Related papers: The conformal-to-Einstein equation on M\"obius sur…
We analyze the generic structure of Einstein tensor projected onto a 2-D spacelike surface S defined by unit timelike and spacelike vectors u_i and n_i respectively, which describe an accelerated observer (see text). Assuming that flow…
In this article, we found a connection between Brown-York mass and the first Dirichlet Eigenvalue of a Schr\"odingier type operator. In particular, we proved a local positive mass type theorem for metrics conformal to the background one…
In this thesis, we wish to examine the black-hole solutions of modified gravity theories inspired by String Theory or Cosmology. Namely, these modifications will take the guise of additional gauge and scalar fields for the so-called…
We study the conformally invariant variational problem for time-like curves in the $n$-dimensional Einstein universe defined by the conformal strain functional. We prove that the stationary curves are trapped into an Einsetin universe of…
In this note, we introduce a new type of warped products called as sequential warped products to cover a wider variety of exact solutions to Einstein's equation. First, we study the geometry of sequential warped products and obtain…
It is shown that solutions to Einstein's field equations with positive cosmological constant can include non-zero rest-mass fields which coexist with and travel unimpeded across a smooth conformal boundary. This is exemplified by the…
We study the Jones and Tod correspondence between selfdual conformal 4-manifolds with a conformal vector field and abelian monopoles on Einstein-Weyl 3-manifolds, and prove that invariant complex structures correspond to shear-free geodesic…
We survey some results on scalar curvature and properties of solutions to the Einstein constraint equations. Topics include an extended discussion of asymptotically flat solutions to the constraint equations, including recent results on the…
We establish a connection between two previously unrelated topics: a particular discrete version of conformal geometry for triangulated surfaces, and the geometry of ideal polyhedra in hyperbolic three-space. Two triangulated surfaces are…
The compatibility conditions for generalised continua are studied in the framework of differential geometry, in particular Riemann-Cartan geometry. We show that Vall\'{e}e's compatibility condition in linear elasticity theory is equivalent…
Using the tractor calculus to study smooth metric measure spaces, we adapt results of Gover and Nurowski to give sharp metric obstructions to the existence of quasi-Einstein metrics on suitably generic manifolds. We do this by introducing…
We discuss the analogy between a classical scalar field with a self-interacting potential, in a curved spacetime described by a quasi--bounded state, and a trapped Bose-Einstein condensate. In this context, we compare the Klein-Gordon…
Recently there has been developed a reformulation of General Relativity - referred to as {\it the null surface version of GR} - where instead of the metric field as the basic variable of the theory, families of three-surfaces in a…
In this paper, we study new exact solutions of Einstein's field equations with the motivation of the relativistic elasticity theory. We construct the static conformal elastic solution by applying conformal transformations to the…
We prove existence and uniqueness of solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a quantum massive scalar field with arbitrary coupling to the scalar curvature. In the semiclassical…
Through the study of some elliptic and parabolic fully nonlinear PDEs, we establish conformal versions of quermassintegral inequality, the Sobolev inequality and the Moser-Trudinger inequality for the geometric quantities associated to the…
It is well-known that solutions to the conformal formulation of the Einstein constraint equations are unique in the cases of constant mean curvature (CMC) and near constant mean curvature (near-CMC). However, the new far-from-constant mean…
Einstein gravitation theory can be extended by preserving its geometrical nature but changing the relation between curvature and energy-momentum tensors. This change accounts for radiative corrections, replacing the Newton gravitation…
The first order corrections to the geometry of the (2+1)-dimensional black hole due to back-reaction of a massless conformal scalar field are computed. The renormalized stress energy tensor used as the source of Einstein equations is…
The main objective of this paper is to investigate the $m$-quasi Einstein manifold when the potential function becomes convex. In this article, it is proved that an $m$-quasi Einstein manifold satisfying some integral conditions with…