Related papers: Numerical Relativity in 3+1 Dimensions
Einstein's field equation of General Relativity (GR) has been known for over 100 years, yet it remains challenging to solve analytically in strongly relativistic regimes, particularly where there is a lack of a priori symmetry. Numerical…
We present a numerically stable system of (3+1) evolution equations for the nonlinear gravitational dynamics of quadratic-curvature corrections to General Relativity (Quadratic Gravity). We also report on the numerical implementation of…
Motivated by the well-known charged BTZ black holes, we look for $(2+1)$-dimensional solutions of $F(R)$ gravity. At first we investigate some near horizon solutions and after that we obtain asymptotically Lifshitz black hole solutions.…
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…
We investigate a class of cosmological solutions of Einstein's field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject…
One of the Holy Grails of observational astronomy is to confirm the prediction that black holes in the Universe are described by the Kerr solution of Einstein's field equations of general relativity. This Topical Collection provides a…
Recent observations of distant supernovae imply, in defiance of expectations, that the universe growth is accelerating, contrary to what has always been assumed that the expansion is slowing down due to gravity. In this paper a…
We present our first successful numerical results of 3D general relativistic simulations in which the Einstein equation as well as the hydrodynamic equations are fully solved. This paper is especially devoted to simulations of test problems…
We present a new derivation of the conservative form of the general relativistic Boltzmann equation and specialize it to the 3+1 metric. The resulting transport equation is intended for use in simulations involving numerical relativity,…
Beyond black holes and neutron stars, new hypothetical compact objects have been proposed as potential astrophysical entities. In general, their properties have not yet been fully explored or understood, nor has it been proven whether or…
Observations of gravitational waves provide new opportunities to study our Universe. In particular, mergers of stellar black holes are the main targets of the current gravitational wave experiments. In order to make accurate predictions, it…
Binary neutron star mergers, which can lead to less massive black holes relative to other known astrophysical channels, have the potential to probe modifications to general relativity that arise at smaller curvature scales compared to more…
One of the most important achievements in general relativity has been discovery of the $(2+1)$-dimensional black hole solutions of Einstein gravity in anti-de Sitter (AdS) spacetime [Phys. Rev. Lett. {\bf69}, 1849 (1992)]. In this paper, we…
We find a choice of variables for the 3+1 formulation of general relativity which casts the evolution equations into (flux-conservative) symmetric-hyperbolic first order form for arbitrary lapse and shift, for the first time. We redefine…
Einstein's theory of General Relativity is one of the pillars of modern physics. For decades, the theory has been mainly tested in the weak field regime with experiments in the Solar System and observations of binary pulsars. Thanks to a…
A new kind of numbers called Hyper Space Complex Numbers and its algebras are defined and proved. It is with good properties as the classic Complex Numbers, such as expressed in coordinates, triangular and exponent forms and following the…
Gravitational waves from merging binary black holes present exciting opportunities for understanding fundamental aspects of gravity, including nonlinearities in the strong-field regime. One challenge in studying and interpreting the…
Gravitational waves radiated during binary black hole coalescence is a perfect probe for studying the characteristics of strong gravity. Advanced techniques for creating numerical relativity substitute models for eccentric binary black hole…
We reformulate Special Relativity by a quaternionic algebra on reals. Using {\em real linear quaternions}, we show that previous difficulties, concerning the appropriate transformations on the $3+1$ space-time, may be overcome. This implies…
We discuss the possibility of a dimensional reduction of the Einstein equations in S3 black-hole lattices. It was reported in previous literature that the evolution of spaces containing curves of local, discrete rotational and reflection…