may well arise from the universal wave function…
The construction of a theory of quantum gravity is an outstanding problem that can benefit from better understanding the laws of nature that are expected to hold in regimes currently inaccessible to experiment. Such fundamental laws can be…
We establish a deformation framework for highly symmetric solutions to the Einstein equations. In this framework, four-dimensional metrics are constructed from three-dimensional {\eta}-Einstein metrics admitting a deformation determined by…
The null surface formalism of GR in three dimensions is presented, and the gauge freedom thereof, which is not just diffeomorphism, is discussed briefly.
One of the central difficulties of settling the $L^2$-bounded curvature conjecture for the Einstein -Vacuum equations is to be able to control the causal structure of spacetimes with such limited regularity. In this paper we show how to…
We study string theory in supersymmetric time-dependent backgrounds. In the framework of general relativity, supersymmetry for spacetimes without flux implies the existence of a covariantly constant null vector, and a relatively simple form…
We examine local physics in the presence of global variables: variables associated with the whole of the spacelike surfaces of a foliation. These could be the (pseudo-)constants of nature and their conjugate times, but our statements are…