arXiv research

Uniqueness theorem for extremal charged black holes in de Sitter space.

In this paper a lower bound for the ADM mass is given in terms of the angular momenta and charges of black holes present in axisymmetric initial data sets for the Einstein-Maxwell equations. This generalizes the mass-angular momentum-charge inequality obtained by Chrusciel and Costa to the case of multiple black holes.…

This paper explores charged black holes in 3+1 dimensions, finding limitations on their existence.

Adds charged black holes to de Sitter space.

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 terms of the remaining quantities. In this note, we establish the lower bound for a …

We study a multiply warped products manifold associated with the Reissner-Nordstrom metric to investigate the physical properties inside the black hole event horizons. It is shown that, different from the uncharged Schwarzschild metric, the Ricci curvature components inside the Reissner-Nordstrom black hole horizons ar…

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 general sufficient condition for the formation of black holes due to concentrati…

We present a proof of the Riemannian Penrose inequality with charge in the context of asymptotically flat initial data sets for the Einstein-Maxwell equations, having possibly multiple black holes with no charged matter outside the horizon, and satisfying the relevant dominant energy condition. The proof is based on a …

Proves stability of charged black holes with small charge.

We prove a mass-angular momentum-charge inequality for a broad class of maximal, asymptotically flat, bi-axisymmetric initial data within the context of five-dimensional minimal supergravity. We further show that the charged Myers-Perry black hole initial data are the unique minimizers. In addition, we establish a rigi…

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 at non-singular points, but in addition remain well-defined and smooth at singula…

New black hole models with both null and spacelike singularities.

Using black-hole inequalities and the increase of the horizon's areas, we show that there are arbitrarily small electro-vacuum perturbations of the standard initial data of the extreme Reissner-Nordstrom black-hole that, (by contradiction), cannot decay in time into any extreme Kerr-Newman black-hole. This proves the e…

Researchers create black holes isometric to extremal Reissner-Nordström.

Study of black hole entropy from 4d theories on hyperbolic manifolds.

We formulate the variational problem for AdS gravity with Dirichlet boundary conditions and demonstrate that the covariant counterterms are necessary to make the variational problem well-posed. The holographic charges associated with asymptotic symmetries are then rederived via Noether's theorem and `covariant phase sp…

The study proves the existence and uniqueness of near-horizon geometries for 5D black holes.

We prove the global non-linear stability, without symmetry assumptions, of slowly rotating charged black holes in de Sitter spacetimes in the context of the initial value problem for the Einstein-Maxwell equations: If one perturbs the initial data of a slowly rotating Kerr-Newman-de Sitter (KNdS) black hole, then in a …

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 energy conditions, thus lending credence to the most general form of Bekenstein's b…

We use the inverse mean curvature flow to establish Penrose-type inequalities for time-symmetric Einstein-Maxwell initial data sets which can be suitably embedded as a hypersurface in Euclidean space $\mathbb R^{n+1}$, $n\geq 3$. In particular, we prove a positive mass theorem for this class of charged black holes. As …

The paper proves extremal black holes form at a critical point of gravitational collapse.

Study of charged scalar fields on Reissner-Nordström spacetimes via energy estimates.

We present a proof of the Riemannian Penrose inequality with charge $r\leq m + \sqrt{m^2-q^2}$, where $A=4πr^2$ is the area of the outermost apparent horizon with possibly multiple connected components, $m$ is the total ADM mass, and $q$ the total charge of a strongly asymptotically flat initial data set for the Einste…

Proves uniqueness of non-extremal Kerr-Newman black holes under small perturbations.

Charge measurements for instantons and gravitational perturbations.

