Related papers: Numerical relativity with the conformal field equa…
In the present investigation compact stellar models are dealt with in the framework of the modified gravity theory, specifically of $f(\mathbb{T},\mathcal{T})$ type. We have considered that the compact objects are following a spherically…
This thesis is concerned with formulations of the Einstein equations in axisymmetric spacetimes which are suitable for numerical evolutions. We develop two evolution systems based on the (2+1)+1 formalism. The first is a (partially)…
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 study the utilization of conformal compactification within the conformal approach to solving the constraints of general relativity for asymptotically flat initial data. After a general discussion of the framework, particular attention is…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
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…
A detailed account is given on approximation schemes to the Einstein theory of general relativity where the iteration starts from the Newton theory of gravity. Two different coordinate conditions are used to represent the Einstein field…
Inspiralling and coalescing binary black holes are promising sources of gravitational radiation. The orbital motion and gravitational-wave emission of such system can be modelled using a variety of approximation schemes and numerical…
The spinorial version of the conformal vacuum Einstein field equations are used to construct a system of quasilinear wave equations for the various conformal fields. As a part of the analysis we also show how to construct a subsidiary…
It has long been considered that conformal superspace is the natural configuration space for canonical general relativity. However, this was never definitively demonstrated. We have found that the standard conformal method of solving the…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
Solving Einstein's equations precisely for strong-field gravitational systems is essential to determining the full physics content of gravitational wave detections. Without these solutions it is not possible to infer precise values for…
A common approach for the numerical simulation of wave propagation on a spatially unbounded domain is to truncate the domain via an artificial boundary, thus forming a finite computational domain with an outer boundary. Absorbing boundary…
In this work, we study linearised gravitational fields on the entire Minkowski space-time including space-like infinity. The generalised conformal field equations linearised about a Minkowski background are utilised for this purpose. In…
Using a combination of techniques from conformal and complex geometry, we show the potentialization of 4-dimensional closed Einstein-Weyl structures which are half-algebraically special and admit a "half-integrable" almost-complex…
When Einstein's equations for an asymptotically flat, vacuum spacetime are reexpressed in terms of an appropriate conformal metric that is regular at (future) null infinity, they develop apparently singular terms in the associated conformal…
A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…
We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in a wide class of modified theories of gravity. The code utilizes a relaxed Newton-Raphson method to…
The regular finite initial value problem at infinity is used to obtain regularity conditions on the freely specifiable parts of initial data for the vacuum Einstein equations with non-vanishing second fundamental form. These conditions…
These lecture notes provide some introduction to the 3+1 formalism of general relativity, which is the foundation of most modern numerical relativity. The text is rather self-contained, with detailed calculations and numerous examples.…