Related papers: Scaling up the extrinsic curvature in asymptotical…
We study the structure of scalar-tensor theories of gravity based on derivative couplings between the scalar and the matter degrees of freedom introduced through an effective metric. Such interactions are classified by their tensor…
We obtain necessary and sufficient conditions for an initial data set for the vacuum conformal Einstein field equations to give rise to a spacetime development in possession of a Killing spinor. The fact that the conformal Einstein field…
Eight different refinements of trapped surfaces are proposed, of three basic types, each intended as potential stability conditions. Minimal trapped surfaces are strictly minimal with respect to the dual expansion vector. Outer trapped…
Data augmentation is a major component of many machine learning methods with state-of-the-art performance. Common augmentation strategies work by drawing random samples from a space of transformations. Unfortunately, such sampling…
This work analyzes the asymptotic behaviors of the asymptotically flat solutions of Einstein-\ae ther theory in the linear case. The vacuum solutions for the tensor, vector, and scalar modes are first obtained, written as sums of various…
Learning performance data describe correct and incorrect answers or problem-solving attempts in adaptive learning, such as in intelligent tutoring systems (ITSs). Learning performance data tend to be highly sparse (80\%\(\sim\)90\% missing…
A marginally outer trapped hypersurface is a generalization of minimal hypersurfaces originated from general relativity. We show a curvature estimate for stable marginally outer trapped hypersurfaces up to the free boundary satisfying a…
In this work, we study various properties of embedded hypersurfaces in $1+1+2$ decomposed spacetimes with a preferred spatial direction, denoted $e^{\mu}$, which are orthogonal to the fluid flow velocity of the spacetime and admit a proper…
As an extended companion paper to [1], we elaborate in detail how the tensor network construction of a p-adic CFT encodes geometric information of a dual geometry even as we deform the CFT away from the fixed point by finding a way to…
In [5], a rigidity result was obtained for outermost marginally outer trapped surfaces (MOTSs) that do not admit metrics of positive scalar curvature. This allowed one to treat the "borderline case" in the author's work with R. Schoen…
In this note we prove two existence theorems for the Einstein constraint equations on asymptotically Euclidean manifolds. The first is for arbitrary mean curvature functions with restrictions on the size of the transverse-traceless data and…
For a given asymptotically flat initial data set for Einstein equations a new geometric invariant is constructed. This invariant measure the departure of the data set from the stationary regime, it vanishes if and only if the data is…
Data augmentation (DA) turns seemingly intractable computational problems into simple ones by augmenting latent missing data. In addition to computational simplicity, it is now well-established that DA equipped with a deterministic…
It was shown recently that the constraints on the initial data for Einstein's equations may be posed as an evolutionary problem [9]. In one of the proposed two methods the constraints can be replaced by a first order symmetrizable…
By suitably re-scaling the conformal Einstein's equations we are able to apply recent results in the theory of PDE, and prove that they possess slow solutions in a future neighborhood of an initial surface reaching ${\cal I}^+$. The…
Motivated by applications to underwater explosions and volcanic eruptions, this paper considers the evolution of an initial pressure disturbance in the ocean, including effects due to the dynamic and static compression of water and the free…
Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint…
Multiple scalar fields appear in vast modern particle physics and gravity models. When they couple to gravity non-minimally, conformal transformation is utilized to bring the theory into Einstein frame. However, the kinetic terms of scalar…
The manifesto of the current article is to investigate the compact anisotropic matter profiles in the context of one of the modified gravitational theories, known as $f(\mathcal{R}, \mathcal{T})$ gravity, where $\mathcal{R}$ is a Ricci…
We investigate, in the transverse traceless (TT) gauge, the generation of the relic background of gravitational waves, generated during an early inflationary stage, on the framework of a large-scale repulsive gravity model. We calculate the…