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We revisit the problem of solving the Einstein constraint equations in vacuum by a new method, which allows us to prescribe four scalar quantities, representing the full dynamical degrees of freedom of the constraint system. We show that…
We perform three-dimensional numerical relativity simulations of homogeneous and inhomogeneous expanding spacetimes, with a view towards quantifying non-linear effects from cosmological inhomogeneities. We demonstrate fourth-order…
One of the most promising sources of gravitational radiation is coalescence of binary neutron stars or black holes. In order to study gravitational radiation at the merging phase of coalescing binary neutron stars which is called the last…
This paper introduces foundations for a new kind of cosmology. We advocate that computer simulations are needed to address two key cosmological issues. First, the robustness of the emergence of complexity, which boils down to ask: "what…
We consider the problem of building inhomogeneous cosmological models in scalar-tensor theories of gravity. This starts by splitting the field equations of these theories into constraint and evolution equations, and then proceeds by…
Full relativistic simulations in three dimensions are known to develop runaway modes that grow exponentially and are accompanied by violations of the Hamiltonian and momentum constraints. We present here a method that controls the violation…
In this paper, we prove the nonlinear stability in exponential time of Minkowki space-time with a translation space-like Killing field. In the presence of such a symmetry, the 3 + 1 vacuum Einstein equations reduce to the 2 + 1 Einstein…
A new numerical framework, based on the use of a simple first order strongly hyperbolic evolution equations, is introduced and tested in case of 4-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that…
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the…
We study the dynamics of Einstein's equations in Ashtekar's variables from the point of view of the theory of hyperbolic systems of evolution equations. We extend previous results and show that by a suitable modification of the Hamiltonian…
The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A new formulation of constraint-preserving boundary conditions of…
We present a new method of extracting gravitational radiation from three-dimensional numerical relativity codes and providing outer boundary conditions. Our approach matches the solution of a Cauchy evolution of Einstein's equations to a…
To date, essentially all simulation codes that solve the full set of Einstein's equations are performed in the framework of Eulerian hydrodynamics. The exception is our recently developed Numerical Relativity code SPHINCS_BSSN which solves…
The evolution equation of linear cosmic density perturbations in the realm of Einstein-Cartan theory of gravity is obtained.The de Sitter metric fluctuation is computed in terms of the spin-torsion background density.
We present a new evolution system for Einstein's field equations which is based on tetrad fields and conformally compactified hyperboloidal spatial hypersurfaces which reach future null infinity. The boost freedom in the choice of the…
One of the major obstacles to testing alternative theories of gravity with gravitational-wave data from merging binaries of compact objects is the formulation of their field equations, which is often mathematically ill-suited for time…
Theoretical arguments and cosmological observations suggest that Einstein's theory of general relativity needs to be modified at high energies. One of the best motivated higher-curvature extensions of general relativity is…
Recently, Horava proposed a power counting renormalizable theory for (3+1)-dimensional quantum gravity, which reduces to Einstein gravity with a non-vanishing cosmological constant in IR, but possesses improved UV behaviors. In this work,…
Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of…
In contrast to the phenomenon of nullification of the cosmological constant in the equilibrium vacuum, which is the general property of any quantum vacuum, there are many options in modifying the Einstein equation to allow the cosmological…