# Einstein-Riemann Gravity on Deformed Spaces ?

@article{Wess2006EinsteinRiemannGO, title={Einstein-Riemann Gravity on Deformed Spaces ?}, author={Julius Wess}, journal={Symmetry Integrability and Geometry-methods and Applications}, year={2006} }

A differential calculus, differential geometry and the E-R Gravity theory are studied on noncommutative spaces. Noncommutativity is formulated in the star product formalism. The basis for the gravity theory is the infinitesimal algebra of diffeomorphisms. Considering the corresponding Hopf algebra we find that the deformed gravity is based on a deformation of the Hopf algebra.

## 8 Citations

### Noncommutative Geometries and Gravity

- Mathematics
- 2007

We briefly review ideas about “noncommutativity of space-ti me” and approaches toward a corresponding theory of gravity. PACS: 02.40.Gh, 04.50.+h, 04.60.-m

### Space-Time Diffeomorphisms in Noncommutative Gauge Theories ?

- Mathematics
- 2008

In previous work (Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007), 10367-10382) we have shown how for canonical parametrized field theories, where space- time is placed on the same footing as…

### Noncommutative Geometries and Gravity

- Mathematics
- 2007

AbstractWe brieﬂy review ideas about “noncommutativityof space-time” and approaches toward a corre-sponding theory of gravity. PACS: 02.40.Gh, 04.50.+h, 04.60.-mKeywords: Noncommutative geometry,…

### On the noncommutative and nonassociative geometry of octonionic space time, modified dispersion relations and grand unification

- Mathematics
- 2007

The octonionic geometry (gravity) developed long ago by Oliveira and Marques, J. Math. Phys. 26, 3131 (1985) is extended to noncommutative and nonassociative space time coordinates associated with…

### The Euclidean gravitational action as black hole entropy, singularities, and spacetime voids

- Physics
- 2008

We argue why the static spherically symmetric vacuum solutions of Einstein’s equations described by the textbook Hilbert metric g μ ν ( r ) is not diffeomorphic to the metric g μ ν ( ∣ r ∣ )…

### On 2 + 2-Dimensional Spacetimes, Strings, Black-Holes and Maximal Acceleration in Phase Spaces

- Physics
- 2009

We study black-hole-like solutions ( spacetimes with singularities ) of Einstein field equations in 3+1 and 2+2-dimensions. In the 3+1-dim case, it is shown how the horizon of the standard black hole…

### ON (2+2)-DIMENSIONAL SPACE–TIMES, STRINGS AND BLACK HOLES

- Physics
- 2007

We study black hole-like solutions (space–times with singularities) of Einstein field equations in 3+1 and 2+2 dimensions. We find three different cases associated with hyperbolic homogeneous spaces.…

### Quantization in Astrophysics, Brownian Motion, and Supersymmetry

- Physics
- 2020

The present book discusses, among other things, various quantization phenomena found in Astrophysics and some related issues including Brownian Motion. With recent discoveries of exoplanets in our…

## References

SHOWING 1-10 OF 26 REFERENCES

### Noncommutative geometry and gravity

- Mathematics
- 2006

We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of…

### A gravity theory on noncommutative spaces

- Mathematics
- 2005

A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter θ. The algebraic relations remain the same, whereas the…

### Deformed Gauge Theories

- Mathematics
- 2006

Gauge theories are studied on a space of functions with the Moyal-Weyl product. The development of these ideas follows the differential geometry of the usual gauge theories, but several changes are…

### Twisted Gauge Theories

- Mathematics
- 2006

Gauge theories on a space-time that is deformed by the Moyal–Weyl product are constructed by twisting the coproduct for gauge transformations. This way a deformed Leibniz rule is obtained, which is…

### Differential calculus on compact matrix pseudogroups (quantum groups)

- Mathematics
- 1989

The paper deals with non-commutative differential geometry. The general theory of differential calculus on quantum groups is developed. Bicovariant bimodules as objects analogous to tensor bundles…

### Deformation Quantization of Poisson Manifolds

- Mathematics
- 1997

I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the…

### Twist to Close

- Mathematics
- 2006

It has been proposed that the Poincare and some other symmetries of noncommutative field theories should be twisted. Here we extend this idea to gauge transformations and find that twisted gauge…

### On Deformation Theory and Quantization

- Mathematics
- 2008

Deformation theory requires solving Maurer-Cartan equation (MCE) associated to an DGLA (L-infinity algebra). The universal solution of [HS] is obtained iteratively, as a fixed point of a contraction,…

### Chains of twists for classical Lie algebras

- Mathematics
- 1999

For chains of regular injections of Hopf algebras the sets of maximal extended Jordanian twists {k} are considered. We prove that under certain conditions there exists for 0 the twist composed of the…