Related papers: Variational formalism for generic shells in genera…
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…
We consider a general scalar-tensor theory of gravity and review briefly different forms it can be presented (different conformal frames and scalar field parametrizations). We investigate the conditions under which its field equations and…
We establish the dynamical instability of a static, spherically symmetric, and infinitesimally thin shell in general relativity. The shell is made up of a perfect fluid with a barotropic equation of state, and it produces a Schwarzschild…
We present variational and Hamiltonian formulations of incompressible fluid dynamics with free surface and nonvanishing odd viscosity. We show that within the variational principle the odd viscosity contribution corresponds to geometric…
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
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…
This paper compares three different methods about computing joint terms in on-shell action of gravity, which are identifying the joint term by the variational principle in Dirichlet boundary condition, treating the joint term as the limit…
In this work, standard methods of the mixed thin-shell foramlism are refined using the framework of Colombeau's theory of generalized functions. To this end, systematic use is made of smooth generalized functions, in particular…
In its canonical formulation, general relativity is subject to gauge transformations that are equivalent to space-time coordinate changes of general covariance only when the gauge generators, given by the Hamiltonian and diffeomorphism…
A consistent theory of quantum gravity will require a fully quantum formulation of the classical equivalence principle. Such a formulation has been recently proposed in terms of the equality of the rest, inertial and gravitational mass…
Motivated by the power of subregion/subregion duality for constraining the bulk geometry in gauge/gravity duality, we pursue a comprehensive and systematic approach to the behavior of extremal surfaces under perturbations. Specifically, we…
The purpose of this paper is to propose the implementation of some methods from algebraic geometry in the theory of gravitation, and more especially in the variational formalism. It has been assumed that the metric tensor depends on two…
It is shown that exact spherically symmetric solutions to Einstein's Field Equations exist such that, over an open region of the spacetime, they are singularity free, satisfy the dominant energy condition, represent elastic matter with a…
In the MacDowell-Mansouri formulation of general relativity, the spin connection and coframe variables are incorporated into a single Lie algebra-valued connection called the MacDowell-Mansouri connection, $\omega$. From the curvature form…
The gravitational wave solutions obtained from a perturbation about conformally flat backgrounds in Einstein gravity are investigated. A perturbation theory analysis of the Lesame, Ellis and Dunsby results, based on a covariant approach,…
Dynamics of a self-gravitating shell of matter is derived from the Hilbert variational principle and then described as an (infinite dimensional, constrained) Hamiltonian system. A method used here enables us to define singular Riemann…
We find the most general solution to Chern-Simons AdS$_3$ gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin…
Standard quantum mechanics relies on two distinct dynamical principles: unitary evolution and collapse. A mathematically self-contained variational framework is presented that replaces this dualism with a single principle, in which…
A variational principle is constructed for gravity coupled to an asymptotically linear dilaton and a p-form field strength. This requires the introduction of appropriate surface terms -- also known as `boundary counterterms' -- in the…
Emergent modified gravity presents a new class of gravitational theories in which the structure of space-time with Riemannian geometry of a certain signature is not presupposed. Relying on crucial features of a canonical formulation, the…