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The ghost-free theory of massive gravity with two dynamical metrics has been shown to produce viable cosmological expansion, where the late-time acceleration of the Universe is due to the finite range of the gravitational interaction rather…
We show how to reduce the general formulation of the mass-angular momentum inequality, for axisymmetric initial data of the Einstein equations, to the known maximal case whenever a geometrically motivated system of equations admits a…
In this paper we study the even part of the linear stability of the Schwarzschild spacetime as a continuation of [22]. By taking the harmonic gauge, we prove that the energy decays at a rate $\tau^{-2+}$ for the solution of the linearized…
Shape dynamics is a classical theory of gravity which agrees with general relativity in many important aspects, but which possesses different gauge symmetries and can present some fundamental global differences with respect to Einstein…
We argue that the most conservative geometric extension of Einstein gravity describing both positive and negative mass sources and observers is bimetric gravity and contains two copies of standard model matter which interact only…
The Vlasov-Einstein system describes the evolution of an ensemble of particles (such as stars in a galaxy, galaxies in a galaxy cluster etc.) interacting only by the gravitational field which they create collectively and which obeys…
In this talk we show a stiff fluid solution of the Einstein equations for a cylindrically symmetric spacetime. The main features of this metric are that it is non-separable in comoving coordinates for the congruence of the worldlineS of the…
In classical mechanics, the 'geometry of motion' refers to a development to visualize the motion of freely spinning bodies. In this paper, such an approach of studying the rotational motion of axisymmetric variable mass systems is…
If the presence of a gravitational field breaks the Lorentz symmetry valid for special relativity, an "absolute motion" might be detectable. We summarize a scalar theory of gravity with a such "ether", which starts from a tentative…
We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we…
We provide all basic equations and concepts required to carry out a general study on axially symmetric static sources. The Einstein equations and the conservation equations are written down for a general anisotropic static fluid endowed…
In this paper we prove the global existence of classical static solutions of Einstein gravitational theory coupled to a real scalar field where the spacetime admits spherically symmetry. The equations of motions can then be reduced into a…
Some models of modified gravity and their observational manifestations are considered. It is shown, that gravitating systems with mass density rising with time evolve to a singular state with infinite curvature scalar. The universe…
In this paper, we present new axisymmetric and reflection symmetric vacuum solutions to the Einstein field equations. They are obtained using the Hankel integral transform method and all three solutions exhibit naked singularities. Our…
The issue of the physical equivalence between the different coordinate system in Einstein theory is revised. Gauge fixing influences results of measurements and physics are different in two different coordinate system. Spacetime metric…
This paper analyzes the stability of the closed Einstein static universe by using linear homogeneous perturbations in the framework of energy-momentum squared gravity. This newly developed proposal resolves the primordial singularity and…
We quantize a classically stable system of a harmonic oscillator polynomially coupled to a ghost with negative kinetic energy. We prove that due to an integral of motion with a positive discrete spectrum: i) the Hamiltonian has a pure point…
According to Einstein's principle of general covariance, all laws of nature are to be expressed by manifestly covariant equations. In recent work, the covariant law of energy-momentum conservation has been established. Here, we show that…
In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are…
We define a generalized mass for asymptotically flat manifolds using some higher order symmetric function of the curvature tensor. This mass is non-negative when the manifold is locally conformally flat and the $\sigma_k$ curvature vanishes…