A bstract We derive all-order expressions for perturbations of the Einstein-Hilbert action and Einstein equation with general n -th order terms. To this end, we employ Cheung Remmen’s perturbation conventions both in tensor density usual metric formalisms, including Einstein-dilaton theory. Remarkably, find minimal building blocks that generate entire each our formulations. show number terms gr...

In this note, we prove an existence result for the Einstein conformal constraint equations metrics with vanishing Yamabe invariant assuming that mean curvature satisfies explicit near-CMC condition and TT-tensor is small in $$L^2$$ .

Which smooth compact n-manifolds admit Riemannian metrics of constant Ricci curvature? A direct variational approach sheds some interesting light on this problem, but by no means answers it. This article surveys some recent results concerning both Einstein metrics and the associated variational problem, with the particular aim of highlighting the striking manner in which the 4-dimensional case ...

Considering the evolution equations of parabolic type on a non-compact Einstein manifold $(\mathcal M,g)$ with negative Ricci curvature tensor, we establish results existence, uniqueness time-periodic (on time half-axis) and almost periodic

‎The notion of quasi-Einstein metric in physics is equivalent to the notion of Ricci soliton in Riemannian spaces‎. ‎Quasi-Einstein metrics serve also as solution to the Ricci flow equation‎. ‎Here‎, ‎the Riemannian metric is replaced by a Hessian matrix derived from a Finsler structure and a quasi-Einstein Finsler metric is defined‎. ‎In compact case‎, ‎it is proved that the quasi-Einstein met...

We report the existence of novel static spherical black-hole solutions in a vector-tensor gravitational theory called bumblebee gravity model which extends Einstein-Maxwell by allowing vector to nonminimally couple Ricci curvature tensor. A test strong-field regime is performed for first time using recent observations supermassive shadows galaxy M87 and Milky Way from Event Horizon Telescope Co...