Related papers: Metric Renormalization in General Relativity
Cosmic acceleration is widely believed to require either a source of negative pressure (i.e., dark energy), or a modification of gravity, which necessarily implies new degrees of freedom beyond those of Einstein gravity. In this paper we…
A new formal scheme is presented in which Einstein's classical theory of General Relativity appears as the common, invariant sector of a one-parameter family of different theories. This is achieved by replacing the Poincare` group of the…
Cosmological parameter uncertainties are often stated assuming a particular model, neglecting the model uncertainty, even when Bayesian model selection is unable to identify a conclusive best model. Bayesian model averaging is a method for…
We consider the statistical inverse problem of recovering an unknown function $f$ from a linear measurement corrupted by additive Gaussian white noise. We employ a nonparametric Bayesian approach with standard Gaussian priors, for which the…
In the last years, we saw more and more attempts to explain dark matter as a general relativistic effect, at least for some fraction. Following this philosophy, we considered the gravitational distortions due to the inhomogeneous…
We consider the gauge invariance of the standard Yang-Mills model in the framework of the causal approach of Epstein-Glaser and Scharf and determine the generic form of the anomalies. The method used is based Epstein-Glaser approach to…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role…
We address the inverse problem of cosmic large-scale structure reconstruction from a Bayesian perspective. For a linear data model, a number of known and novel reconstruction schemes, which differ in terms of the underlying signal prior,…
In magnetoencephalography (MEG) the conventional approach to source reconstruction is to solve the underdetermined inverse problem independently over time and space. Here we present how the conventional approach can be extended by…
Here, we derive the metric for the spacetime around rotating object for the gravity action having nonlocal correction of $R\Box^{-2} R $ to the Einstein-Hilbert action. Starting with the generic stationary, axisymmetric metric, we solve the…
Usually, General Relativity (GR) is known to be unrenormalizable perturbatively from the viewpoint of quantum field theory. But in the modern sense of renormalizability, there still remains the possibility to investigate whether GR is…
In this paper, we propose a generalization of the Riemann curvature tensor on manifolds (of dimension two or higher) endowed with a Regge metric. Specifically, while all components of the metric tensor are assumed to be smooth within…
We analytically derive the covariant form of the Riemann (curvature) tensor for homogeneous Metric-Affine Cosmologies. That is, we present, in a Cosmological setting, the most general covariant form of the full Riemann tensor including also…
We introduce a new iterative regularization method for solving inverse problems that can be written as systems of linear or non-linear equations in Hilbert spaces. The proposed averaged Kaczmarz (AVEK) method can be seen as a hybrid method…
We explore the idea that the coupling between matter and spacetime is more complex than the one originally envisioned by Einstein. We propose that such coupling takes the form of a new fundamental tensor in the Einstein field equations. We…
While the postulate of covariance of Maxwell's equations for all inertial observers led Einstein to special relativity, it was the further demand of general covariance -- form invariance under general coordinate transformations, including…
Cosmic acceleration is explained quantitatively, purely in general relativity, as an apparent effect due to quasilocal gravitational energy differences that arise in the decoupling of bound systems from the global expansion of the universe.…
The issue of implementing the principle of general relativity in Einstein equations has been widely discussed, since Kretschmann's well-known criticism stated that general covariance of the Einstein equations is not suffice to express the…
We consider inverse problems in Hilbert spaces under correlated Gaussian noise and use a Bayesian approach to find their regularised solution. We focus on mildly ill-posed inverse problems with the noise being generalised derivative of…