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Recent observations of Type 1a supernovae indicating an accelerating universe have once more drawn attention to the possible existence, at the present epoch, of a small positive Lambda-term (cosmological constant). In this paper we review…
Under appropriate spectral assumptions we prove two existence results for positive solutions of Lichnerowicz-type equations on complete manifolds. We also give a priori bounds and a comparison result that immediately yields uniqueness for…
We present a local gluing construction for general relativistic initial data sets. The method applies to generic initial data, in a sense which is made precise. In particular the trace of the extrinsic curvature is not assumed to be…
We find initial data for numerical relativity simulations of inhomogeneous cosmologies. This involves treating an exceptional case of the general relativity constraint equations. We devise analytic and numerical methods to treat this…
A multidimensional cosmological model with space-time consisting of n (n>1) Einstein spaces M_i is investigated in the presence of a cosmological constant Lambda and a homogeneous minimally coupled free scalar field. Generalized de Sitter…
A class of vacuum initial-data sets is described which are based on certain expressions for the extrinsic curvature first studied and employed by Bowen and York. These expressions play a role for the momentum constraint of general…
We construct compact initial data of constant mean curvature $\widetilde{K}$ for Einstein's 4d vacuum equations with $\widehat{\Lambda} = \Lambda - (\widetilde{K}^2/3)$ positive, where $\Lambda$ is the cosmological constant, via the…
For a class of arbitrary large initial data with radial symmetry or cylindrical symmetry, we prove the existence of global solutions for the $3D$ relativistic Vlasov-Poisson system for the plasma physics case. The compact support assumption…
A new class of exact solutions of Einstein's field equations with perfect fluid for an LRS Bianchi type-I spacetime is obtained by using a time dependent deceleration parameter. We have obtained a general solution of the field equations…
We show that there exist asymptotically flat almost-smooth initial data for Einstein-perfect fluid's equation that represent an isolated liquid-type body. By liquid-type body we mean that the fluid energy density has compact support and…
Next year we will celebrate 100 years of the cosmological term, $\Lambda$, in Einstein's gravitational field equations, also 50 years since the cosmological constant problem was first formulated by Zeldovich, and almost about two decades of…
Cosmological models in Lyra's geometry are constructed and investigated with the assumption of a minimal interaction of matter with the displacement vector field and the dynamical $\Lambda$ - term. Exact solutions of the model equations are…
We construct and parametrize solutions to the constraint equations of general relativity in a neighborhood of Minkowski spacetime with arbitrary prescribed decay properties at infinity. We thus provide a large class of initial data for the…
A 3+1 decomposition of the twistor and valence-2 Killing spinor equation is made using the space spinor formalism. Conditions on initial data sets for the Einstein vacuum equations are given so that their developments contain solutions to…
In this note, we show that the conical solution-operator method of Mao-Tao in [Localized initial data for Einstein equations] applies to a simple construction of vacuum asymptotically flat initial data at minimal and borderline decay…
LRS Bianchi type-I models have been studied in the cosmological theory based on Lyra's geometry. A new class of exact solutions has been obtained by considering a time dependent displacement field for variable deceleration parameter models…
The relativistic Vlasov-Maxwell system of plasma physics is considered with initial data on a past light cone. This characteristic initial value problem arises in a natural way as a mathematical framework to study the existence of solutions…
Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field $k$. We survey some results on algebras of finite global dimension and address some open problems.
Einstein's field equations with variable gravitational and cosmological ``constant'' are considered in presence of perfect fluid for Bianchi type-I spacetime. Consequences of the four cases of the phenomenological decay of $\Lambda$ have…
We consider the free-boundary relativistic Euler equations in Minkowski spacetime $\mathbb{M}^{1+3}$ equipped with a physical vacuum boundary, which models the motion of a relativistic gas. We concern ourselves with the family of…