Related papers: Well-posed formulation of Einstein-Maxwell effecti…
For axially symmetric solutions of Einstein equations there exists a gauge which has the remarkable property that the total mass can be written as a conserved, positive definite, integral on the spacelike slices. The mass integral provides…
While there exist now formulations of initial boundary value problems for Einstein's field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two…
We prove that when the equations are restricted to the principal part the standard version of the BSSN formulation of the Einstein equations is equivalent to the NOR formulation for any gauge, and that the KST formulation is equivalent to…
We consider the Maxwell-Lorentz equations, i.e., the equation of motion of a charged dust coupled to Maxwell's equations, on an arbitrary general-relativistic spacetime. We decompose this system of equations into evolution equations and…
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure…
We present new exact solutions for the Einstein-Maxwell system in static spherically symmetric interior spacetimes. For a particular form of the gravitational potentials and the electric field intensity, it is possible to integrate the…
A simple derivation is given of the Einstein-Maxwell field equations from the 2nd ordinary exterior differential of a precursor to the soldering form for n-dimensional differentiable manifolds having a general linear connection and in…
The first order form of a Maxwell theory and U(1) gauge theory in which a gauge invariant mass term appears is analyzed using the Dirac procedure. The form of the gauge transformation which leaves the action invariant is derived from the…
The well-formulation and the well-posedness of the Cauchy problem is discussed for {\it hybrid metric-Palatini gravity}, a recently proposed modified gravitational theory consisting of adding to the Einstein-Hilbert Lagrangian an $f(R)$…
A general recipe proposed elsewhere to define, via Noether theorem, the variation of energy for a natural field theory is applied to Einstein-Maxwell theory. The electromagnetic field is analysed in the geometric framework of natural…
We formulate a well-posedness and approximation theory for a class of generalised saddle point problems. In this way we develop an approach to a class of fourth order elliptic partial differential equations using the idea of splitting into…
The concept of electromagnetic field can be neatly formulated by recognizing that the simplest form of the four-force is indeed feasible. We show that Maxwell's equations almost entirely stem from the properties of spacetime, notably from…
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…
This paper is to study the inelastic Boltzmann equation without Grad's angular cutoff assumption, where the well-posedness theory of the solution to the initial value problem is established for the Maxwellian molecules in a space of…
In a series of recent works based on foliation-based quantization in which renormalizability has been achieved for the physical sector of the theory, we have shown that the use of the standard graviton propagator interferes, due to the…
The problem of motion in General Relativity has lost its academic status and become an active research area since the next generation of gravity wave detectors will rely upon its solution. Here we will show, within scalar gravity, how ideas…
We use a recently derived integral representation of the one-loop effective action in Einstein-Maxwell theory for an explicit calculation of the part of the effective action containing the information on the low energy limit of the…
We consider Einstein-Maxwell-self-interacting scalar field theory described by a potential $V\left( \phi \right) $ in $2+1-$dimensions. The self-interaction potential is chosen to be a highly non-linear double-Liouville type. Exact…
The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order…
The Einstein-Hilbert worldspace action is used to investigate the dynamics of extended object. In the Robertson-Walker worldspace, this is seen to introduce a pressureless density which could contribute to dark matter. Such pressureless…