Related papers: A Simple, Direct Finite Differencing of the Einste…
A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at…
A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order…
Cosmological tensor perturbations equations are derived for Hamiltonian cosmology based on Ashtekar's formulation of general relativity, including typical quantum gravity effects in the Hamiltonian constraint as they are expected from loop…
We consider the cosmology of the Ricci-tensor-squared gravity in the Palatini variational approach. The gravitational action of standard general relativity is modified by adding a function f(R^abR_ab) to the Einstein-Hilbert action, and the…
Using the Einstein gravitation theory we show how to obtain the basic equations which predict the gravitational waves. This paper was written to graduate and post-graduate students of Physics. We deduce the equations didactically following…
With the arrival of the era of gravitational wave astronomy, the strong gravitational field regime will be explored soon in various aspects. In this article, we provide a general review over cylindrical systems in Einstein's theory of…
We propose a new formulation for 3+1 numerical relativity, based on a constrained scheme and a generalization of Dirac gauge to spherical coordinates. This is made possible thanks to the introduction of a flat 3-metric on the spatial…
Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are…
The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface $Z$ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations…
We study inverse problems for the Einstein equations with source fields in a general form. Under a microlocal linearization stability condition, we show that by generating small gravitational perturbations and measuring the responses near a…
Here show that, pure affine actions based solely on the Riemann curvature tensor lead to Einstein field equations for gravitation. The matter and radiation involved are general enough to impose no restrictions on material dynamics or vacuum…
We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a…
Starting with a field theoretic approach in Minkowski space, the gravitational energy momentum tensor is derived from the Einstein equations in a straightforward manner. This allows to present them as {\it acceleration tensor} = const.…
Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat generalized connections are associated with any…
Axisymmetric numerical simulations of rotating stellar core collapse to a neutron star are performed in the framework of full general relativity. The so-called Cartoon method, in which the Einstein field equations are solved in the…
A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially…
Taking a hint from Dirac's large number hypothesis, we note the existence of cosmologically combined conservation laws that work to cosmologically long time. We thus modify Einstein's theory of general relativity with fixed gravitation…
The Einstein equations for a plane-symmetric gravitational field coupled to an arbitrary nonlinear sigma model (NSM) are shown to be represented in the form of dynamical equations of a {\it generalized effective NSM}. The gravitational…