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We introduce a new, open-source computational general relativity framework for the Wolfram Language called Gravitas, which boasts a number of novel and distinctive features as compared to the many pre-existing computational and numerical…
We investigate the evolution of cosmological perturbations in models of dark energy described by a time-like unit normalized vector field specified by a general function $\mathcal{F}(\mathcal{K})$, so-called Generalized Einstein-Aether…
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 paper is the first part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the…
The Einstein evolution equations are studied in a gauge given by a combination of the constant mean curvature and spatial harmonic coordinate conditions. This leads to a coupled quasilinear elliptic--hyperbolic system of evolution…
The asymptotic behavior of geometry near the boundary of maximal Cauchy development is studied using a perturbative method, which at the zeroth order reduces Einstein's equations to an exactly solvable set of equations---Einstein's…
This paper is the third part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the…
We present several improvements to the Cauchy-characteristic evolution procedure that generates high-fidelity gravitational waveforms at $\mathcal{I}^+$ from numerical relativity simulations. Cauchy-characteristic evolution combines an…
We analyze existence and properties of solutions of two-dimensional general relativistic initial data sets with a negative cosmological constant, both on spacelike and characteristic surfaces. A new family of such vacuum, spacelike data…
The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion dynamics of self-gravitating particles within the Einstein theory of general relativity. We study the Cauchy problem for spatially homogeneous and isotropic solutions…
In the Cauchy problem of general relativity one considers initial data that satisfies certain constraints. The evolution equations guarantee that the evolved variables will satisfy the constraints at later instants of time. This is only…
General hypersurfaces of any causal character can be studied abstractly using the hypersurface data formalism. In the null case, we write down all tangential components of the ambient Ricci tensor in terms of the abstract data. Using this…
In this paper, we sketch the proof of the extension of the stability theorem of the Minkowski space in General Relativity done explicitly in previous work by the present author. We discuss solutions of the Einstein vacuum (EV) equations. We…
In this paper, we consider the initial value problem for the Einstein-Vlasov-Scalar field equations in temporal gauge, where the initial data are prescribed on two characteristic smooth intersecting hypersurfaces. From a suitable choice of…
We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary dimensions. We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime…
In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditions. Such conditions have to be chosen carefully. In…
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV…
The conformal method is a technique for finding Cauchy data in general relativity solving the Einstein constraint equations, and its parameters include a conformal class, a conformal momentum (as measured by a densitized lapse), and a mean…
A consistent approach to Cosmology requires an explicit averaging of the Einstein equations, to describe a homogeneous and isotropic geometry. Such an averaging will in general modify the Einstein equations. The averaging procedure due to…
We study the evolution of a self-gravitating compressible fluid in spherical symmetry and we prove the existence of weak solutions with bounded variation for the Einstein-Euler equations of general relativity. We formulate the initial value…