In this paper, we consider very rough solutions to Cauchy problem for the Einstein vacuum equations in CMC spacial harmonic gauge, and obtain the local well-posedness result in Hs, s > 2. The novelty of our approach lies in that, without resorting to the standard paradifferential regularization over the rough, Einstein metric g, we manage to implement the commuting vector field approach to prov...

The aim of this paper is to evaluate the energy distribution of some 2 + 1 black hole solutions applying the Landau-Lifshitz and Weinberg definitions. The metrics under consideration describe the charged black hole, the solution coupling to a static scalar field and the static and circularly symmetric exact solution of the Einstein-massless scalar equation. Further, we compare the expressions f...

We show, using purely classical considerations and logical extrapolation of results belonging to point particle theories, that the metric background field in which a string propagates must satisfy an Einstein or an Einstein–like equation. Additionally, there emerge restrictions on the worldsheet curvature, which seems to act as a source for spacetime gravity, even in the absence of other matter...

We study five-dimensional Einstein gravity coupled covariantly to 3-brane with induced gravity on the brane, and consider warped D=4 de Sitter background field solution on the brane. Following background field method we obtain the field equation described by the Lagrangean terms bilinear in quantized gravitational field. In such a free field approximation on curved background we calculate expli...

DARK-BRIGHT SOLITONS AND VORTICES IN BOSE-EINSTEIN CONDENSATES MAY 2014 DONG YAN B.S., ZHEJIANG UNIVERSITY, CHINA M.S., UNIVERSITY OF MASSACHUSETTS AMHERST Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Panayotis G. Kevrekidis This dissertation focuses on the properties of nonlinear waves in Bose-Einstein condensates (BECs). The fundamental model here is the nonlinear Schrödi...

We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein-Maxwell fiel...

Assuming SO(3)-spherical symmetry, the 4–dimensional Einstein equation reduces to an equation conformally related to the field equation for 2–dimensional gravity following from the Lagrangian L = |R|1/3. Solutions for 2–dimensional gravity always possess a local isometry because the traceless part of its Ricci tensor identically vanishes. Combining both facts, we get a new proof of Birkhoff’s t...

Hence .0V is a quantity which can only increase with the time and may be regarded as the entropy of the universe. This quantity proves to be equivalent to the expression that Lenz took for the entropy of the Einstein universe, but, in general, the expression for the entropy of a system in a gravitational field does not reduce to so simple a form. 1 Tolman, R. C., these PROCzSDINGs, 14, No. 3, 2...

We give an explicit proof of the result that non trivial conserved n−2 forms for a spin 2 field on a background corresponding to a solution to Einstein’s equation (with or without cosmological constant) are characterized uniquely by the Killing vector fields of the background. ∗ Research Associate of the National Fund for Scientific Research (Belgium). In dimensions n > 2, a consistent theory f...