Consequences of minimal length discretization on line element, metric tensor, and geodesic equation

Tawfik, A.; Diab, Abdel Magied; Shenawy, Sameh; Dahab, Eiman Abou El

doi:10.1002/asna.202113880

Cited by 15 publications

(10 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This theory implies a maximal acceleration a max ≤ 1 l . Note that Caianiello's approach is similar to the proposal by Tawfik (2021) in this volume.…”

Section: 3mentioning

confidence: 57%

A review on algebraic extensions in general relativity

Hess

2021

Astron Nachr

View full text Add to dashboard Cite

A brief review on algebraic extensions of general relativity is presented. After a short summary of first attempts by Max Born and Albert Einstein, all possible algebraic extensions will be discussed, with the pseudo-complex (pc) extension left as the only viable one, because it does not contain ghost solutions. Also some metric extensions are presented, such as the non-symmetric gravitation theory and the Finsler metric. Some predictions of the pc extension are discussed, such as the structure of light emission of an accretion disk around a black hole, the redshift at the surface of a compact star as a function in the azimuthal angle, and whether there is an upper limit for the mass of a neutron star.

show abstract

“…This theory implies a maximal acceleration a max ≤ 1 l . Note that Caianiello's approach is similar to the proposal by Tawfik (2021) in this volume.…”

Section: 3mentioning

confidence: 57%

A review on algebraic extensions in general relativity

Hess

2021

Astron Nachr

View full text Add to dashboard Cite

show abstract

“…from the spacetime discretization on the relativistic eight‐dimensional manifold, the quantum‐induced revisiting fundamental tensor is suggested as Tawfik et al (2021a), (2021b)

{\tilde{g}}_{\mu \nu}=\left(1+\mathcal{T}\kern0.1em {\left|\ddot{x}\right|}^2\right)\kern0.1em {g}_{\mu \nu}.

…”

Section: Methods and Formalismmentioning

confidence: 99%

On quantum‐induced revisiting Einstein tensor in the relativistic regime

Tawfik

2022

Astron Nachr

Self Cite

View full text Add to dashboard Cite

For a rigorous approach to reconcile principles of general relativity (GR) and quantum mechanics (QM), we suggest applying the generalized relativistic noncommutative Heisenberg algebra on spacetime coordinates and momenta of a test particle on curved Riemann geometry manifold, which in turn is extended to an eight-dimensional manifold. The natural generalization of the four-dimensional Riemann geometry is the Finsler geometry, in which the quadratic restriction on the length measure is relaxed. With the minimum measurable length derived from the relativistic generalized four-dimensional uncertainty principle, the quantum-induced corrections to the fundamental tensor could be determined in the relativistic regime. Accordingly, the affine connections could be revisited. With the quantum-induced revisiting Riemann curvature tensor and its contractions, the Ricci curvature tensor, and then the Ricci scalar, we have been able to construct a quantum-induced revision of the Einstein tensor, in which besides quantum-induced corrections, additional geometric structures emerge. On the surface of the 2-sphere, we compared the quantum-induced revisiting and non-revisiting Einstein tensor and concluded that the difference between both versions strongly depends on the minimum measurable length and the local geodesics of the test particle through the additional curvature. K E Y W O R D Salternatives to general relativity, general relativity in relativistic quantum regime, generalized noncommutative Heisenberg algebra, reconciling principles of quantum mechanics with general relativity

show abstract

“…For example, gravity 23 and the "deformed" commutation relations have features of UV/IR correspondence 24 . Therefore, we assume that the minimal length discretization could be analyzed from the UV/IR correspondence 10 . Indeed, ∆x rapidly increases (IR) as the ∆p increases beyond the Planck scale (UV) [25][26][27] .…”

Section: Generalized Uncertainly Principle and Minimal Length Uncerta...mentioning

confidence: 99%

“…As discussed in ref. 10 , using the variational principle and extremization of the path s AB , the geodesic equation could be derived as follows.…”

Section: Discretized Geodesic Equation and Its Propertiesmentioning

confidence: 99%

See 1 more Smart Citation

Minimal length discretization and properties of modified metric tensor and geodesics

Tawfik¹,

T.²,

Tarabia³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

We argue that the minimal length discretization generalizing the Heisenberg uncertainty principle, in which the gravitational impacts on the non-commutation relations are thoughtfully taken into account, radically modifies the spacetime geometry. The resulting metric tensor and geodesic equation combine the general relativity terms with additional terms depending on higher-order derivatives. Suggesting solutions for the modified geodesics, for instance, isn't a trivial task. We discuss on the properties of the resulting metric tensor, line element, and geodesic equation.

show abstract

Consequences of minimal length discretization on line element, metric tensor, and geodesic equation

Cited by 15 publications

References 18 publications

A review on algebraic extensions in general relativity

A review on algebraic extensions in general relativity

On quantum‐induced revisiting Einstein tensor in the relativistic regime

Minimal length discretization and properties of modified metric tensor and geodesics

Contact Info

Product

Resources

About