Related papers: Kerr-Schild--Kundt Metrics are Universal
We explicitly calculate the Riemannian curvature of D-dimensional metrics recently discussed by Chen, Lu and Pope. We find that they can be concisely written by using a single function. The Einstein condition which corresponds to the…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…
We study the class of six-dimensional $\Lambda$-vacuum spacetimes which admit a non-degenerate multiple Weyl aligned null direction l (thus being of Weyl type~II or more special) with a ``generic'' optical matrix. Subject to an additional…
In the general relativity theory the basic ingredient to describe gravity is the geometry, which interacts with all forms of matter and energy, and as such, the metric could be interpreted as a true physical quantity. However the metric is…
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner…
In the paper we analyze the quantum-mechanical equivalence of the metrics of a centrally symmetric uncharged gravitational field. We consider the Schwarzschild metrics in the spherical, isotropic and harmonic coordinates, and the…
In this paper, we study the Bergman metric of a finite ball quotient $\mathbb{B}^n/\Gamma$, where $\Gamma \subseteq \mathrm{Aut}(\mathbb{B}^n)$ is a finite, fixed point free, abelian group. We prove that this metric is K\"ahler--Einstein if…
Starting with the most general four-dimensional spacetime possessing two commuting Killing vectors and a nontrivial Killing tensor, we analytically integrate Einstein-Yang-Mills equations for a completely arbitrary gauge group. It is…
Kerr-Schild solutions to the vacuum Einstein equations are considered from the viewpoint of integral equations. We show that, for a class of Kerr-Schild fields, the stress-energy tensor can be regarded as a total divergence in Minkowski…
We introduce the coherent algebra of a compact metric measure space by analogy with the corresponding concept for a finite graph. As an application we show that upon topologizing the collection of isomorphism classes of compact metric…
A theory which achieves a complete geometrical unification of gravitation and electromagnetism (GUGE) is presented. This new theory is based on a recent proposal of proper time redefinition that leads to the construction of a Riemann…
A quantum field theory formalism is reviewed that leads to a self-consistent, finite quantum gravity, Yang-Mills and Higgs theory, which is unitary and gauge invariant to all orders of perturbation theory. The gauge hierarchy problem is…
We explore the notion of approximate global symmetries in quantum field theory and quantum gravity. We show that a variety of conjectures about quantum gravity, including the weak gravity conjecture, the distance conjecture, and the…
Einstein's General Theory of Relativity predicts that accelerating mass distributions produce gravitational radiation, analogous to electromagnetic radiation from accelerating charges. These gravitational waves have not been directly…
Observed physical phenomena can be described well by quantum mechanics or general relativity. People may try to find an unified fundamental theory which mainly aims to merge gravity with quantum theory. However, difficulty in merging those…
Measurement outcomes provide data for a physical theory. Unless they are objective they support no objective scientific knowledge. So the outcome of a quantum measurement must be an objective physical fact. But recent arguments purport to…
A class of SO(n+1) symmetric solutions of the (N+n+1)-dimensional Einstein equations is found. It contains 5-dimensional metrics of Gross and Perry and Millward.
In this paper, generalized metrics mean metrics taking values in general linearly ordered Abelian groups. Using the Hahn fields, we first prove that for every generalized metric space, if the set of the Archimedean equivalence classes of…
We generalize our previous theorem for FLRW spacetimes within the framework of generic metric gravity theories. In earlier work, we proved that, in the absence of matter fields, the field equations of any metric gravity theory constructed…
I argue that the (extended) Standard Model (SM) of particle physics and the renormalizable Feynman-Weinberg theory of quantum gravity comprise a theory of everything. I show that imposing the appropriate cosmological boundary conditions…