Related papers: Boundary Terms, Variational Principles and Higher …
The Hamiltonian for dynamic geometry generates the evolution of a spatial region along a vector field. It includes a boundary term which determines both the value of the Hamiltonian and the boundary conditions. The value gives the…
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…
We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate…
The $f(R)$ theory of gravity can be expressed as a scalar tensor theory with a scalar degree of freedom $\phi$. By a conformal transformation, the action and its Gibbons-York-Hawking boundary term are written in the Einstein frame and the…
Focussing on theories for which the higher derivative terms are considered as small corrections in the Lagrangian to Einstein's two-derivative theory of general relativity (GR), we prove the classical version of the covariant entropy bound…
We provide a well-defined variational principle for 3-dimensional flat space Einstein gravity by adding one half of the Gibbons-Hawking-York boundary term to the bulk action. We check the 0-point function, recovering consistency with…
We show the well-posed variational principle in constraint systems. In a naive procedure of the variational principle with constraints, the proper number of boundary conditions does not match with that of physical degrees of freedom…
The Hamiltonian for dynamic geometry generates the evolution of a spatial region along a vector field. It includes a boundary term which determines both the value of the Hamiltonian and the boundary conditions. The value gives the…
Variational principles in mechanics, field theory and geometric analysis are usually formulated on closed admissible classes, where boundary variations are either fixed or independently cancelled through natural boundary conditions.…
Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann-Lemaitre-Robertson-Walker…
Wald's entropy formula allows one to find the entropy of black holes' event horizon within any diffeomorphism invariant theory of gravity. When applied to general relativity, the formula yields the Bekenstein-Hawking result but, for any…
In this review we consider first order gravity in four dimensions. In particular, we focus our attention in formulations where the fundamental variables are a tetrad $e_a^I$ and a SO(3,1) connection ${\omega_{aI}}^J$. We study the most…
Various Hamiltonian formulations of f(R) gravity can be found in the literature. Some authors follow the Ostrogradsky treatment of higher derivative theories and introduce as extra variables first order time derivatives of the metric…
In this work, we construct traversable wormhole geometries in the context of f(R) modified theories of gravity. We impose that the matter threading the wormhole satisfies the energy conditions, so that it is the effective stress-energy…
In this note, we revisit a variational principle introduced by Padmanabhan for describing gravitation using a field action composed solely of a boundary term. We demonstrate that this procedure can also be applied to derive Maxwell's and…
The standard formulation of the AdS/CFT correspondence is incomplete since it requires adding to a supergravity action some a priori unknown boundary terms. We suggest a modification of the correspondence principle based on the Hamiltonian…
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…
After reformulating $F($Riemann$)$ gravity theory as a second derivative theory by introducing two auxiliary fields to the bulk action, we derive the surface term as well as the corner term supplemented to the bulk action for a generic…
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…
In this work, a way to consider together two originally different corrections to the Friedmann equations is presented. The first is the Barrow entropy, which imposes a fractal structure on the black hole horizon area. While the second is…