Related papers: Positive mass theorems for asymptotically AdS spac…
We showed a positive energy theorem for asymptotically flat initial data sets with the concept of spectral PSC by He-Shi-Yu, Bi-Hao-He-Shi-Zhu and Brendle-Wang; and the Jang equation in Schoen-Yau, Eichmair and Jang. Then, we proved a…
We prove the positive mass theorem for asymptotical flat (AF for short) manifolds with finitely many isolated conical singularities. We do not impose the spin condition. Instead we use the conformal blow up technique which dates back to…
In this paper, we prove the spacetime positive mass theorem for asymptotically flat spin initial data sets with arbitrary ends and a non-compact boundary. Moreover, we demonstrate a quantitative shielding theorem, subject to the tilted…
We prove a harmonic asymptotics density theorem for asymptotically flat initial data sets with compact boundary that satisfy the dominant energy condition. We use this to settle the spacetime positive mass theorem, with rigidity, for…
We study topologically massive (2+1)-dimensional gravity with a negative cosmological constant. The masses of the linearized curvature excitations about AdS_3 backgrounds are not only shifted from their flat background values but, more…
We study the conserved charges of supersymmetric solutions in the topologically massive gravity theory for both asymptotically flat and constant curvature geometries.
Lorentzian simplicial quantum gravity is a non-perturbatively defined theory of quantum gravity which predicts a positive cosmological constant. Since the approach is based on a sum over space-time histories, it is perturbatively…
For n+1 dimensional asymptotically AdS spacetimes which have holographic duals on their n dimensional conformal boundaries, we show that the imposition of causality on the boundary theory is sufficient to prove positivity of mass for the…
We establish a spacetime positive mass theorem and rigidity statement for asymptotically flat spin initial data sets with a codimension one singularity controlled by a matching Bartnik data condition involving spacetime rotations, and…
The Bartnik mass is a quasi-local mass tailored to asymptotically flat Riemannian manifolds with non-negative scalar curvature. From the perspective of general relativity, these model time-symmetric domains obeying the dominant energy…
We obtain an integral inequality for asymptotically linear harmonic functions on asymptotically flat 3-manifolds with noncompact boundary, which implies positivity of a convex combination of ADM masses of two conformally related metrics…
We affirm the rigidity conjecture of the spacetime positive mass theorem in dimensions less than eight. Namely, if an asymptotically flat initial data set satisfies the dominant energy condition and has $E=|P|$, then $E=|P|=0$, where $(E,…
We establish Gromov-Hausdorff stability of the Riemannian positive mass theorem under the assumption of a Ricci curvature lower bound. More precisely, consider a class of orientable complete uniformly asymptotically flat Riemannian…
In a recent paper, Hod has proven no-go theorem for asymptotically flat static regular boson stars. In the present work, we extend discussions to the gravity with a negative cosmological constant. We consider a scalar field vanishing at…
A review of positive energy theorems for asymptotically hyperbolic manifolds
We present positive energy theorems in asymptotically translationally invariant spacetimes which can be applicable to black strings and charged branes. We also address the bound property of the tension and charge of branes.
Linearized gravitational waves in de Sitter space-time are analyzed in detail to obtain guidance for constructing the theory of gravitational radiation in presence of a positive cosmological constant in full, nonlinear general relativity.…
We study a class of non-smooth asymptotically flat manifolds on which metrics fails to be $C^1$ across a hypersurface $\Sigma$. We first give an approximation scheme to mollify the metric, then we prove that the Positive Mass Theorem still…
Recent cosmological observations suggest the existence of a positive cosmological constant $\Lambda$ with the magnitude $\Lambda(G\hbar/c^3) \approx 10^{-123}$. This review discusses several aspects of the cosmological constant both from…
In this paper we show that one can have asymptotically de Sitter (dS), anti-de Sitter (AdS) and flat solutions in Gauss-Bonnet gravity without any need to a cosmological constant term in field equations. First, we introduce static solutions…