Electrovacuum solution

In general relativity, an electrovacuum solution (electrovacuum) is an exact solution of the Einstein field equation in which the only nongravitational mass–energy present is the field energy of an electromagnetic field, which must satisfy the (curved-spacetime) source-free Maxwell equations appropriate to the given geometry. For this reason, electrovacuums are sometimes called (source-free) Einstein–Maxwell solutions. In general relativity, the geometric setting for physical phenomena is a Lorentzian manifold, which is interpreted as a curved spacetime, and which is specified by defining a metric tensor (or by defining a frame field). The Riemann curvature tensor of this manifold and associated quantities such as the Einstein tensor , are well-defined. In general relativity, they can be interpreted as geometric manifestations (curvature and forces) of the gravitational field. We also need to specify an electromagnetic field by defining an electromagnetic field tensor on our Lorentzian manifold. To be classified as an electrovacuum solution, these two tensors are required to satisfy two following conditions The electromagnetic field tensor must satisfy the source-free curved spacetime Maxwell field equations and The Einstein tensor must match the electromagnetic stress–energy tensor, . The first Maxwell equation is satisfied automatically if we define the field tensor in terms of an electromagnetic potential vector . In terms of the dual covector (or potential one-form) and the electromagnetic two-form, we can do this by setting . Then we need only ensure that the divergences vanish (i.e. that the second Maxwell equation is satisfied for a source-free field) and that the electromagnetic stress–energy matches the Einstein tensor. The electromagnetic field tensor is antisymmetric, with only two algebraically independent scalar invariants, Here, the star is the Hodge star. Using these, we can classify the possible electromagnetic fields as follows: If but , we have an electrostatic field, which means that some observers will measure a static electric field, and no magnetic field.

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Concepts associés (5)

Cours associés (7)

Séances de cours associées (50)

Petrov classification

In differential geometry and theoretical physics, the Petrov classification (also known as Petrov–Pirani–Penrose classification) describes the possible algebraic symmetries of the Weyl tensor at each event in a Lorentzian manifold. It is most often applied in studying exact solutions of Einstein's field equations, but strictly speaking the classification is a theorem in pure mathematics applying to any Lorentzian manifold, independent of any physical interpretation. The classification was found in 1954 by A.

Frame fields in general relativity

A frame field in general relativity (also called a tetrad or vierbein) is a set of four pointwise-orthonormal vector fields, one timelike and three spacelike, defined on a Lorentzian manifold that is physically interpreted as a model of spacetime. The timelike unit vector field is often denoted by and the three spacelike unit vector fields by . All tensorial quantities defined on the manifold can be expressed using the frame field and its dual coframe field.

Electrovacuum solution

PHYS-454: Quantum optics and quantum information

This lecture describes advanced concepts and applications of quantum optics. It emphasizes the connection with ongoing research, and with the fast growing field of quantum technologies. The topics cov

MATH-111(e): Linear Algebra

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et ses applications.

ME-443: Hydroacoustique pour aménagements hydroélectriques

Introduction aux phénomènes propagatifs dans les circuits hydrauliques, calculs de coups de béliers, comportement transitoire d'aménagements hydroélectriques, simulation numériques 1D du comportement

Équations optiques de Bloch PHYS-454: Quantum optics and quantum information

Couvre la dérivation et les solutions des équations optiques de Bloch pour un système quantique à deux niveaux.

Chaos quantique et brouillage

Explore le concept de brouillage dans les systèmes chaotiques quantiques, reliant le chaos classique au chaos quantique et mettant l'accent sur la sensibilité aux conditions initiales.

Introduction aux équations différentielles partielles MATH-351: Advanced numerical analysis

Couvre les bases des équations différentielles partielles, en mettant l'accent sur la modélisation du transfert de chaleur et les méthodes de solution numérique.