Related papers: Conformally covariant parametrizations for initial…
This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…
In this short note we find covariant canonical formulation of modified Eddington gravity action coupled to scalar field. We also discuss limitation of this formulation and suggest its possible generalization.
Based on the gauge invariant variables proposed in our previous paper [K. Nakamura, Prog. Theor. Phys. vol.110 (2003), 723.], some formulae of the perturbative curvatures of each order are derived. We follow the general framework of the…
We extend Dain's construction of a geometric invariant characterising static initial data sets for the vacuum Einstein field equations to situations with a non-vanishing extrinsic curvature. This invariant gives a measure of how much the…
Emergent modified gravity presents a new set of generally covariant gravitational theories in which the space-time metric is not directly given by one of the fundamental fields. A metric compatible with the modified dynamics of gravity is…
We test Einstein gravity using cosmological observations of both expansion and structure growth, including the latest data from supernovae (Union2.1), CMB (WMAP7), weak lensing (CFHTLS) and peculiar velocity of galaxies (WiggleZ). We fit…
We construct new examples of Einstein metrics by perturbing the conformal infinity of geometrically finite hyperbolic metrics and by applying the inverse function theorem in suitable weighted H\"older spaces.
The aim of this paper is to find higher order geometrical corrections to the Einstein-Hilbert action that can lead to only second order equations of motion. The metric formalism is used, and static spherically symmetric and…
It is found that the induced gravity with conformal couplings requires the conformal invariance in both classical and quantum levels for consistency. This is also true for the induced gravity with an extended conformal coupling interacting…
We introduce the natural lift of spacetime diffeomorphisms for conformal gravity and discuss the physical equivalence between the natural and gauge natural structure of the theory. Accordingly, we argue that conformal transformations must…
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…
Inspired by Verlinde's idea, some modified versions of entropic gravity have appeared in the literature. Extending them in a unified formalism, we derive the generalized gravitational equations accordingly. From gravitational equations, the…
Modified gravity theories such as Einstein scalar Gauss Bonnet (EsGB) contain higher derivative terms in the spacetime curvature in their action, which results in modifications to the Hamiltonian and momentum constraints of the theory. In…
Versions of parameterized pseudo-Newtonian gravity theories specially designed for cosmology have been introduced in recent cosmology literature. The modifications demand a zero-pressure fluid in the context of versions of modified…
We propose a new point of view for interpreting Newton's and Einstein's theories of gravity. By taking inspiration from Continuum Mechanics and its treatment of anisotropies, we formulate new gravitational actions for modified theories of…
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
Covariant generalizations of well-known wave equations predict the existence of inertial-gravitational effects for a variety of quantum systems that range from Bose-Einstein condensates to particles in accelerators. Additional effects arise…
Certain versions of mimetic gravity have recently been claimed to present potential covariant theories of canonically modified spherically symmetric gravity, motivated by ingredients from loop quantum gravity. If such an equivalence were to…
We develop a framework for constructing initial data sets for perturbations about spherically symmetric matter distributions. This framework facilitates setting initial data representing astrophysical sources of gravitational radiation…
We review the current status and prospects for the conformal invariant fourth order theory of gravity which has recently been advanced by Mannheim and Kazanas as a candidate alternative to the standard second order Einstein theory. We…