Related papers: Geometric aspects of covariant Wick rotation
This paper sheds light on the essential characteristics of geodesics, which frequently occur in considerations from motion in Euclidean space. Focus is mainly on a method of obtaining them from the calculus of variations, and an explicit…
In a general-relativistic spacetime (Lorentzian manifold), gravitational lensing can be characterized by a lens map, in analogy to the lens map of the quasi-Newtonian approximation formalism. The lens map is defined on the celestial sphere…
Complexifying space time has many interesting applications, from the construction of higher dimensional unification, to provide a useful framework for quantum gravity and to better define some local symmetries that suffer singularities in…
There are not many tools to quantitatively monitor the emergence of classical geometric features from a quantum spacetime, whose microscopic structure may be a highly quantum-fluctuating "spacetime foam". To improve this situation, we…
Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In E-representation there are three basic elements (point,…
Recently, a proposal has been made to figure out the expected discrete nature of spacetime at the smallest scales in terms of atoms of spacetime, capturing their effects through a scalar $\rho$, related to their density, function of the…
We analyze parallel transport of a vector field around an equatorial orbit in Kerr and stationary axisymmetric spacetimes that are reflection symmetric about their equatorial planes. As in Schwarzschild spacetime, there is a band structure…
By considering a new form of dimensional reduction for noncommutative field theory, we show that the signature of spacetime may be changed. In particular, it is demonstrated that a temporal dimension can emerge from a purely Euclidean…
A Hamiltonian approach to the equations of general relativity is proposed using the powerful mathematical language of multivector-valued differential forms. In the approach, the gravitational coordinates are the 12 spatial components of the…
In the literature, there are several papers establishing a correspondence between a deformed kinematics and a nontrivial (momentum dependent) metric. In this work, we study in detail the relationship between the trajectories given by a…
It has been established that the famous three-dimensional Thurston geometries have four intrinsically Lorentzian analogs. We explore these spacetimes in three-dimensional general relativity nonminimally coupled to a scalar field together…
A key insight used in developing the theory of Causal Dynamical Triangulations (CDTs) is to use the causal (or light-cone) structure of Lorentzian manifolds to restrict the class of geometries appearing in the Quantum Gravity (QG) path…
The Wick rotation is commonly considered only as an useful computational trick. However, as it was suggested by Hartle and Hawking already in early eighties, Wick rotation may gain physical meaning at the Planck epoch. While such…
I introduce a covariant four-vector $\mathcal{G}^a[v]$, which can be interpreted as the momentum density attributed to the spacetime geometry by an observer with velocity $v^a$, and describe its properties: (a) Demanding that the total…
A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-field. By canonically quantizing the coupling model in the framework of loop quantum gravity, we obtain a quantum…
We obtain the complete theory of Newton-Cartan gravity in a curved spacetime by considering the large $c$ limit of the vielbein formulation of General Relativity. Milne boosts originate from local Lorentzian transformations, and the special…
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 the Dirac equation coupled to an external electromagnetic field in curved four-dimensional spacetime with a given timelike worldline $\gamma$ representing a classical clock. We use generalised Fermi normal coordinates in a…
We study the euclidean covariant loop-quantum-gravity vertex numerically, using a cylindrically symmetric boundary state and a convenient value of the Barbero-Immirzi parameter. We show that a classical geometry emerges already at low spin.…
We consider four-dimensional general relativity with a negative cosmological constant in the presence of a finite size boundary, $\Gamma$, for both Euclidean and Lorentzian signature. As our boundary condition, we consider the `conformal'…