Related papers: Discrete and finite Genral Relativity
The Maxwell extension of the conformal algebra is presented. With the help of gauging the Maxwell-conformal group, a conformally invariant theory of gravity is constructed. In contrast to the conventional conformally invariant actions, our…
We briefly discuss new models of an `affine' theory of gravity in multidimensional space-times with symmetric connections. We use and generalize Einstein's proposal to specify the space-time geometry by use of the Hamilton principle to…
We consider the deformation of the Schwarzschild solution in general relativity due to spherically symmetric quantum fluctuations of the metric and the matter fields. In this case, the 4D theory of gravity with Einstein action reduces to…
A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the…
We review the solution space for the field equations of Einstein's General Relativity for various static, spherically symmetric spacetimes. We consider the vacuum case, represented by the Schwarzschild black hole; the de…
The possibility of the extension of spatial diffeomorphisms to a larger family of symmetries in a class of classical field theories is studied. The generator of the additional local symmetry contains a quadratic kinetic term and a potential…
It is a review paper. General relativity (GR) is presented in the field theoretical form, where gravitational field (metric perturbations) together with other physical fields are propagated in an auxiliary arbitrary curved background…
The nature of gravity is fundamental to our understanding of our own solar system, the galaxy and the structure and evolution of the Universe. Einstein's general theory of relativity is the standard model that is used for almost ninety…
The Schwarzschild geometry is investigated within the context of effective-field-theory models of gravity. Starting from its harmonic-coordinate expression, we derive the metric in standard coordinates by keeping the leading one-loop…
The theory of macroscopic gravity provides a formalism to average the Einstein field equations from small scales to largest scales in space-time. It is well known that averaging is an operation that does not commute with calculating the…
It is known that the standard Schwarzschild interior metric is conformally flat and generates a constant density sphere in any spacetime dimension in Einstein and Einstein--Gauss--Bonnet gravity. This motivates the questions: In EGB does…
Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which,…
The modern notion of a black hole singularity is considered with reference to the Schwarzschild solution to Einstein's field equations of general relativity. A brief derivation of both the original and the modern line elements is given. The…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
The central equations in classical general relativity are the Einstein Field Equations, which accurately describe not only the generation of pseudo-Riemannian curvature by matter and radiation manifesting as gravitational effects, but more…
One of the main technical obstacles in constructing a consistent theory of quantum gravity is that the metric itself defines the causal structure required for quantization. This motivates implementing quantum aspects of gravity through an…
We consider general relativity with cosmological constant minimally coupled to electromagnetic field and assume that four-dimensional space-time manifold is the warped product of two surfaces with Lorentzian and Euclidean signature metrics.…
We consider discretizations of the Einstein action of general relativity such that the resulting discrete equations of motion form a consistent constrained system. Upon ``spin foam'' quantization of the system, consistency allows a natural…
Recently, Chandrasekaran, Penington and Witten (CPW) have shown that the generalized entropy of the Schwarzschild black hole at the bifurcation surface equals the entropy of an extended von Neumann algebra of quantum observables in the…
After recalling the differential geometry of non-metric connections in the formalism of differential forms, we introduce the idea of a Non-Metricity (NM) connection, whose connection $1$--forms coincides with the non-metricity $1$--forms…