Related papers: Analytical external spherical solutions in entangl…
The vacuum solutions around a spherically symmetric and static object in the Starobinsky model are studied with a perturbative approach. The differential equations for the components of the metric and the Ricci scalar are obtained and…
We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the…
By using of the Euler-Lagrange equations, we find a static spherically symmetric solution in the Einstein-aether theory with the coupling constants restricted. The solution is similar to the Reissner-Nordstrom solution in that it has an…
Gompf's end-sum techniques are used to establish the existence of an infinity of non-diffeomorphic manifolds, all having the same trivial ${\bf R^4}$ topology, but for which the exotic differentiable structure is confined to a region which…
One method for the numerical treatment of future null-infinity is to decouple coordinates from the tensor basis and choose each in a careful manner. This dual-frame approach is hampered by logarithmically divergent terms that appear in a…
We develop hybrid projection methods for computing solutions to large-scale inverse problems, where the solution represents a sum of different stochastic components. Such scenarios arise in many imaging applications (e.g., anomaly detection…
A strategy for generating entanglement in two separated optomechanical oscillators is analysed, using entangled radiation produced from downconversion and stored in an initiating cavity. We show that the use of pulsed entanglement with…
We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a…
Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical…
We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface $\Sigma$ that separates two subsystems of quantum strongly coupled…
Recent works by the second author and Maxwell et al. have shown that the Einstein-scalar field conformal constraint equations are highly complex and generally intractable, even in the vacuum case. In this article, to gain a clearer…
We present an exact static black hole solution of Einstein field equations in the framework of Horndeski Theory by imposing spherical symmetry and choosing the coupling constants in the Lagrangian so that the only singularity in the…
In this article, we provide a pedagogical review of the Tolman-Oppenheimer-Volkoff (TOV) equation and its solutions which describe static, spherically symmetric gaseous stars in general relativity. Our discussion starts with a systematic…
In this work, we consider a very simple gravitational theory that contains a scalar field with its kinetic and potential terms minimally coupled to gravity, while the scalar field is assumed to have a coulombic form. In the context of this…
We solve, numerically, the massless spin-2 equations, written in terms of a gauge based on the properties of conformal geodesics, in a neighbourhood of spatial infinity using spectral methods in both space and time. This strategy allows us…
Satisfactory description of gravitational and gravity potentials is needed for a proper modelling of a wide spectrum of physical problems on various size scales, ranging from atmosphere dynamics up to the movements of stars in a galaxy. In…
We present an algorithm for the rapid numerical integration of smooth, time-periodic differential equations with small nonlinearity, particularly suited to problems with small dissipation. The emphasis is on speed without compromising…
This paper is a self-contained presentation of certain aspects of the theory of weighted Sobolev spaces and elliptic operators on non-compact Riemannian manifolds. Specifically, we discuss (i) the standard and weighted Sobolev Embedding…
We study the most general case of spherically symmetric vacuum solutions in the framework of the Covariant Horava Lifshitz Gravity, for an action that includes all possible higher order terms in curvature which are compatible with…
We present a numerical technique for solving evolution equations, as the wave equation, in the description of rotating astrophysical compact objects in comoving coordinates, which avoids the problems associated with the light cylinder. The…