Related papers: Metric Renormalization in General Relativity
The non-relativistic versions of the generalized Poincar\'{e} algebras and generalized $AdS$-Lorentz algebras are obtained. This non-relativistic algebras are called, generalized Galilean algebras type I and type II and denoted by…
One of the concepts of Relativity theory that challenges conventional intuition the most is time dilation and length contraction. Usual approaches for describing relativistic effects in quantum systems merely postulate the consequences of…
With the dark energy phenomena explored over a decade, in this present work we discuss a specific case of the generalized Einstein-aether theories, in which the modified Friedmann Equation is similar to that in the Dvali-Gabadadze-Porrati…
We revisit the generalized connection of Double Field Theory. We implement a procedure that allow us to re-write the Double Field Theory equations of motion in terms of geometric quantities (like generalized torsion and non-metricity…
A generalization of the Bernstein matrix concentration inequality to random tensors of general order is proposed. This generalization is based on the use of Einstein products between tensors, from which a strong link can be established…
A geometric procedure is elaborated for transforming (pseudo) Riemanian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or Finsler, geometries which, in their…
This paper develops a bias correction scheme for a multivariate normal model under a general parameterization. In the model, the mean vector and the covariance matrix share the same parameters. It includes many important regression models…
The standard approach to renormalization relies, technically, on the asymptotic perturbation of Gaussian measures embodied in Feynman diagram theory. From a mathematical standpoint this is not good enough, because thereby solving the…
The metrics of general relativity generally fall into two categories: Those which are solutions of the Einstein equations for a given source energy-momentum tensor, and the "reverse engineered" metrics -- metrics bespoke for a certain…
Explanations of the late-time cosmic acceleration within the framework of general relativity are plagued by difficulties. General relativistic models are mostly based on a dark energy field with fine-tuned, unnatural properties. There is a…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
Recently a model of metric fluctuations has been proposed which yields an effective Schr\"odinger equation for a quantum particle with a modified inertial mass, leading to a violation of the weak equivalence principle. The renormalization…
A Bayesian hierarchical model for total variation regularisation is presented in this paper. All the parameters of an inverse problem, including the "regularisation parameter", are estimated simultaneously from the data in the model. The…
The Hubble diagram is one of the cornerstones of observational cosmology. It is usually analysed assuming that, on average, the underlying relation between magnitude and redshift matches the prediction of a…
Employing the quasi-Maxwell form of the Einstein field equations in the context of gravitoelectromagnetism, we introduce a general relativistic analog of Poisson's equation as a natural outcome of the corresponding spacetime decomposition…
We investigate the back reaction of cosmological perturbations on the evolution of the Universe using the renormalization group method. Starting from the second order perturbed Einstein's equation, we renormalize a scale factor of the…
The metric-affine variational principle is applied to generate teleparallel and symmetric teleparallel theories of gravity. From the latter is discovered an exceptional class which is consistent with a vanishing affine connection. Based on…
We consider the quantum dynamics of Bose-Einstein condensates at absolute zero, and demonstrate that an analogue gravity model going beyond the standard linearized analogue gravity paradigm \`a la Unruh must take into account the…
Standard general relativity fails to take into account the changes in coordinates induced by the variation of metric in the Hilbert action principle. We propose to include such changes by introducing a fundamental compensating tensor field…
We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann-Hilbert problem. Given a loop $\gamma(z), | z |=1$ of elements…