Related papers: Gravity and Complexity
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…
In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the…
This paper is a continuation of the papers [gr-qc/9409010, gr-qc/9505034]. A revision of the Einstein equation shows that its dynamic incompleteness, contrary to a popular opinion, cannot be circumvented by so-called coordinate conditions.…
The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the…
The field equations of modified gravity theories, when considering a homogeneous and isotropic cosmological model, always become autonomous differential equations. This relies on the fact that in such models all variables only depend on…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
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…
The content of Einstein's theory of gravitation is encoded in the properties of the solutions to his field equations. There has been obtained a wealth of information about these solutions in the ninety years the theory has been around. It…
A broad class of generalized Einstein's gravity can be cast into Einstein's gravity with a minimally coupled scalar field using suitable conformal rescaling of the metric. Using this conformal equivalence between the theories, we derive the…
We consider general curvature-invariant modifications of the Einstein-Hilbert action that become important only in regions of extremely low space-time curvature. We investigate the far future evolution of the universe in such models,…
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…
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…
Research during the last one decade or so suggests that the gravitational field equations in a large class of theories (including, but not limited to, general relativity) have the same status as the equations of, say, gas dynamics or…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
The topos theory is a theory which is used for deciding a number of problems of theory of relativity, gravitation and quantum physics. In the article spherically symmetric solution of the vacuum Einstein equations in the Intuitionistic…
Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, one argues that it is not unconceivable that classical physical systems may "compute the hard or even the…
We consider certain aspects of cosmological dynamics of a spatially curved Universe in $f(T)$ gravity. Local analysis allows us to find conditions for bounces and for static solutions; these conditions appear to be in general less…
The interpretations of solutions of Einstein field's equations led to the prediction and the observation of physical phenomena which confirm the important role of general relativity, as well as other relativistic theories in physics. In…
A new set of field equations for a space-time dependent Newton's constant $G(x)$ and cosmological constant $\Lambda(x)$ in the presence of matter is presented. We prove that it represents the most general mathematically consistent,…
In this essay we offer a comprehensible overview of the gravitational aether scenario. This is a possible extension of Einstein's theory of relativity to the quantum regime via an effective approach. Quantization of gravity usually faces…