Related papers: On Mason's rigidity theorem
We investigate the existence of dS vacua in supersymmetry-breaking Scherk-Schwarz toroidal compactifications of type II string theory, using the well-understood ingredients of curvature, fluxes and 1-loop Casimir energy. Starting from the…
We consider a general class of four-dimensional geometries admitting a null vector field that has no twist and no shear but has an arbitrary expansion. We explicitly present the Petrov classification of such Robinson-Trautman (and Kundt)…
We give a definition of mass for conformally compactifiable initial data sets. The asymptotic conditions are compatible with existence of gravitational radiation, and the compactifications are allowed to be polyhomogeneous. We show that the…
We establish a rigidity theorem for Brendle and Hung's recent systolic inequality, which involves Gromov's notion of \(T^{\rtimes}\)-stabilized scalar curvature. Our primary technique is the construction of foliations by free boundary…
The orthogonal decomposition of the Webster curvature provides us a way to characterize some canonical metrics on a pseudo-Hermitian manifold. We derive some subelliptic differential inequalities from the Weitzenb\"ock formulas for the…
A new notion of quasilocal mass is defined for generic, compact, two dimensional, spacelike surfaces in four dimensional spacetimes with negative cosmological constant. The definition is spinorial and based on work for vanishing…
In this paper the generalization of the Gribov pendulum equation in the Coulomb gauge for curved spacetimes is analyzed on static spherically symmetric backgrounds. A rigorous argument for the existence and uniqueness of solution is…
The closed-universe recollapse conjecture is studied for a class of closed spherically symmetric spacetimes which includes those having as a matter source: (1) a massless scalar field; (2) a perfect fluid obeying the equation of state $\rho…
We study the geometry generated by a massless cosmic string. We find that this is given by a Riemann flat spacetime with a conical singularity along the worldsheet of the string. The geometry of such a spacetime is completely fixed by the…
We construct Kundt solutions of Minimal Massive Gravity theory and show that, similar to Topologically Massive Gravity (TMG), most of them are constant scalar invariant (CSI) spacetimes, that correspond to deformations of round and warped…
Among all electromagnetic theories which (a) are derivable from a Lagrangian, (b) satisfy the dominant energy condition, and (c) in the weak field limit coincide with classical linear electromagnetics, we identify a certain subclass with…
Critical phenomena in gravitational collapse are characterized by the emergence of surprising structure in solution space, namely the appearance of universal power-laws and periodicities near the threshold of collapse, and a universal…
A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates existence of…
In this paper we analyse Abelian diagonal orthogonally transitive spacetimes with spacelike orbits for which the matter content is a stiff perfect fluid. The Einstein equations are cast in a suitable form for determining their geodesic…
By using the method of group analysis, we obtain a new exact evolving and spherically symmetric solution of the Einstein-Cartan equations of motion, corresponding to a space-time threaded with a three-form Kalb-Ramond field strength. The…
We prove that any smooth Riemannian manifold of non-negative scalar curvature and with a strictly mean convex and compact boundary component can be (C^2) extended beyond the component to have non-negative scalar curvature and to enjoy…
We describe gauge theories which allow to retrieve a large class of gravitational theories, including, MacDowell-Mansouri gravity and its topological extension to Loop Quantum Gravity via the Pontrjagin characteristic class involving the…
Let $\mathcal{E}$ be an asymptotically Euclidean end in an otherwise arbitrary complete and connected Riemannian spin manifold $(M,g)$. We show that if $\mathcal{E}$ has negative ADM-mass, then there exists a constant $R > 0$, depending…
Five tensor equations are obtained for a thin shell in Gauss-Bonnet gravity. There is the well known junction condition for the singular part of the stress tensor intrinsic to the shell, which we also prove to be well defined. There are…
The general structure of the conformal boundary $\mathscr{I}^+$ of asymptotically de Sitter spacetimes is investigated. First we show that Penrose's quasi-local mass, associated with a cut ${\cal S}$ of the conformal boundary, can be zero…