Related papers: Geometrical inequalities bounding angular momentum…
A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several…
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…
A universal geometric inequality for bodies relating energy, size, angular momentum, and charge is naturally implied by Bekenstein's entropy bounds. We establish versions of this inequality for axisymmetric bodies satisfying appropriate…
Angular momentum and mass-charge inequalities for axisymmetric maximal time-symmetric initial data in Einstein-Maxwell gravity with dark matter sector were derived. The dark matter sector is mimicked by another U(1)-gauge field coupled to…
A universal inequality that bounds the charge of a body by its size is presented, and is proven as a consequence of the Einstein equations in the context of initial data sets which satisfy an appropriate energy condition. We also present a…
We consider the quasi-black hole limit of a stationary body when its boundary approaches its own gravitational radius, i.e., its quasi-horizon. It is shown that there exists a perfect correspondence between the different mass contributions…
Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's…
In 4-dimensional General Relativity, black holes are described by the Kerr solution and are completely specified by their mass $M$ and by their spin angular momentum $J$. A fundamental limit for a black hole in General Relativity is the…
The most general formulation of Penrose's inequality yields a lower bound for ADM mass in terms of the area, charge, and angular momentum of black holes. This inequality is in turn equivalent to an upper and lower bound for the area in…
In an effort to understand the Penrose inequality for black holes with angular momentum, an axisymmetric, vacuum, asymptotically Euclidean initial data set subject to certain quasi-stationary conditions is considered for a case study. A new…
It is well known that the three parameters that characterize the Kerr black hole (mass, angular momentum and horizon area) satisfy several important inequalities. Remarkably, some of these inequalities remain valid also for dynamical black…
We treat the problem of N interacting, axisymmetric black holes and obtain two relations among physical parameters of the system including the force between the black holes. The first relation involves the total mass, the angular momenta,…
A highly accurate computer program is used to study axially symmetric and stationary spacetimes containing a Black Hole surrounded by a ring of matter. It is shown that the matter ring affects the properties of the Black Hole drastically.…
In this essay I first discuss the physical relevance of the inequality $m\geq \sqrt{|J|}$ for axially symmetric (non-stationary) black holes, where m is the mass and J the angular momentum of the spacetime. Then, I present a proof of this…
Black holes have often provided profound insights into the nature of gravity and the structure of space-time. The study of the mathematical properties of black objects is a major research theme of contemporary theoretical physics. This…
Maxwell's equations are invariant under both duality rotations and conformal transformations. Recently Bandos, Lechner, Sorokin, and Townsend have found a nonlinear generalisation of electrodynamics which possesses both of these symmetries.…
We analyse how different Generalised Uncertainty Principles could place bounds on the compactness of self-gravitating systems. By considering existing experimental bounds on the relevant parameters, we conclude that the compactness of large…
We prove that for sub-extremal axisymmetric and stationary black holes with arbitrary surrounding matter the inequality $8\pi|J|<A$ holds, where $J$ is the angular momentum and $A$ the horizon area of the black hole.
We show how to reduce the general formulation of the mass-angular momentum-charge inequality, for axisymmetric initial data of the Einstein-Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations…
Bekenstein bounds for the entropy of a body imply an universal inequality between size, energy, angular momentum and charge. We prove this inequality in Electromagnetism. We also prove it, for the particular case of zero angular momentum,…