相关论文: Field equations from a surface term

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…

An action principle of singular hypersurfaces in general relativity and scalar-tensor type theories of gravity in the Einstein frame is presented without assuming any symmetry. The action principle is manifestly doubly covariant in the…

It is well known that the Einstein-Hilbert action in two dimensions is topological and yields an identically vanishing Einstein tensor. Consequently one is faced with difficulties when formulating a non-trivial gravity model. We present a…

The field equations associated with the Born-Infeld-Einstein action including matter are derived using a Palatini variational principle. Scalar, electromagnetic, and Dirac fields are considered. It is shown that an action can be chosen for…

The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order…

The Hilbert action principle for the Einstein equations has two boundary terms that must be subtracted in order to obtain a true stationary point. In this paper, I obtain both of them.

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…

We derive the equations of motion of an action-dependent version of the Einstein-Hilbert Lagrangian, as a specific instance of the Herglotz variational problem. Action-dependent Lagrangians lead to dissipative dynamics, which cannot be…

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 shown that the well-known triviality of the Einstein field equations in two dimensions is not a sufficient condition for the Einstein-Hilbert action to be a total divergence, if the general covariance is to be preserved, that is, a…

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…

Here show that, pure affine actions based solely on the Riemann curvature tensor lead to Einstein field equations for gravitation. The matter and radiation involved are general enough to impose no restrictions on material dynamics or vacuum…

We derive new representations of the Einstein-Hilbert action in which graviton perturbation theory is immensely simplified. To accomplish this, we recast the Einstein-Hilbert action as a theory of purely cubic interactions among gravitons…

Gravity is derived from an entropic action coupling matter fields with geometry. The fundamental idea is to relate the metric of Lorentzian spacetime to a quantum operator, playing the role of an renormalizable effective density matrix and…

The equations of motion of massive particles in GR are completely determined by the field equation. We utilize the particular form of Einstein's field equation and propose for the $N$-body problem of the equations that are Lorentz invariant…

When generalizing the principle of least action for fields containing higher order derivatives, in general, it is not possible not to take into account the surface integrated term since it gives direct contribution to the forms of the…

Certain peculiar features of Einstein-Hilbert (EH) action provide clues towards a holographic approach to gravity which is independent of the detailed microstructure of spacetime. These features of the EH action include: (a) the existence…

We describe an action principle, within the framework of the Eddington gravity, which incorporates the matter fields in a simple manner. Interestingly, the gravitational field equations derived from this action is identical to the…

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…