Maxwell fields inherit stationarity from stationary metrics.
problem Maxwell fields in asymptotically flat solutions of Einstein-Maxwell equations.
method Proving Maxwell fields inherit stationarity of the metric.
result Maxwell fields inherit stationarity from stationary metrics.
Paper proves trapped surface formation for Einstein-Maxwell-charged scalar field system.
problem Formation of trapped surfaces in Einstein-Maxwell-charged scalar field system.
method Generalized Christodoulou's approach for spherical symmetry and improved for Minkowskian data.
result Improved bound on trapped surface formation for Minkowskian data.
Maxwell meets Korn: A New Coercive Inequality for Tensor Fields with Square-Integrable Exterior Derivative
This is the second in a series of papers in which we take a systematic study of gauge field theories such as the Maxwell equations and the Yang-Mills equations, on curved space-times. In this paper, we study the Maxwell equations in the domain of outer-communication of the Schwarzschild black hole. We show that if we a…
New instantons show Einstein-Maxwell fields are more complex.
problem Disprove Euclidean Einstein-Maxwell black hole uniqueness.
method Explicit construction of new three-parameter family of asymptotically flat instantons.
result Demonstrate subtle properties of coupled gravitational and electromagnetic fields.
Solves inverse problem for Maxwell equations using vector fields.
problem Inverse problem for Maxwell equations in vacuum.
method Abstract theory of implicit differential equations over pre-symplectic manifolds.
result Provides solution for Maxwell equations using vector fields.
This paper defines directional derivatives and solves Maxwell's equations in curved 3D space.
problem Analyzing electromagnetic fields in curved non-flat 3D space.
method Defined directional derivatives and used Frenet formulas to express Serret-Frenet relations. Solved Maxwell's equations for electric and magnetic fields.
result Solved Maxwell's equations for electromagnetic fields in curved 3D space.
Researchers solve field equations for special gravitational instantons.
problem Solving field equations for conformally Kähler Riemannian four-manifolds.
method Developed a framework to solve the field equations for generalised gravitational instantons using conformal self-duality and cosmological Einstein-Maxwell.
result Found conformally self-dual and Einstein-Maxwell generalisations of specific geometries.
Study finds obstacles to solutions for specific equations on compact surfaces.
problem Existence of solutions to self-dual equations on compact surfaces.
method Depends on Higgs field zeroes and vortex number.
result Infinitely many Higgs fields for which solutions cannot exist.
Study on type-D metrics aligned with Einstein-Maxwell equations, deriving solutions.
problem Understanding metrics with specific Weyl tensor types and their properties.
method Reinterpretation of Araneda's results using Toda field equation and application of Ward's method.
result Metrics can be expressed using solutions of the SU(∞)-Toda field equation and axisymmetric solutions of the Laplacian. Paper proves trapped surface formation for EMCSF system without symmetry assumptions.
problem Formation of trapped surfaces for the Einstein--Maxwell--charged scalar field system.
method Scale-critical trapped surface formation result established from past null infinity.
result Focusing of gravitational waves, concentration of electromagnetic fields, or condensation of scalar fields can lead to trapped surface formation.
Stable knots and links can exist in electromagnetic fields.
problem Stability of knots and links in electromagnetic fields.
method Proving the existence of electromagnetic fields preserving link topology.
result Every link can be realized as stable field lines in electromagnetic fields.
The paper studies conformally Einstein-Maxwell Kähler metrics and automorphism group structure.
problem Analyzing conformally Einstein-Maxwell Kähler metrics and their automorphism groups.
method Using a Hessian formula for the Calabi functional and extending the Lichnerowicz-Matsushima Theorem.
result Proves a reductiveness result of the reduced Lie algebra of holomorphic vector fields for conformally Einstein-Maxwell Kähler manifolds.
Study proves stability of big bang singularity in complex system.
problem Stability of Kasner solutions in Einstein-Maxwell-scalar field-Vlasov system.
method Detailed mathematical structures and new delicate arguments.
result Nonlinear stability with Kasner exponents in full strong sub-critical regime.
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…
Study shows how electromagnetic and gravitational waves can form trapped surfaces.
problem Formation of trapped surfaces from initial data with electromagnetic fields.
method Established a scale-critical semi-global existence result from past null infinity for the Einstein-Maxwell system.
result Generalized approach for studying Einstein vacuum equations and extended a result to scale-critical regime.
