Non-commutative effects on gravitational measurements

Abstract

The general theory of relativity is currently the accepted theory of gravity and as such, a large repository of test results has been obtained since its inception in 1915. However, in this paper we only focus on what are considered as the main tests but in non-commutative (NC) geometries. Using the coordinate coherent state formalism, we calculate the gravitational redshift, deflection, and time delay of light, separately, for NC inspired Schwarzschild and Reissner–Nordström black holes. We show the NC predictions have different behavior than the general relativity. We also provide an upper bound on the NC parameter by comparing the NC corrections with the accuracies of gravitational measurements in the case of typical primordial black holes produced in the early Universe. In this regard, we use observational data for the scale factor a at the end of inflation to obtain physical satisfactory results.

Gravitational Measurements in Higher Dimensions

“…Inspired by this idea, we do investigate deviations from GR predictions due to the gravitational leakage into the extra dimensions, and we are more interested in some possible observational or experimental consequences of extra dimensions in such gravitational systems. This issue deserves further research along the lines that we have already proposed in [72].…”

“…However, the values of the peaks are the same for all dimensions, i.e., it does not depend on the dimension, and by increasing the dimension of spacetime, the peak occurs in smaller x. For instance, there is a regular peak at x = 3 for extremal limit η = 1.9 in four dimensions [72]. It has been shown in [43] that there exists a similar finite maximum temperature at r h = 3 √ θ that the black hole can reach before cooling down to absolute zero, which states that there is no curvature singularity at the origin and the geometry is regular there.…”

“…The values of r • √ θ are extractable from Figure 8. Moreover, using the fact that the length of √ θ is less than 7 × 10 −19 [72], one can obtain a lower bound on the length of extra dimensions L, as provided in Table 2.…”

“…Although theories with extra dimensions have received much attention in recent years, unfortunately, the size of extra dimensions has not been investigated properly. To tackle this problem, we finally obtain a lower bound on the size of extra dimensions using the bound obtained for the non-commutative length scale in our previous work [72].…”

The Bound of the Non-Commutative Parameter Based on Gravitational Measurements

“…Recently, there has been a lot of research in determining a lower bound of the NC parameter and studies on quantum gravity effects, with several approaches [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Our aim is to estimate a lower bound on the NC parameter using the four classical experimental tests of GR inspired by the NC geometry based on the gauge theory of gravity and compared to the other results obtained by another approach of NC geometry [12,16]. In this study, we give the NC corrections based on the four classical predictions of GR in the NC gauge theory of gravity.…”