Related papers: Conformal Rigidity from Focusing
We study the effects of trans-planckian censorship conjecture (TCC) bounds on geodesic completeness of spacetime and the associated existence for an infinite proper time. Using Gronwall's lemma, TCC bounds can be derived directly, leading…
Given a time function $\tau$ on a spacetime $M$, we define a `null distance function', $\hat{d}_\tau$, built from and closely related to the causal structure of $M$. In basic models with timelike $\nabla \tau$, we show that 1)…
We address the problem of finding conditions under which a compact Lorentzian manifold is geodesically complete, a property, which always holds for compact Riemannian manifolds. It is known that a compact Lorentzian manifold is geodesically…
Conformal symmetry provides a systematic approximation to QCD in both its perturbative and nonperturbative domains. One can use the AdS/CFT correspondence between Anti-de Sitter space and conformal gauge theories to obtain an analytically…
We reconsider the restoration of the residual gauge symmetry (RGS) due to topological effects as a possible criterion for color confinement. Although the RGS is ``spontaneously broken'' in the perturbative vacuum, it must be restored in the…
We show that a complete Euclidean submanifold with minimal index of relative nullity $\nu_0>0$ and Ricci curvature with a certain controlled decay must be a $\nu_0$-cylinder. This is an extension of the classical Hartman cylindricity…
The null distance for Lorentzian manifolds was recently introduced by Sormani and Vega. Under mild assumptions on the time function of the spacetime, the null distance gives rise to an intrinsic, conformally invariant metric that induces…
Given a complete Riemannian metric of nonnegative scalar curvature on $\Sigma \times (-\infty, 0 ] $, where $\Sigma$ denotes a $2$-sphere, we exhibit conditions that imply the existence of a closed minimal surface homologous to the…
Einstein's General theory of relativity permits spacetime singularities, where null geodesic congruences focus in the presence of matter, which satisfies an appropriate energy condition. In this paper, we provide a minimal defocusing…
In order for spacetimes with static extra dimensions to have 4-dimensional de Sitter expansion they must have at least positive curvature, warping sourced by the 4-d expansion, or violate the null energy condition everywhere in the extra…
We address the problem of consistent Campiglia-Laddha superrotations in $d>4$ by solving Bondi-Sachs gauge vacuum Einstein equations at the non-linear level with the most general boundary conditions preserving the null nature of infinity.…
Using the Navarro-Frenk-White (NFW) dark matter density profile we reconstruct an effective field theory model for gravity at large distances from a central object by demanding that the vacuum solution has the same gravitational properties…
This thesis is concerned with the development and application of conformal techniques to numerical calculations of asymptotically flat spacetimes. The conformal compactification technique enables us to calculate spatially unbounded domains,…
The Raychaudhuri equation for a geodesic congruence in the presence of a zero-point length has been investigated. This is directly related to the small-scale structure of spacetime and possibly captures some quantum gravity effects. The…
Building upon previous works characterizing GRW space-times using concircular and torse-forming vectors, this paper investigates a Lorentzian manifold equipped with a concircularly semi-symmetric metric connection. We demonstrate that such…
The target space of a nonlinear sigma model is usually required to be positive definite to avoid ghosts. We introduce a unique class of nonlinear sigma models where the target space metric has a Lorentzian signature, thus the associated…
I investigate a discrete model of quantum gravity on a causal null-lattice with \SLC structure group. The description is geometric and foliates in a causal and physically transparent manner. The general observables of this model are…
In absence of matter Einstein gravity with a cosmological constant $\La$ can be formulated as a scale-free theory depending only on the dimensionless coupling constant G \Lambda where G is Newton constant. We derive the conformal field…
We continue our investigation of the configuration space of general relativity begun in I (gr-qc/9411009). Here we examine the Hamiltonian constraint when the spatial geometry is momentarily static (MS). We show that MS configurations…
We prove that there are no restrictions on the spatial topology of asymptotically flat solutions of the vacuum Einstein equations in (n+1)-dimensions. We do this by gluing a solution of the vacuum constraint equations on an arbitrary…