相关论文: Comments on Joint Terms in Gravitational Action
In this paper, we analyze the variation of the gravitational action on a bounded region of spacetime whose boundary contains segments with various characters, including null. We develop a systematic approach to decompose the derivative of…
A finite action principle for three-dimensional gravity with negative cosmological constant, based on a boundary condition for the asymptotic extrinsic curvature, is considered. The bulk action appears naturally supplemented by a boundary…
A new variational approach for general relativity and modified theories of gravity is presented. In addition to the metric tensor, two independent affine connections enter the action as dynamical variables. In the matter action the…
Unimodular gravity can be formulated so that transverse diffeomorphisms and Weyl transformations are symmetries of the theory. For this formulation of unimodular gravity, we work out the two-point and three-point $h_{\mu\nu}$ contributions…
The junction conditions for general theories of gravity based on actions that depend on arbitrary functions of the curvature scalar invariants (including differential invariants) are obtained using the distributional formalism. In case of…
We discuss BF theories defined on manifolds with spatial boundaries. Variational arguments show that one needs to augment the usual action with a boundary term for specific types of boundary conditions. We also show how to use this…
Starting from the original Einstein action, sometimes called the Gamma squared action, we propose a new setup to formulate modified theories of gravity. This can yield a theory with second order field equations similar to those found in…
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…
In this work, we study the magnetic effects of gravity in the framework of special relativity. Imposing covariance of the gravitational force with respect to the Lorentz transformations, we show from a thought experiment that a…
We investigate the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime with a fixed time-flow vector. For existence of a well-defined Hamiltonian variational principle taking into…
The equivalence between Chern-Simons and Einstein-Hilbert actions in three dimensions established by A.~Ach\'ucarro and P.~K.~Townsend (1986) and E.~Witten (1988) is generalized to the off-shell case. The technique is also generalized to…
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 construct various limits of JT gravity, including Newton-Cartan and Carrollian versions of dilaton gravity in two dimensions as well as a theory on the three-dimensional light cone. In the BF formulation our boundary conditions relate…
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…
We present an action principle formulation for the study of motion of an extended body in General Relativity in the limit of weak gravitational field. This gives the classical equations of motion for multipole moments of arbitrary order…
We study a gravitational action which is a linear combination of the Hilbert-Palatini term and a term quadratic in torsion and possessing local Poincare invariance. Although this action yields the same equations of motion as General…
We review computations of joint invariants on a linear symplectic space, discuss variations for an extension of group and space and relate this to other equivalence problems and approaches, most importantly to differential invariants.
We intend to clarify the interplay between boundary terms and conformal transformations in scalar-tensor theories of gravity. We first consider the action for pure gravity in five dimensions and show that, on compactifing a la Kaluza-Klein…
Our main aim in this paper is to promote the coframe variational method as a unified approach to derive field equations for any given gravitational action containing the algebraic functions of the scalars constructed from the Riemann…
A method of calculation for the variational derivatives for gravitational actions in the pseudo-Riemannian case is proposed as a practical variant of the first order formalism with constraints. The method is then used to derive the metric…