Investigating Loop Quantum Gravity with Event Horizon Telescope Observations of the Effects of Rotating Black Holes

Abstract A mathematically consistent rotating black hole model in loop quantum gravity (LQG) is yet lacking. The scarcity of rotating black hole solutions in LQG substantially hampers the development of testing LQG from observations, e.g., from the Event Horizon Telescope (EHT) observations. The EHT observation revealed event horizon-scale images of the supermassive black holes Sgr A* and M87*. The EHT results are consistent with the shadow of a Kerr black hole of general relativity. We present LQG-motivated rotating black hole (LMRBH) spacetimes, which are regular everywhere and asymptotically encompass the Kerr black hole as a particular case. The LMRBH metric describes a multi-horizon black hole in the sense that it can admit up to three horizons, such that an extremal LMRBH, unlike the Kerr black hole, refers to a black hole with angular momentum a > M . The metric, depending on the parameters, describes (1) black holes with only one horizon (BH-I), (2) black holes with an event horizon and a Cauchy horizon (BH-II), (3) black holes with three horizons (BH-III), or (4) no-horizon spacetime, which we show is almost ruled out by EHT observations. We constrain the LQG parameter with the aid of the EHT shadow observational results of M87* and Sgr A*, respectively, for inclination angles of 17° and 50°. In particular, the VLTI bound for Sgr A*, δ ∈ (−0.17, 0.01), constrains the parameters ( a , l ) such that for 0 < l ≤ 0.347851 M ( l ≤ 2 × 10 6 km), the allowed range of a is (0, 1.0307 M ). Together with the EHT bounds of Sgr A* and M87* observables, our analysis concludes that a substantial part of BH-I and BH-II parameter space agrees with the EHT results of M87* and Sgr A*. While the EHT M87* results totally rule out BH-III, but not that by Sgr A*.

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