Paper discusses existence of Einstein-Maxwell Kähler metrics.
problem Existence of Einstein-Maxwell Kähler metrics.
method Review and extensions of volume minimization principle, toric K-stability.
result Numerical analysis suggests the existence of a Killing vector field.
This paper studies Sasakian quasi-Killing spinors on 3D Sasakian manifolds.
problem Characterizing Sasakian quasi-Killing spinors on 3D Sasakian manifolds.
method Detailed analysis and geometric properties of Sasakian quasi-Killing spinors.
result Almost all Sasakian quasi-Killing spinors solve the Einstein-Dirac system with a non-zero cosmological constant.
Constructs solutions to Einstein-Maxwell-current system using Sasakian manifolds.
problem Solving the Einstein-Maxwell-Current system with inhomogeneous charged particle density.
method Using Sasakian manifolds to specify magnetic field and electric current.
result Solutions with arbitrary function describing charged particle density and curvature.
Physics-constrained neural nets solve EM fields of charged particle beams.
problem Solving Maxwell's equations for intense charged particle beams.
method 3D Convolutional Neural Networks (CNNs) constrained by physics.
result 3D CNNs generate electromagnetic fields from current and charge densities.
We study which geometric structure can be constructed from the vierbein (frame/coframe) variables and which field models can be related to this geometry. The coframe field models, alternative to GR, are known as viable models for gravity, since they have the Schwarzschild solution. Since the local Lorentz invariance is…
The paper finds exact solutions to a complex Einstein-Dirac-Maxwell system on 4D Sasakian spacetimes.
problem Finding exact solutions to an Einstein-Dirac-Maxwell system with Sasakian quasi-Killing spinors.
method Constructing a family of exact solutions on four-dimensional static Sasakian spacetimes using the Sasakian frame.
result Closed and open universe models are found with specific energy conditions.
Maxwell equations decay to Coulomb solutions on black hole spacetimes.
problem Decay of Maxwell solutions in Schwarzschild-de Sitter spacetimes.
method Differential transformation of Maxwell tensor components, Fackerell-Ipser equation, vector field method.
result Super-polynomial decay rate of Maxwell solutions to Coulomb solutions.
The study connects electromagnetic structures to Legendrian fields on the 3-sphere.
problem Understanding the topology of stable electromagnetic structures.
method Connecting null solutions to Maxwell's equations with Legendrian fields on the 3-sphere.
result Any (possibly knotted) toroidal surface can be realized as a magnetic surface of a null solution, implying stability.
Stability of extremal Reissner-Nordström black holes proven in spherical symmetry.
problem Stability of extremal Reissner-Nordström black holes in spherical symmetry.
method Proved nonlinear asymptotic stability through spherically symmetric characteristic data.
result Existence of a submanifold Mstab leading to stable solutions. Classifies automorphisms of conformally Kähler, Einstein-Maxwell metrics.
problem Classifying holomorphic automorphisms of conformally Kähler, Einstein-Maxwell metrics.
method Structure theorem for holomorphic automorphisms, extending classical results.
result Completes classification of conformally Kähler, Einstein--Maxwell metrics on CP1imesCP1. Abstract discusses symplectic structure and Maxwell equations on Yang-Mills fields.
problem Formulating Maxwell equations on Yang-Mills fields using symplectic structures.
method Endowed a symplectic structure on the fiber product of tangent and cotangent bundles of connections, derived Hamiltonian equations and moment maps.
result Proved Maxwell equations and derived new conserved quantities from moment maps.
FLASH-MAX predicts electromagnetic fields from sparse data in seconds.
problem Predicting homogeneous electromagnetic fields from sparse pointwise observations.
method Exact-by-construction neural network architecture that satisfies Maxwell's equations symbolically.
result FLASH-MAX achieves sub-1% relative validation error from 1K sparse observations in seconds.
Characterizes Killing vector fields leading to conformally Kähler, Einstein-Maxwell metrics.
problem Characterizing Killing vector fields leading to conformally Kähler, Einstein-Maxwell metrics.
method Characterizes Killing vector fields leading to conformally Kähler, Einstein-Maxwell metrics.
result Characterizes Killing vector fields leading to conformally Kähler, Einstein-Maxwell metrics.
