Related papers: Actions for signature change
Riemannian geometry is a particular case of Hamiltonian mechanics: the orbits of the hamiltonian $H=\frac{1}{2}g^{ij}p_{i}p_{j}$ are the geodesics. Given a symplectic manifold (\Gamma,\omega), a hamiltonian $H:\Gamma\to\mathbb{R}$ and a…
The variational principle for a thin dust shell in General Relativity is constructed. The principle is compatible with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to ``natural boundary conditions'' on…
Theory of electromagnetic field, specified by an effective action functional, is considered. The causality condition is imposed in the form of a requirement that the group velocities of propagation of small and soft disturbances over the…
In classical mechanics, we can describe the dynamics of a given system using either the Lagrangian formalism or the Hamiltonian formalism, the choice of either one being determined by whether one wants to deal with a second degree…
We extend the cosmological predictions from assuming the total action of the universe is finite. When initial and final singularities in curvature invariants are avoided, it leads to singularities in the gravitational action of the…
A positive semi-definite Euclidean action for arbitrary four-topologies can be constructed by adding appropriate Yang-Mills and topological terms to the Samuel-Jacobson-Smolin action of gravity with (anti)self-dual variables. Moreover,…
In this work we construct a gauge invariant description of free massive particle with an arbitrary integer spin. Such description allows one to investigate the problem of consistent interactions for massive high spin particles using the…
Considering an action in F(G) modified gravity, the static spherically symmetric solutions are investigated. Introducing the Lagrangian multipliers {\alpha} we obtain the Lagrangian and equations of motion. we obtain two type solutions for…
We consider a scalar field action for which the Lagrangian density is a power of the massless Klein-Gordon Lagrangian. The coupling of gravity to this matter action is considered. In this case, we show the existence of nontrivial scalar…
Covariant models of loop quantum gravity generically imply dynamical signature change at high density. This article presents detailed derivations that show the fruitful interplay of this new kind of signature change with wave-function…
Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian…
We establish a Lagrangian variational framework for general relativistic continuum theories that permits the development of the process of Lagrangian reduction by symmetry in the relativistic context. Starting with a continuum version of…
The aim of this note is to give a geometric insight into the classical second order optimality conditions for equality-constrained minimization problem. We show that the Hessian's positivity of the Lagrangian function associated to the…
In this work, we propose an Action Principle for Action-dependent Lagrangian functions by generalizing the Herglotz variational problem to the case with several independent variables. We obtain a necessary condition for the extremum…
The Weingarten relations satisfied by rotationally symmetric surfaces in Euclidean 3-space E3 are considered from three points of view: restrictions on the slope of the relation at umbilic points, the action of SL2(R) as fractional linear…
We consider static, spherically symmetric vacuum solutions to the equations of a theory of gravity with the Lagrangian f(R) where R is the scalar curvature and f is an arbitrary function. Using a well-known conformal transformation, the…
We revise the twistor--like superfield approach to describing super--p--branes by use of the basic principles of the group--manifold approach \cite{rheo}. A super--p--brane action is constructed solely of geometrical objects as the integral…
As is well known, in order for the Einstein--Hilbert action to have a well defined variation, and therefore to be used for deriving field equation through the stationary action principle, it has to be amended by the addition of a suitable…
I review the problem of dark energy focusing on the cosmological constant as the candidate and discuss its implications for the nature of gravity. Part 1 briefly overviews the currently popular `concordance cosmology' and summarises the…
We consider the problem of creating locally supersymmetric theories in signature (10,2). The most natural algebraic starting point is the F-algebra, which is the de Sitter-type (10,2) extension of the super-Poincare algebra. We derive the…