相关论文: Generalized Darmois-Israel junction conditions

A generalization to the Gibbons-Hawking-York boundary term for metric $f(R)$ gravity theories is introduced. A redefinition of the Gibbons-Hawking-York term is proposed. The proposed new definition is used to derive a consistent set of…

We propose a regularization procedure for the novel Einstein-Gauss-Bonnet theory of gravity, which produces a set of field equations that can be written in closed form in four dimensions. Our method consists of introducing a counter term…

We study the elliptic equation with a line Dirac delta function as the source term subject to the Dirichlet boundary condition in a two-dimensional domain. Such a line Dirac measure causes different types of solution singularities in the…

Symmetries of generalized gravitational actions, yielding field equations which typically involve at most second-order derivatives of the metric, are considered. The field equations for several different higher-derivative theories in the…

The possibility of the existence of small correction terms to the canonical commutation relations and the uncertainty relations has recently found renewed interest. In particular, such correction terms could induce finite lower bounds…

We introduce a new set of generalized Fokker-Planck equations that conserve energy and mass and increase a generalized entropy until a maximum entropy state is reached. The concept of generalized entropies is rigorously justified for…

This paper uses products of distributions to obtain new junction conditions for relativistic shocks. In general, the shock is accompanied by a surface layer, and the new conditions generalize both Taub's jump conditions for shocks, and…

We consider the quantum gravity and cosmology of a Jordan-Brans-Dicke theory, predicted by string effective actions. We study its canonical formalism and find that the constraint algebra is that of general relativity, as a consequence of…

Singular source terms expressed as weighted summations of Dirac-delta functions are regularized through approximation theory with convolution operators. We consider the numerical solution of scalar and one-dimensional hyperbolic…

The Israel equations for thin shells in General Relativity are derived directly from the least action principle. The method is elaborated for obtaining the equations for double layers in quadratic gravity from the least action principle.

This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…

We present a general approach to construct a class of generalized topological field theories with constraints by means of generalized differential calculus and its application to connection theory. It turns out that not only the ordinary BF…

We study the gravitational potential generated by static, spherically symmetric matter distributions in a quadratic $f(R)$ gravity model. In the weak-field regime, the linearized field equations lead to a fourth-order modified Poisson…

By using a general version of curvature condition, derivative inequalities are established for a large class of subelliptic diffusion semigroups. As applications, the Harnack/cost-entropy/cost-variance inequalities for the diffusion…

We study the Dirac equation minimally coupled to general relativity using quantum field theory and the semiclassical gravity approximation. Previous studies of the Einstein-Dirac system did not quantize the Dirac field and required multiple…

We study a model of the generalized Brans-Dicke gravity presented in both the Jordan and in the Einstein frames, which are conformally related. We show that the scalar field equations in the Einstein frame are reduced to the geodesics…

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 field theoretic renormalization group is applied to a simple model of random walk on a rough fluctuating surface. We consider the Fokker--Planck equation for a particle in a uniform gravitational field. The surface is modelled by the…

Let $A$ be an algebra and let $X$ be an $A$-bimodule. A $\Bbb C-$linear mapping $d:A \to X$ is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) $\delta:A \to X$ such that…

Degenerate hyperbolic equations are dealing with many important issues for applied nature. While a variety of degenerate equations and boundary conditions, successfully matched to these differential equation, most in the characteristic…