Quantum Coherence and Path-Distinguishability of Two Entangled Particles

An interference experiment with entangled particles is theoretically analyzed, where one of the entangled pair (particle 1) goes through a multi-slit before being detected at a fixed detector. In addition, one introduces a mechanism for finding out which of the n slits did particle 1 go through. The other particle of the entangled pair (particle 2) goes in a different direction, and is detected at a variable, spatially separated location. In coincident counting, particle 2 shows n-slit interference. It is shown that the normalized quantum coherence of particle 2, $\mathcal{C}_2$, and the path-distinguishability of particle 1, $\mathcal{D}_{Q1}$, are bounded by an inequality $\mathcal{D}_{Q1} + \mathcal{C}_2 \le 1$. This is a kind of {\em nonlocal} duality relation, which connects the path distinguishability of one particle to the quantum coherence of the other.Comment: Published versio

An upper limit on the charge of Sgr A* black hole from EHT observations

The Event Horizon Telescope (EHT), recently released the image of supermassive black hole Sgr A* showing an angular shadow diameter $d_{sh}= 48.7 \pm 7\,\mu$as and Schwarzschild shadow deviation $\delta = -0.08^{+0.09}_{-0.09}~\text{(VLTI)},-0.04^{+0.09}_{-0.10}~\text{(Keck)}$ using black hole mass $M = 4.0^{+1.1}_{-0.6} \times 10^6 M_\odot$. The EHT image of Sgr A* is consistent with a Kerr black hole's expected appearance and the results directly prove the existence of a supermassive black hole at the center of the Milky Way. Here, we use the EHT observational results of Sgr A* to investigate the constraints on its charge with the aid of Kerr-like black holes, paying attention to three leading rotating models viz., Kerr-Newman, Horndeski and hairy black holes. Modelling supermassive black hole Sgr A* as these Kerr-like black holes, we observe that the EHT results of Sgr A* place more strict upper limits on the parameter space of Kerr-Newman and Horndeski black holes than those placed by the EHT results of M87*. A systematic bias analysis reveals that, observational results of future EHT experiments place more precise limits on the charge of Sgr A* black hole. Thus, the Kerr-like black holes and Kerr black holes are indiscernible in substantial region of the EHT constrained parameter space; the claim is substantiated by our bias analysis.Comment: 12 pages, 8 figures, 1 table. Accepted for publication in the Astrophysical Journa

Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A∗^*

Horizon-scale images of black holes (BHs) and their shadows have opened an unprecedented window onto tests of gravity and fundamental physics in the strong-field regime. We consider a wide range of well-motivated deviations from classical General Relativity (GR) BH solutions, and constrain them using the Event Horizon Telescope (EHT) observations of Sagittarius A$^*$ (Sgr A$^*$), connecting the size of the bright ring of emission to that of the underlying BH shadow and exploiting high-precision measurements of Sgr A$^*$'s mass-to-distance ratio. The scenarios we consider, and whose fundamental parameters we constrain, include various regular BHs, string-inspired space-times, violations of the no-hair theorem driven by additional fields, alternative theories of gravity, novel fundamental physics frameworks, and BH mimickers including well-motivated wormhole and naked singularity space-times. We demonstrate that the EHT image of Sgr A$^*$ places particularly stringent constraints on models predicting a shadow size larger than that of a Schwarzschild BH of a given mass, with the resulting limits in some cases surpassing cosmological ones. Our results are among the first tests of fundamental physics from the shadow of Sgr A$^*$ and, while the latter appears to be in excellent agreement with the predictions of GR, we have shown that a number of well motivated alternative scenarios, including BH mimickers, are far from being ruled out at present.Comment: 82 pages, 47 figures, 50+ models tested. v3: fixed a few figures, clarified several points, included various analytical expressions for shadow sizes within the different models, added a few references, included a summary table (Table II). Version accepted for publication in Classical and Quantum Gravit

Estimating the Cosmological Constant from Shadows of Kerr–de Sitter Black Holes

The Event Horizon Telescope collaboration has revealed the first direct image of a black hole, as per the shadow of a Kerr black hole of general relativity. However, other Kerr-like rotating black holes of modified gravity theories cannot be ignored, and they are essential as they offer an arena in which these theories can be tested through astrophysical observation. This motivates us to investigate asymptotically de Sitter rotating black holes wherein interpreting the cosmological constant Λ as the vacuum energy leads to a deformation in the vicinity of a black hole—new Kerr–de Sitter solution, which has a richer geometric structure than the original one. We derive an analytical formula necessary for the shadow of the new Kerr–de Sitter black holes and then visualize the shadow of black holes for various parameters for an observer at given coordinates (r0,θ0) in the domain (r0,rc) and estimate the cosmological constant Λ from its shadow observables. The shadow observables of the new Kerr–de Sitter black holes significantly deviate from the corresponding observables of the Kerr–de Sitter black hole over an appreciable range of the parameter space. Interestingly, we find a finite parameter space for (Λ, a) where the observables of the two black holes are indistinguishable

Tests of Loop Quantum Gravity from the Event Horizon Telescope Results of Sgr A*

The Event Horizon Telescope (EHT) collaboration’s image of the compact object at the Galactic center is the first direct evidence of the supermassive black hole (BH) Sgr A*. The shadow of Sgr A* has an angular diameter d _sh = 48.7 ± 7 μ as with fractional deviation from the Schwarzschild BH shadow diameter $\delta =-{0.08}_{-0.09}^{+0.09},-{0.04}_{-0.10}^{+0.09}$ (for the VLTI and Keck mass-to-distance ratios). Sgr A*'s shadow size is within 10% of Kerr predictions, equipping us with yet another tool to analyze gravity in the strong-field regime, including testing loop quantum gravity (LQG). We use Sgr A*'s shadow to constrain the metrics of two well-motivated LQG-inspired rotating BH (LIRBH) models characterized by an additional deviation parameter L _q , which recover the Kerr spacetime in the absence of quantum effects ( L _q → 0). When increasing the quantum effects through L _q , the shadow size increases monotonically, while the shape gets more distorted, allowing us to constrain the fundamental parameter L _q . We use the astrophysical observables shadow area A and oblateness D to estimate the BH parameters. It may be useful in extracting additional information about LIRBHs. While the EHT observational results completely rule out the wormhole region in LIRBH-2, a substantial parameter region of the generic BHs in both models agrees with the EHT results. We find that the upper bounds on L _q obtained from the shadow of Sgr A*— L _q ≲ 0.0423 and L _q ≲ 0.0821 for the two LIRBHs, respectively—are more stringent than those obtained from the EHT image of M87*