相关论文: Boundary Terms for Causal Sets

Evidence is provided for a conjecture that, in the continuum limit, the mean of the causal set action of a causal set sprinkled into a globally hyperbolic Lorentzian spacetime, M, of finite volume equals the Einstein Hilbert action of M…

The causal set action of dimension $d$ is investigated for causal sets that are Poisson sprinklings into submanifolds of $d$-dimensional Minkowski space. Evidence, both analytic and numerical, is provided for the conjecture that the mean of…

We investigate the extrinsic geometry of causal sets in $(1+1)$-dimensional Minkowski spacetime. The properties of boundaries in an embedding space can be used not only to measure observables, but also to supplement the discrete action in…

Considering a generalization of the Gibbons-Hawking-York covariant boundary action that depends on both the extrinsic and the intrinsic geometry of the boundary, we derive boundary conditions for the cosmological background and tensor…

We study the continuum limit of the Benincasa-Dowker-Glaser causal set action on a causally convex compact region. In particular, we compute the action of a causal set randomly sprinkled on a small causal diamond in the presence of…

The main goal of this paper is to get in a straightforward form the field equations in metric f(R) gravity, using elementary variational principles and adding a boundary term in the action, instead of the usual treatment in an equivalent…

The effective action of string theory on a spacetime manifold with boundary has both bulk and boundary terms. We propose that both bulk and boundary actions, may be found by imposing the effective action to be invariant under the gauge…

A consistent variational procedure applied to the gravitational action requires according to Gibbons and Hawking a certain balance between the volume and boundary parts of the action. We consider the problem of preserving this balance in…

A complete and systematic approach to compute the causal boundary of wave-type spacetimes is carried out. The case of a 1-dimensional boundary is specially analyzed and its critical appearance in pp-wave type spacetimes is emphasized. In…

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…

The Einstein-Hilbert action for general relativity is not well posed in terms of the metric $g_{ab}$ as a dynamical variable. There have been many proposals to obtain an well posed action principle for general relativity, e.g., addition of…

It is common knowledge that the Einstein-Hilbert action does not furnish a well-posed variational principle. The usual solution to this problem is to add an extra boundary term to the action, called a counter-term, so that the variational…

Using the method of images we derive the boundary term of the Einstein-$\Gamma^2$ action in half-space from the spherical worldsheet to first order in $\alpha'$ and to linear order in the metric perturbation around flat half-space. The…

We consider a general formalism for treating a Hamiltonian (canonical) field theory with a spatial boundary. In this formalism essentially all functionals are differentiable from the very beginning and hence no improvement terms are needed.…

We discuss the criteria that must be satisfied by a well-posed variational principle. We clarify the role of Gibbons-Hawking-York type boundary terms in the actions of higher derivative models of gravity, such as F(R) gravity, and argue…

We present a new development of the causal boundary of spacetimes, originally introduced by Geroch, Kronheimer and Penrose. Given a strongly causal spacetime (or, more generally, a chronological set), we reconsider the GKP ideas to…

It is well-known that the presence of a spacetime boundary requires the conventional Einstein-Hilbert (EH) action to be supplemented by the Gibbons-Hawking (GH) boundary term in order to retain the standard variational procedure. When the…

The ordinary Poisson brackets in field theory do not fulfil the Jacobi identity if boundary values are not reasonably fixed by special boundary conditions. We show that these brackets can be modified by adding some surface terms to lift…

The continuum limit of a 4-dimensional, discrete d'Alembertian operator for scalar fields on causal sets is studied. The continuum limit of the mean of this operator in the Poisson point process in 4-dimensional Minkowski spacetime is shown…

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…