Related papers: Null Surfaces and the Bach Equations
We develop the framework that reveals the intrinsic conserved stress tensor and current associated with the null infinity of a three-dimensional ($3d$) asymptotically flat spacetime. These are, respectively, canonical conjugates of…
We prove a Bernstein theorem for $\Phi$-anisotropic minimal hypersurfaces in all dimensional Euclidean spaces that the only entire smooth solutions $u: \mathbb{R}^{n}\rightarrow \mathbb{R}$ of $\Phi$-anisotropic minimal hypersurfaces…
The theory of massive gravity proposed by Bergshoeff, Hohm and Townsend is considered in the special case of the pure irreducibly fourth order quadratic Lagrangian. It is shown that the asymptotically locally flat black holes of this theory…
We determine the class of $p$-forms $F$ which possess vanishing scalar invariants (VSI) at arbitrary order in a $n$-dimensional spacetime. Namely, we prove that $F$ is VSI if and only if it is of type N, its multiple null direction $l$ is…
We study generalized scalar field models coupled to impurities in Minkowski spacetime with arbitrary dimensions. The investigation concerns a class of models that depends explicitly on the spacetime coordinates and also, it reveals the…
We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past…
In this article we study self-gravitating static solutions of the Einstein-ScalarField system in arbitrary dimensions. We discuss the existence and the non-existence of geodesically complete solutions depending on the form of the scalar…
The Conformal Einstein equations and the representation of spatial infinity as a cylinder introduced by Friedrich are used to analyse the behaviour of the gravitational field near null and spatial infinity for the development of data which…
We carry out in full generality and without fixing specific boundary conditions, the symmetry and charge analysis near a generic null surface for two and three dimensional (2d and 3d) gravity theories. In 2d and 3d there are respectively…
It is known that, in an asymptotically flat spacetime, null infinity cannot act as an initial-value surface for massive real scalar fields. Exploiting tools proper of harmonic analysis on hyperboloids and global norm estimates for the wave…
Perturbations of the linearized vacuum Einstein equations on a null cone in the Bondi-Sachs formulation of General Relativity can be derived from a single master function with spin weight two, which is related to the Weyl scalar \Psi_0, and…
The spherically symmetric null hypersurfaces in a Schwarzschild spacetime are smooth away from the singularities and foliate the spacetime. We prove the existence of more general foliations by null hypersurfaces without the spherical…
We express Einstein's field equations for a spherically symmetric ball of general fluid such that they are conducive to an initial value problem. We show how the equations reduce to the Vaidya spacetime in a non-null coordinate frame,…
We present a perturbative formulation of quantum gravity for asymptotically flat vacuum spacetimes based on the Null Surface Formulation (NSF), in which the expansion is ultraviolet-finite term by term up to the orders computed, without the…
In contrast to the Schwarzschild solution, the infinite red-shift surfaces and null surfaces of the Kerr solution to the axially-symmetric Einstein field equations are distinct. Some three-dimensional depictions of these surfaces are…
First and foremost, we show that a 4-dimensional conformally flat generalized Ricci recurrent spacetime $(GR)_4$ is an Einstein manifold. We examine such a spacetime as a solution of $f(R, G)$-gravity theory and it is shown that the…
Matching of a LTB metric representing dust matter to a background FRW universe across a null hypersurface is studied. In general, an unrestricted matching is possible only if the background FRW is flat or open. There is in general no…
A new approach to space-time asymptotics is presented, refining Penrose's idea of conformal transformations with infinity represented by the conformal boundary of space-time. Generalizing examples such as flat and Schwarzschild space-times,…
In this manuscript we prove global existence and linear asymptotic behavior of small solutions to nonlinear wave equations. We assume that the quadratic part of the nonlinearity satisfies a non-resonant condition which is a generalization…
A number of recent observations have suggested that the Einstein's theory of general relativity may not be the ultimate theory of gravity. The f(R) gravity model with R being the scalar curvature turns out to be one of the best bet to…