scholarly journals NONCOMMUTATIVE GEOMETRIES: AN OVERVIEW

2008 ◽  
Vol 23 (08) ◽  
pp. 1253-1256
Author(s):  
CLAUDIO PERINI
Keyword(s):  
General Relativity ◽  
Minkowski Space ◽  
Introductory Overview ◽  
Heisenberg Principle

I make a very introductory overview of noncommutative geometries, focusing on the DFR model for Minkowski space; in this model the noncommutativity, or “fuzziness”, of spacetime events emerges at semiclassical level putting together the Heisenberg principle with general relativity.

scholarly journals FROM SPINOR GEOMETRY TO COMPLEX GENERAL RELATIVITY

2005 ◽  
Vol 02 (04) ◽  
pp. 675-731 ◽  
Author(s):  
GIAMPIERO ESPOSITO
Keyword(s):  
General Relativity ◽  
Minkowski Space ◽  
Dual Space ◽  
Conformal Gravity ◽  
Penrose Transform ◽  
Minkowski Space Time ◽  
Two Component ◽  
Spinor Geometry ◽  
Complex General Relativity ◽  
Component Spinor

An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, two-component spinor calculus, conformal gravity, α-planes in Minkowski space-time, α-surfaces and twistor geometry, anti-self-dual space-times and Penrose transform, spin-3/2 potentials, heaven spaces and heavenly equations.

On spherical free gravitational waves

1993 ◽  
Vol 443 (1918) ◽  
pp. 445-449 ◽  
Keyword(s):  
General Relativity ◽  
Minkowski Space ◽  
Gravitational Waves

The theory of spherical gravitational waves propagated in Minkowski space is considered in the context of the non-radial oscillations of stars in general relativity. (For a review see Ferrari 1992.)

scholarly journals Theory of quantum gravity beyond Einstein and space-time dynamics with quantum inflation

2015 ◽  
Vol 30 (28n29) ◽  
pp. 1545002 ◽  
Author(s):  
Yue-Liang Wu
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Minkowski Space ◽  
Gauge Field ◽  
Gravitational Force ◽  
Proper Time ◽  
Space Time ◽  
Coordinate Space ◽  
Gauge Symmetries ◽  
Minkowski Space Time

In this talk, I present a theory of quantum gravity beyond Einstein. The theory is established based on spinnic and scaling gauge symmetries by treating the gravitational force on the same footing as the electroweak and strong forces. A bi-frame space-time is initiated to describe the laws of nature. One frame space-time is a globally flat coordinate Minkowski space-time that acts as an inertial reference frame for the motions of fields, the other is a locally flat non-coordinate Gravifield space-time that functions as an interaction representation frame for the degrees of freedom of fields. The Gravifield is sided on both the globally flat coordinate space-time and locally flat non-coordinate space-time and characterizes the gravitational force. Instead of the principle of general coordinate invariance in Einstein theory of general relativity, some underlying principles with the postulates of coordinate independence and gauge invariance are motivated to establish the theory of quantum gravity. When transmuting the Gravifield basis into the coordinate basis in Minkowski space-time, it enables us to obtain equations of motion for all quantum fields and derive basic conservation laws for all symmetries. The gravity equation is found to be governed by the total energy–momentum tensor defined in the flat Minkowski space-time. When the spinnic and scaling gauge symmetries are broken down to a background structure that possesses the global Lorentz and scaling symmetries, we arrive at a Lorentz invariant and conformally flat background Gravifield space-time that is characterized by a cosmic vector with a non-zero cosmological mass scale. We also obtain the massless graviton and massive spinnon. The resulting universe is in general not isotropic in terms of conformal proper time and turns out to be inflationary in light of cosmic proper time. The conformal size of the universe has a singular at the cosmological horizon to which the cosmic proper time must be infinitely large. We show a mechanism for quantum inflation caused by the quantum loop contributions. The Gravifield behaves as a Goldstone-like field that transmutes the local spinnic gauge symmetry into the global Lorentz symmetry, which makes the spinnic gauge field becomes a hidden gauge field. As a consequence, the bosonic gravitational interactions can be described by the Goldstone-like Gravimetric field and space-time gauge field. The Einstein theory of general relativity is expected to be an effective low energy theory. Two types of gravity equation are resulted, one is the extension to Einstein’s equation of general relativity, and the other is a new type of gravitational equation that characterizes the spinnon dynamics.

Characteristic initial data and wavefront singularities in general relativity

1983 ◽  
Vol 385 (1789) ◽  
pp. 345-371 ◽  
Keyword(s):  
General Relativity ◽  
Initial Data ◽  
Minkowski Space ◽  
The Self ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Null Hypersurfaces ◽  
Einstein's Field Equations ◽  
Arbitrary Space

The structure of singularities (caustics), self-intersections of wavefronts (null hypersurfaces) and wavefront families (null coordinates) in arbitrary space-times is discussed in detail and illustrated by explicit examples of stable wavefront singularities in Minkowski space. It is shown how characteristic initial data determine the caustics and the self-intersections of the characteristics of Einstein’s field equations.

scholarly journals The homeomorphism of Minkowski space and the separable complex Hilbert space: the physical, mathematical and philosophical interpretations

2021 ◽  
Author(s):  
Vasil Penchev
Keyword(s):  
Hilbert Space ◽  
General Relativity ◽  
Quantum Information ◽  
Minkowski Space ◽  
Reference Frame ◽  
Riemannian Space ◽  
Complex Hilbert Space ◽  
Axiom Of Choice ◽  
The Axiom Of Choice

A homeomorphism is built between the separable complex Hilbert space and Minkowski space by meditation of quantum information. That homeomorphism can be interpreted physically as the invariance to a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture hinting at another way for proving it, more concise and meaningful physically. Furthermore, the conjecture can be generalized and interpreted in relation to the pseudo-Riemannian space of general relativity therefore allowing for both mathematical and philosophical interpretations of the force of gravitation due to the mismatch of choice and ordering. Mathematically, that homeomorphism means the invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” and can be defined generally as “information invariance”. Philosophically, the same homeomorphism implies transcendentalism The fundamental concepts of “choice”, “ordering” and “information” unify physics, mathematics, and philosophy.

scholarly journals Branching in Relativistic Space-Times

2021 ◽  
pp. 293-341
Author(s):  
Nuel Belnap ◽  
Thomas MÜller ◽  
Tomasz Placek
Keyword(s):  
General Relativity ◽  
Minkowski Space ◽  
General Relativistic

The chapter shows how local indeterminism underlying BST combines with relativistic space-times. First it defines particular BST structures in which histories are isomorphic to Minkowski space-times. It further argues that many general relativistic space-times are one-history structures of BST. It introduces the notion of non-Hausdorff differential manifolds and investigates if they can be interpreted modally, as structures of BST with multiple histories. It investigates bifurcating curves in non-Hausdorff manifolds, which are natural representations of alternative evolutions of point-like objects. As the required bifurcating curves are unlikely in General Relativity, whereas there are cases of indeterministic general relativistic space-times, the chapter concludes that General Relativity is globally indeterministic, but locally deterministic.

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