Unified geometric formulation of Maxwell-Vlasov system using presymplectic and symmetry reduction.
problem Unified geometric formulation of Maxwell-Vlasov system.
method Skinner-Rusk formalism, presymplectic geometry, reduction by diffeomorphism group, affine Hamiltonian controls.
result Unified geometric structure unifying Lagrangian, Hamiltonian, gauge, reduction, and control-theoretic aspects.
Small bodies follow geodesics in general relativity.
problem Understanding the motion of small bodies in space-time.
method Analyzes the motion of small bodies as timelike geodesics or Lorentz-force curves in general relativity.
result Clarifies the relationship between modeling bodies as distributions or smooth fields.
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.
Area-charge inequalities and local rigidity of free boundary MOTS in charged initial data sets
problem Area-charge inequalities and local rigidity of free boundary MOTS in charged initial data sets
method Area-charge inequalities and local rigidity of free boundary MOTS in charged initial data sets
result Prove area-charge inequalities for free boundary MOTS in initial data sets for the Einstein-Maxwell equations with vanishing magnetic fields
Future stability of a specific type of Kaluza-Klein spacetime is proven.
problem Stability of a particular class of Kaluza-Klein vacua.
method Einstein flow on a product manifold, Kaluza-Klein reduction, wave map type and Maxwell type equations, slice-adapted gauge.
result Future stability of the Milne universe within the class of spacetimes.
The aim of this paper is to create a large geometrical background on the dual 1-jet space J^{1*}(T,M) for a multi-time Hamiltonian approach of the electromagnetic and gravitational physical fields. Our geometric-physical construction is achieved starting only from a given quadratic Hamiltonian function of polymomenta H…
We establish a type of positive energy theorem for asymptotically anti-de Sitter Einstein-Maxwell initial data sets by using Witten's spinoral techniques.
Proves rigidity of extremal Kerr-Newman horizons.
problem Classifying near-horizon geometries of extremal Kerr-Newman horizons.
method Proves intrinsic geometry constraints leading to rigidity.
result Proves extremal Kerr-Newman horizons are unique.
Survey paper examines obstructions to solving Kähler geometry problems.
problem Existence of Kähler-Ricci solitons, Sasaki-Einstein metrics, and conformally Einstein-Maxwell Kähler metrics.
method Obstructions are derived as derivatives of volume functionals for vector fields.
result Identifies vector fields for which existence problems should be attempted.
In this paper, we prove a far-from-CMC result similar to the ones obtained by Holst, Nagy, Tsogtgerel and Maxwell for the conformal Einstein-scalar field constraint equations on compact Riemannian manifolds with positive (modified) Yamabe invariant.
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills fields, because the scalar field introduces three extra terms into the Lichnerowicz e…
Formulates a new class of gravity theories coupled to scalar and gauge fields.
problem Global formulation of theories of gravity coupled to scalar and gauge fields.
method Global mathematical formulation of a class of generalized four-dimensional theories of gravity.
result Global solutions can be interpreted as classical U-folds.
Mathematical model of spacetime diffeomorphisms as matter fields.
problem Modeling spacetime diffeomorphisms as matter fields.
method Introducing a Lagrangian algebraically expressed via metrics and analyzing nonlinear field equations.
result Explicit solutions for massless and massive cases in Minkowski space.
Proof confirms cosmic censorship for charged gravitational collapse.
problem Cosmic censorship for Einstein-Maxwell-Charged Scalar Field system.
method Systematic approach to incorporate charge and complex scalar field, new trapped surface criterion, modified BV area estimates, and new instability theorems.
result Cosmic censorship holds for charged gravitational collapse.
We describe classes of potential structures (covector fields) on Minkowski space that admit subgroups of the Poincaré group. We describe also seven classes of Maxwell spaces that admit subgroups of the Poincaré group.
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…
The paper developes a geometrization of a Kronecker h-regular vertical fundamental metrical d-tensor G(i)(j)(α)(β) on the jet fibre bundle of order one J1(T,M). This geometrization gives a mathematical model for both gravitational and electromagnetic field theory, in a general setting. In this context, the…
3+1 decompositions of differential forms on a Lorentzian manifold (M,g;+ - - -) with respect to arbitrary observer field and the decomposition of the standard operations acting on them are studied, making use of the ideas of the theory of connections on principal bundles. Simple explicit general formulas are given as w…
New black hole models with both null and spacelike singularities.
problem Understanding singularities in black hole spacetimes.
method Developed a new spacelike-characteristic gluing method to construct black hole spacetimes.
result First examples of black holes with coexisting null and spacelike singularities.