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We apply thermodynamics method to generate exact solution with maximum symmetric surface for Einstein equation without solving it. The exact solutions are identified with which people have solved before. The horizons structure of solutions…
The ultra-long relaxation time of glass transition makes it difficult to construct atomic models of amorphous materials by conventional methods. We propose a novel method for building such atomic models using data assimilation method by…
The asymptotic structure of space-time is studied by imposing conditions on the asymptotics of the metric. These conditions are weak enough to include large classes of physically relevant isolated space-times, but have a rich enough…
This paper continues the investigation of the formation of naked singularities in the collapse of collisionless matter initiated in [RV]. There the existence of certain classes of non-smooth solutions of the Einstein-Vlasov system was…
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…
The Hamiltonian system of general relativity and its quantization without any matter or gauge fields are discussed on the basis of the symplectic geometrical theory. A symplectic geometry of classical general relativity is constructed using…
Analogue space-times (and in particular metamaterial analogue space-times) have a long varied and complex history. Much of the previous related work has focused on spherically symmetric models; however, axial symmetry is much more relevant…
We describe a proof of M.T. Anderson's result on the rigidity of complete stationary initial data for the Einstein vacuum equations in spacetime dimension 3 + 1, under an extra assumption on the norm of the stationary Killing vector field.…
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV…
I study the time--symmetric initial--data problem in theories with a massless scalar field (dilaton), free or coupled to a Maxwell field in the stringy way, finding different initial--data sets describing an arbitrary number of black holes…
We investigate the existence and the global causal structure of plane symmetric spacetimes with weak regularity when the matter consists of an irrotational perfect fluid with pressure equal to its mass-energy density. Our theory encompasses…
Assuming the minimal time to send a bit of information in the Einstein clock synchronization of the two clocks located at different positions, we introduce the extended metric to the information space. This modification of relativity…
We study the evolution of a self-gravitating compressible fluid in spherical symmetry and we prove the existence of weak solutions with bounded variation for the Einstein-Euler equations of general relativity. We formulate the initial value…
We linearize the Einstein equations when the metric is Bondi-Sachs, when the background is Schwarzschild or Minkowski, and when there is a matter source in the form of a thin shell whose density varies with time and angular position. By…
We compute families of solutions to the Einstein vacuum equations of the type of Brill waves, but with slow fall-off towards spatial infinity. We prove existence and uniqueness of solutions for physical data and numerically construct some…
We study the semiclassical Einstein field equations with a Klein-Gordon field in ultrastatic and static spacetimes. In both cases, the equations for the spacetime metric become constraint equations. In the ultrastatic case, the Hadamard…
We present new exact solutions for the Einstein-Maxwell system in static spherically symmetric interior spacetimes. For a particular form of the gravitational potentials and the electric field intensity, it is possible to integrate the…
The regular finite initial value problem at infinity is used to obtain regularity conditions on the freely specifiable parts of initial data for the vacuum Einstein equations with non-vanishing second fundamental form. These conditions…
The Einstein equations in wave map gauge are a geometric second order system for a Lorentzian metric. To study existence of solutions of this hyperbolic quasi diagonal system with initial data on a characteristic cone which are not zero in…
A general way to construct chain models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. As an example the chain models with $A_n$ symmetry and…