Related papers: Junction conditions in a general field theory
In this work we present a general method to obtain the junction conditions of modified theories of gravity whose action can be written in the form $f\left(X_1,...,X_n\right)$, where $X_1$ to $X_n$ are any combination of scalar dependencies,…
We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these…
In this work we study the problem of generalizing the Gibbons-Hawking-York boundary terms for general quadratic theories of gravity and propose a simple condition to obtain them. From these terms we derive the junction conditions for a…
We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…
In this paper we consider second-order field theories in a variational setting. From the variational principle the Euler-Lagrange equations follow in an unambiguous way, but it is well known that this is not true for the Cartan form. This…
We prove Euler-Lagrange and natural boundary necessary optimality conditions for fractional problems of the calculus of variations which are given by a composition of functionals. Our approach uses the recent notions of Riemann-Liouville…
Using the notion of distribution-valued tensor, we discuss the junction conditions within the framework of f(Q)-gravity. We obtain the necessary and sufficient conditions for two distinct solutions of the field equations to be smoothly…
The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be…
This paper provides necessary and sufficient conditions of optimality for variational problems that deal with a fractional derivative with respect to another function. Fractional Euler--Lagrange equations are established for the fundamental…
We prove Euler-Lagrange and natural boundary necessary optimality conditions for problems of the calculus of variations which are given by a composition of nabla integrals on an arbitrary time scale. As an application, we get optimality…
Junction conditions play a crucial role in constructing new gravity solutions. In this paper, we derive the junction condition for gluing together an arbitrary number of spacetimes along a common interface. We develop a geometric technique…
In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In…
We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They…
Junction conditions are discussed within the framework of $f(R)$-gravity with torsion. After deriving general junction conditions, the cases of coupling to a Dirac field and a spin fluid are explicitly dealt with. The main differences with…
The aim of this paper is to propose an unambiguous intrinsic formalism for higher-order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, which implies the existence of…
We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives. We obtain necessary optimality…
The present article introduces a generalization of the (multisymplectic) Hamiltonian field theory for a Lagrangian density, allowing the formulation of this kind of field theories for variational problem of more general nature than those…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
This paper addresses both necessary and relevant sufficient extremum conditions for a variational problem defined by a smooth Lagrangian, involving higher derivatives of several variable vector valued functions. A general formulation of…
This work contains an exposition of foundations of the variational calculus in fibered manifolds. The emphasis is laid on the geometric aspects of the theory. Especially functionals defined by real functions (Lagrange functions) or…