Constraints on self-dual black hole in loop quantum gravity with S0-2 star in the Galactic Center

Abstract

One of remarkable features of loop quantum gravity (LQG) is that it can provide elegant resolutions to both the black hole and big bang singularities. In the mini-superspace approach based on the polymerization procedure in LQG, a self-dual black hole metric which is effective and regular is constructed. It modifies the Schwarzschild spacetime by the polymeric function P , purely due to the geometric quantum effects from LQG. In this paper, we consider its effects on the orbital signatures of S0-2 star orbiting Sgr A* in the central region of our Milky Way, and compare it with the publicly available astrometric and spectroscopic data, including the astrometric positions, the radial velocities, and the orbital procession for the S0-2 star. We perform a Monte Carlo Markov Chain (MCMC) simulation to probe the possible LQG effects on the orbit of S0-2 star. We do not find any significant evidence of the self-dual spacetime arsing from LQG and thus place an upper bound on the polymeric function P < 0.039 at 95% confidence level. This bound leads to a constraint on the polymeric parameter δ of LQG to be δ < 1.7.

Massless Dirac perturbations in a consistent model of loop quantum gravity black hole: quasinormal modes and particle emission rates

“…Hence, substituting V in the expression above by (39), we can obtain that the GF for the massless Dirac radiation for the BMM black hole should always be greater than or equal to the following curves plotted in figures 12-14. As we could see from those graphics, an increase in the value of the LQG parameter λ implied in a decrease of the minimum value of the GF (or transfer rate) of the massless Dirac field as seen by an assymptotic observer.…”

“…So, finally, in order to study the signature of LQG polymerised model on the radiation spectra and on the GF of the Dirac field of the LQG black hole, we need to recall the equation of motion of this perturbing field on the background of our LQG black hole spacetimes [33]. We derived this equation of motion in the previous section, and the final equation we found was (37), with the short-ranged potential given by (39).…”

“…In the historical endeavor towards the study of black holes in a LQG formulation, the first attempt was made by Modesto [10,12]. He employed semiclassical techniques in the minisuperspace quantization scheme [39]. One of the main successes accomplished by these first models was the possibility to address the problem of the black hole singularity [10].…”

“…In other words, we only needed to consider the functions presented in the spacetime metric (1) into (38) to obtain the short-ranged potential V(b(b * )), given by (39), that will be considered in the next sections.…”

“…With equation (42), we can finally evaluate the quasinormal frequencies of the massless Dirac field for the BMM Black Hole. For this purpose, we only need to replace the potential V in that formula by one of the potentials derived in the previous section, and given by equation (39). We will choose this potential to be V + (b), without any loss of generality.…”