Related papers: Boundary terms of the Einstein-Hilbert action
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…
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…
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…
Einstein's vierbein formulation of general relativity based on the notion of distant parallelism (teleparallelism) naturally introduces a covariant surface term in addition to the Einstein-Hilbert action. We investigate the action principle…
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…
A key tenet of general relativity is the dynamical nature of space-time, ideally represented as an initial value problem. Here we explore the variational formulation of classical Einstein-Hilbert gravity as initial value problem by…
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…
We propose a boundary action to complement the recently developed duality manifest actions in string and M-theory using generalized geometry. This boundary action combines the Gibbons-Hawking term with boundary pieces that were previously…
The Gibbons-Hawking-York (GHY) boundary term makes the Dirichlet problem for gravity well defined, but no such general term seems to be known for Neumann boundary conditions. In this paper, we view Neumann {\em not} as fixing the normal…
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…
If gravity is an emergent phenomenon, as suggested by several recent results, then the structure of the action principle for gravity should encode this fact. With this motivation we study several features of the Einstein-Hilbert action and…
The Einstein-Hilbert (EH) action is peculiar in many ways. Some of the Peculiar features have already been highlighted in literature. In the present article, we have discussed some peculiar features of EH action which has not been discussed…
We study the conditions of integrability when the boundary terms are considered in the variation of the geometric contribution of the Einstein-Hilbert action. We explore the emergent physical dynamics that is obtained when we make a…
The Einstein-Hilbert Lagrangian has no well-defined variational derivative with respect to the metric. This issue has to be tackled by adding a suitable surface term to the action, which is a peculiar feature of gravity. We also know that…
A connection-independent formulation of general relativity is presented, in which the dynamics does not depend on the choice of connection. The gravity action in this formulation includes one additional scalar term in addition to the…
The Einstein-Hilbert action has a bulk term and a surface term (which arises from integrating a four divergence). I show that one can obtain Einstein's equations from the surface term alone. This leads to: (i) a novel, completely self…
The field equations of general relativity can be derived from the Einstein action, which is quadratic in connection coefficients, rather than the standard action involving the Gibbons-Hawking-York term and counterterm. We show that it is…
We propose a boundary term to the Einstein-Gauss-Bonnet action for gravity, which is constructed as the dimensional continuation of the Chern-Weil theorem, and such that the extremization of the full action yields the equations of motion…
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…