The information loss occurs in an evaporating black hole only if the time evolution ends at the singularity. But as we shall see, the black hole solutions admit analytical extensions beyond the singularities, to globally hyperbolic solutions. The method used is similar to that for the apparent singularity at the event …

We construct a time-symmetric asymptotically flat initial data set to the Einstein-Maxwell Equations which satisfies the inequality: m - 1/2(R + Q^2/R) < 0, where m is the total mass, R=sqrt(A/4) is the area radius of the outermost horizon and Q is the total charge. This yields a counter-example to a natural extension …

This paper describes the black hole threshold in a moduli space of spherically symmetric spacetimes.

Formula for BPS black hole entropy derived from Vinberg cones.

We show the existence of a Hawking vector field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth Einstein-Maxwell space-time without assuming the underlying space-time is analytic. It extends one result of Friedrich, Rácz and Wald, which was limited to the interior of th…

Second part of series studying charged scalar fields on Reissner--Nordström spacetimes.

Study shows how charged MOTS restrict spacetime configurations.

In a recent paper, the authors established the uniqueness of photon spheres in static vacuum asymptotically flat spacetimes by adapting Bunting and Masood-ul-Alam's proof of static vacuum black hole uniqueness. Here, we establish uniqueness of suitably defined sub-extremal photon spheres in static electro-vacuum asympt…

In this paper, a complete analysis of symmetries and conservation laws for the charged squashed Kaluza--Klein black hole spacetime in a Riemannian space is discussed. First, a comprehensive group analysis of the underlying space-time metric using Lie point symmetries are presented and then it the $n$-dimensional optima…

The Einstein/Maxwell equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities phi: R^3Σ-> H^2_C, where Sigma is a subset of the axis of symmetry, and H^2_C is the complex hyperbolic plane. Motivated by this problem, we prove the existence and uniqueness of harmonic m…

New instantons show Einstein-Maxwell fields are more complex.

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 admits a solution. It is also shown that the same reduction argument applies to …

Study large N oscillations in 3D theories related to black hole physics.

In arXiv:0905.2622v1 and arXiv:0910.4785v1, Bray and Khuri outlined an approach to prove the Penrose inequality for general initial data sets of the Einstein equations. In this paper we extend this approach so that it may be applied to a charged version of the Penrose inequality. Moreover, assuming that the initial dat…

Motivated by black hole physics in N=2, D=4 supergravity, we study the geometry of quaternionic-Kahler manifolds M obtained by the c-map construction from projective special Kahler manifolds M_s. Improving on earlier treatments, we compute the Kahler potentials on the twistor space Z and Swann space S in the complex co…

Closed and broken electromagnetic orbits in Kerr-Newman spacetime

We establish a class of area-angular momentum-charge inequalities satisfied by stable marginally outer trapped surfaces in 5-dimensional minimal supergravity which admit a $U(1)^2$ symmetry. A novel feature is the fact that such surfaces can have the nontrivial topologies $S^1 \times S^2$ and $L(p,q)$. In addition to t…

An analytic extension of the Reissner-Nordstrom solution at and beyond the singularity is presented. The extension is obtained by using new coordinates in which the metric becomes degenerate at $r=0$. The metric is still singular in the new coordinates, but its components become finite and smooth. Using this extension …

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 assumption of the maximal condition, and use a notion of size which is easily computab…

We reinterpret the proof of the Riemannian Penrose inequality by H. Bray. The modified argument turns out to have a nice feature so that the flow of Riemannian metrics appearing Bray's proof gives a Lorentzian metric of a spacetime. We also discuss a possible extension of our approach to charged black holes.

New approach simplifies proof of wave equations on black holes.

We note an area-charge inequality orignially due to Gibbons: if the outermost horizon $S$ in an asymptotically flat electrovacuum initial data set is connected then $|q|\leq r$, where $q$ is the total charge and $r=\sqrt{A/4π}$ is the area radius of $S$. A consequence of this inequality is that for connected black hole…

We study a class of supersymmetric spinning particle models derived from the radial quantization of stationary, spherically symmetric black holes of four dimensional N= 2 supergravities. By virtue of the c-map, these spinning particles move in quaternionic Kaehler manifolds. Their spinning degrees of freedom describe m…