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Many numerical codes now under development to solve Einstein's equations of general relativity in 3+1 dimensional spacetimes employ the standard ADM form of the field equations. This form involves evolution equations for the raw spatial…
Some models within the framework of Gauss-Bonnet gravities are considered in the presence of a non-minimally coupled scalar field. By imposing a particular constraint on the scalar field coupling, an extension of the called…
A broader perspective is suggested for the study of higher dimensional cosmological models. [1986: Considerations involving the Einstein constraints and the Ricci form of the evolution equations for spatially homogeneous spacetimes in 4 or…
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…
The evolution of inhomogeneities in a spherical collapse model is studied by expanding the Einstein equation in powers of inverse radial parameter. In the linear regime, the density contrast is obtained for flat, closed and open universes.…
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…
A scale--dependent effective action for gravity is introduced and an exact nonperturbative evolution equation is derived which governs its renormalization group flow. It is invariant under general coordinate transformations and satisfies…
There is strong evidence indicating that the particular form used to recast the Einstein equation as a 3+1 set of evolution equations has a fundamental impact on the stability properties of numerical evolutions involving black holes and/or…
A Lagrangian density is provided, that allows to recover the Z4 evolution system from an action principle. The resulting system is then strongly hyperbolic when supplemented by gauge conditions like '1+log' or 'freezing shift', suitable for…
We show that by adding suitable lower-order terms to the Z4 formulation of the Einstein equations, all constraint violations except constant modes are damped. This makes the Z4 formulation a particularly simple example of a lambda-system as…
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…
The Einstein field equations for a class of irrotational non-orthogonally transitive $G_{2}$ cosmologies are written down as a system of partial differential equations. The equilibrium points are self-similar and can be written as a…
We present a code for solving the coupled Einstein-hydrodynamics equations to evolve relativistic, self-gravitating fluids. The Einstein field equations are solved in generalized harmonic coordinates on one grid using pseudospectral…
We show that the 3+1 vacuum Einstein field equations in Ashtekar's variables constitutes a first order symmetric hyperbolic system for arbitrary but fixed lapse and shift fields, by suitable adding to the system terms proportional to the…
We study the dynamics of black holes in Einstein-scalar-Gauss-Bonnet theories that exhibit spontaneous black hole scalarization using recently introduced methods for solving the full, non-perturbative equations of motion. For one sign of…
Motivated by the newest progress in geometric flows both in mathematics and physics, we apply the geometric evolution equation to study some black-hole problems. Our results show that, under certain conditions, the geometric evolution…
A method for studying the causal structure of space-time evolution systems is presented. This method, based on a generalization of the well known Riemann problem, provides intrinsic results which can be interpreted from the geometrical…
A refined version of a recently introduced method for analysing the dynamics of an inhomogeneous irrotational dust universe is presented. A fully non-perturbative numerical computation of the time dependence of volume in this framework…
This paper is devoted to study the stability/instability of the expansionfree self gravitating source in the framework of Einstein Gauss-Bonnet gravity. The source has been taken as Tolman-Bondi model which is homogenous in nature. The…
This is the first of a series of papers describing a numerical implementation of the conformally rescaled Einstein equation, an implementation designed to calculate asymptotically flat spacetimes, especially spacetimes containing black…