arXiv research

Study static Einstein-Maxwell space invariant by translation.

Proves a Minkowski inequality for static Einstein-Maxwell space-time.

Constructs solutions to Einstein-Maxwell-current system using Sasakian manifolds.

The paper explores stable surfaces in Einstein-Maxwell theory, proving mass bounds and nonexistence results.

We construct infinite-dimensional families of non-singular static space times, solutions of the vacuum Einstein-Maxwell equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.

Paper proves trapped surface formation for Einstein-Maxwell-charged scalar field system.

New instantons show Einstein-Maxwell fields are more complex.

We prove that Maxwell fields of asymptotically flat solutions of the Einstein-Maxwell equations inherit the stationarity of the metric.

We classify up to automorphisms all left-invariant non-Einstein solutions to the Einstein--Maxwell equations on 4-dimensional Lie algebras.

Adds charged black holes to de Sitter space.

Any constant-scalar-curvature Kaehler (cscK) metric on a complex surface may be viewed as a solution of the Einstein-Maxwell equations, and this allows one to produce solutions of these equations on any 4-manifold that arises as a compact complex surface with b_1 even. It is shown, however, that not all solutions of th…

New solution to Einstein-Maxwell equations invariant under dilations.

This paper produces explicit strongly Hermitian Einstein-Maxwell solutions on the smooth compact $4$-manifolds that are $S^2$-bundles over compact Riemann surfaces of any genus. This generalizes the existence results by C. LeBrun in arXiv:1411.3992 and arXiv:1504.06669. Moreover, by calculating the (normalized) Einstei…

Uniform K-stability ensures existence of special metrics on toric manifolds.

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

Study finds obstacles to solutions for specific equations on compact surfaces.

Page's Einstein metric on CP_2 # (-CP_2) is conformally related to an extremal Kaehler metric. Here we construct a family of conformally Kähler solutions of the Einstein-Maxwell equations that deforms the Page metric, while sweeping out the entire Kaehler cone of CP_2 # (-CP_2).The same method also yields analogous sol…

Paper proves new inequalities for Einstein-Maxwell data sets.

We prove variants of known singularity theorems ensuring the existence of a region of finite lifetime that are particularly well applicable if the solution admits a conformal extension, a property satisfied e.g. by maximal Cauchy developments of Einstein-Maxwell initial values close to the trivial ones.

Researchers solve field equations for special gravitational instantons.

We prove that if a compact smooth polarized complex manifold admits in the corresponding Hodge Kähler class a conformally Kähler, Einstein--Maxwell metric, or more generally, a Kähler metric of constant $(ξ, a, p)$-scalar curvature, then this metric minimizes the $(ξ,a,p)$-Mabuchi functional. Our method of proof extend…

A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the presence of matter it is possible to construct a conformal gauge which allows to kno…

In this note we prove that a special family of Killing potentials on certain Hirzebruch complex surfaces, found by Futaki and Ono, gives rise to new conformally Kähler, Einstein-Maxwell metrics. The correspondent Kähler metrics are ambitoric but they are not given by the Calabi ansatz. This answers in positive question…

In this paper, we study a coupled system of equations on oriented compact 4-manifolds which we call the Bach-Merkulov equations. These equations can be thought of as the conformally invariant version of the classical Einstein-Maxwell equations in general relativity. Inspired by the work of C. LeBrun on Einstein-Maxwell…

Study on type-D metrics aligned with Einstein-Maxwell equations, deriving solutions.

Study shows how electromagnetic and gravitational waves can form trapped surfaces.

We obtain a structure theorem for the group of holomorphic automorphisms of a conformally Kähler, Einstein-Maxwell metric, extending the classical results of Matsushima, Licherowicz and Calabi in the Kähler-Einstein, cscK, and extremal Kähler cases. Combined with previous results of LeBrun, Apostolov-Maschler and Futak…

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…

Stability of extremal Reissner-Nordström black holes proven in spherical symmetry.

In this expository paper we review on the existence problem of Einstein-Maxwell Kähler metrics, and make several remarks. Firstly, we consider a slightly more general set-up than Einstein-Maxwell Kähler metrics, and give extensions of volume minimization principle, the notion of toric K-stability and other related resu…

Area-charge inequalities and local rigidity of free boundary MOTS in charged initial data sets

Paper proves trapped surface formation for EMCSF system without symmetry assumptions.

Study proves stability of big bang singularity in complex system.

Proves rigidity of extremal Kerr-Newman horizons.

The Einstein-Maxwell equations on a smooth compact 4-manifold are reformulated as a purely Riemannian variational problem analogous to Calabi's variational problem for extremal Kahler metrics. Next, Seiberg-Witten theory is used to show that these two problems are in fact intimately related. Extremal Kahler metrics are…

The complete on-shell action of topological Einstein-Maxwell gravity in four-dimensions is presented. It is shown explicitly how this theory for SU(2) holonomy manifolds arises from four-dimensional Euclidean N=2 supergravity. The twisted local BRST symmetries and twisted local Lorentz symmetries are given and the acti…

Let $(M,g)$ be a compact Kähler manifold and $f$ a positive smooth function such that its Hamiltonian vector field $K = J\mathrm{grad}_g f$ for the Kähler form $ω_g$ is a holomorphic Killing vector field. We say that the pair $(g,f)$ is conformally Einstein-Maxwell Kähler metric if the conformal metric $\tilde g = f^{-…

Researchers create initial data for multiple collapsing boson stars.

Generalising the results in arXiv:1612.00281, we construct infinite-dimensional families of non-singular stationary space times, solutions of Yang-Mills-Higgs-Einstein-Maxwell-Chern-Simons-dilaton-scalar field equations with a negative cosmological constant. The families include an infinite-dimensional family of soluti…

We establish a type of positive energy theorem for asymptotically anti-de Sitter Einstein-Maxwell initial data sets by using Witten's spinoral techniques.

Carter tensor analysis aids wave equation on Kerr-Newman spacetime.

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

We prove involutivity of Einstein, Einstein-Maxwell and other field equations by calculating the Spencer cohomology of these systems. Relation with Cartan method is traced in details. Basic implications through Cartan-Kahler theory are derived.

Review of gravitational instantons in physics.

The paper proves positive energy-momentum theorems for charged AdS initial data sets.

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…

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

A compactness theorem is proved for a family of Kähler surfaces with constant scalar curvature and volume bounded from below, diameter bounded from above, Ricci curvature bounded and the signature bounded from below. Furthermore, a splitting theorem and some rigidity theorems are proved for Einstein-Maxwell systems.