Related papers: Birkhoff's invariant and Thorne's Hoop Conjecture

The exceptional Dehn filling conjecture of the second author concerning the relationship between exceptional slopes $\alpha, \beta$ on the boundary of a hyperbolic knot manifold $M$ has been verified in all cases other than small Seifert…

For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the ADM mass and the area of an outermost apparent horizon, if the data are restricted suitably.…

A reformulation of the Hoop Conjecture based on the concept of trapped circle is presented. The problems of severe compactness in every spatial direction, and of how to superpose the hoops with the surface of the black hole, are resolved. A…

By extending the method developed by Arav, Gauntlett, Roberts and Rosen, we construct supersymmetric $AdS_2\times{\Sigma}$ solutions of gauged $\mathcal{N}=8$ supergravity which are asymptotic to the $SU(3)\times{U}(1)$-invariant Warner…

Thanks for the releasing image of supermassive black holes (BHs) by the event horizon telescope (EHT) at the heart of the $M87$ galaxy. After the discovery of this mysterious object, scientists paid attention to exploring the BH shadow…

Arising from admissible extended scale-critical short-pulse initial data, we show that 3+1 dimensional Einstein vacuum equations admit dynamical Kerr black hole formation solutions. Our hyperbolic arguments combine the scale-critical…

The Event Horizon Telescope, a global submillimeter wavelength very long baseline interferometry array, produced the first image of supermassive black hole M87* showing a ring of diameter $\theta_d= 42\pm 3\,\mu$as, inferred a black hole…

We derive a class of inner-extremal regular black hole solutions characterized by a degenerate inner horizon. These geometries arise as polymerized vacuum configurations inspired by loop quantum gravity and constitute effective…

We give a thorough description of the shape of rotating axisymmetric stable black-hole (apparent) horizons applicable in dynamical or stationary regimes. It is found that rotation manifests in the widening of their central regions…

The classical Penrose inequality, a relation between the ADM mass and the area of any cross section of the black hole event horizon, was introduced as a test of the weak cosmic censorship conjecture: if it fails, the trapped surface is not…

We establish a Penrose-type inequality with angular momenta for four dimensional, biaxially symmetric, maximal, asymptotically flat initial data sets $(M,g,k)$ for the Einstein equations with fixed angular momenta and horizon inner boundary…

The classical Birkhoff conjecture claims that the boundary of a strictly convex integrable billiard table is necessarily an ellipse (or a circle as a special case). In this article we prove a complete local version of this conjecture: a…

We consider static, spherically symmetric, electrically or/and magnetically charged configurations of a minimally coupled scalar field with an arbitrary potential $V(\phi)$ in general relativity. Using the inverse problem method, we obtain…

In a recent paper[1], it has been shown that, there cannot be any rotating (Kerr) Black Hole (BH) with finite mass in order that the generic properties associated with the symmetries of stationary axisymmetric Einstein equations are obeyed,…

Recently, Durkee and Reall have conjectured a criterion for linear instability of rotating, extremal, asymptotically Minkowskian black holes in $d\ge 4$ dimensions, such as the Myers-Perry black holes. They considered a certain elliptic…

We investigate the correlated stability conjecture for AdS black holes obtained from the higher dimensional Ricci cubic gravity. It shows that the Ricci tensor perturbations exhibit unstable modes for small AdS black holes when solving…

We prove a version the Penrose inequality for black hole space-times which are perturbations of the Schwarzschild exterior in a slab around a null hypersurface $\underline{\mathcal{N}}_0$. $\underline{\mathcal{N}}_0$ terminates at past null…

We conjecture the following entropy bound to be valid in all space-times admitted by Einstein's equation: Let A be the area of any two-dimensional surface. Let L be a hypersurface generated by surface-orthogonal null geodesics with…

We calculate near-horizon solutions for four-dimensional 4-charge and five-dimensional 3-charge black holes in heterotic string theory from the part of the ten-dimensional tree-level effective action which is connected to gravitational…

The Birkhoff conjecture says that the boundary of a strictly convex integrable billiard table is necessarily an ellipse. In this article, we consider a stronger notion of integrability, namely integrability close to the boundary, and prove…