Related papers: Area-charge inequality and local rigidity in charg…
The Riemannian Penrose inequality is a remarkable geometric inequality between the ADM mass of an asymptotically flat manifold with non-negative scalar curvature and the area of its outermost minimal surface. A version of the Riemannian…
We establish inequalities relating the size of a material body to its mass, angular momentum, and charge, within the context of axisymmetric initial data sets for the Einstein equations. These inequalities hold in general without the…
We present a rigorous proof of the Spacetime Penrose Inequality relating the ADM mass to the area of trapped surfaces in asymptotically flat initial data sets satisfying the dominant energy condition. The main theorem establishes that the…
A lower bound for the ADM mass is established in terms of angular momentum, charge, and horizon area in the context of maximal, axisymmetric initial data for the Einstein-Maxwell equations which satisfy the weak energy condition. If, on the…
The space-time curvature carried by electromagnetic fields is discovered and a new unification of geometry and electromagnetism is found. Curvature is invariant under charge reversal symmetry. Electromagnetic field equations are examined…
Comparison theorems are foundational to our understanding of the geometric features implied by various curvature constraints. This paper considers manifolds with a positive lower bound on either scalar, 2-Ricci, or Ricci curvature, and…
For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with…
We give a lower bound for the Lorentz length of the ADM energy-momentum vector (ADM mass) of 3-dimensional asymptotically flat initial data sets for the Einstein equations. The bound is given in terms of linear growth `spacetime harmonic…
The inequality between area and charge $A\geq 4\pi Q^2$ for dynamical black holes is proved. No symmetry assumption is made and charged matter fields are included. Extensions of this inequality are also proved for regions in the spacetime…
We analyze the dynamics of charged test particles in a singular, horizonless spacetime arising as the massless limit of a charged wormhole in the Einstein--Maxwell--Scalar (EMS) framework. The geometry, sustained solely by an electric…
In this article, we revisit the initial data rigidity theorem of Eichmair, Galloway and Mendes (arxiv:2009.09527). The goal is to strengthen their result by showing that the initial data sets concerned carry a vector field that is lightlike…
We prove that the essential smoothness of the gravitational metric at shock waves in GR, a PDE regularity issue for weak solutions of the Einstein equations, is determined by a geometrical condition which we introduce and name the {\it…
We revisit electric and magnetic surface charges and edge modes in four-dimensional Maxwell theory and QED on a spacetime with a finite spatial boundary. Using the S-wall, which implements electromagnetic duality, we clarify the dual…
We obtain improved local well-posedness results for the Lorentzian timelike minimal surface equation. In dimension $d=3$, for a surface of arbitrary co-dimension, we show a gain of $1/3$ derivative regularity compared to a generic equation…
When a charge accelerates, its field-lines curve in a typical pattern. This pattern resembles the curvature induced on the field-lines by a neighboring charge. Not only does the latter case involve a similar curvature, it moreover results…
In the present paper we consider 5D spacetimes satisfying the Einstein-Maxwell-dilaton gravity equations which are $U(1)^2$ axisymmetric but otherwise highly dynamical. We derive inequalities between the area, the angular momenta, the…
Stationary circularly symmetric solutions of General Relativity with negative cosmological constant coupled to the Maxwell field are analyzed in three spacetime dimensions. Taking into account that the fall-off of the fields is slower than…
Vacuum quasi-topological gravity with infinitely many terms in the action satisfies Markov's limiting curvature hypothesis: the spherically symmetric solutions are regular and all curvature invariants are bounded by solution-independent…
We consider Einstein gravity on a patch of AdS$_3$ spacetime between two radii $r_1, r_2$. We compute surface charges and their algebra at an arbitrary radius $r$ such that it reduces to a given set of surface charges at $r_1, r_2$. The…
We give a comprehensive discussion, including a detailed proof, of the area-angular momentum-charge inequality for axisymmetric black holes. We analyze the inequality from several viewpoints, in particular including aspects with a…