Constraints on a Tidal Charge of the Supermassive Black Hole in M87* with the EHT Observations in April 2017

Abstract

More than two years ago the Event Horizon Telescope collaboration presented the first image reconstruction around the shadow for the supermassive black hole in M87*. It gives an opportunity to evaluate the shadow size. Recently, the Event Horizon Telescope collaboration constrained parameters (“charges”) of spherical symmetrical metrics of black holes from an estimated allowed interval for shadow radius from observations of M87* in 2017. Earlier, analytical expressions for the shadow radius as a function of charge (including a tidal one) in the case of Reissner–Nordström metric have been obtained. Some time ago, Bin-Nun proposed to apply a Reissner–Nordström metric with a tidal charge as an alternative to the Schwarzschild metric in Sgr A*. If we assume that a Reissner–Nordström black hole with a tidal charge exists in M87*, therefore, based on results of the shadow size evaluation for M87* done by the Event Horizon Telescope collaboration we constrain a tidal charge. Similarly, we evaluate a tidal charge from shadow size estimates for Sgr A*.

Shadows around Sgr A* and M87* as a tool to test gravity theories

“…Considerations of Randall -Sundrum theories with extra dimension were led to conclusions on existence of Reissner -Nordström solutions with a tidal charge. Based on our analytical expressions for shadow sizes as a function of charge we constrained tidal charge for Sgr A* and improved our previous results done by Zakharov (2022). Similar constraints on electric charge were obtained recently by Event Horizon Telescope Collaboration: Akiyama et al (2022b).…”

“…As it was firstly noted many years ago, the photon capture cross section for a charged black hole has to be considerably smaller than the capture cross section of a Schwarzschild black hole as one can see in corresponding figures presented by Zakharov et al (2005b); Zakharov (2014); Event Horizon Telescope Collaboration: Kocherlakota et al (2021). The critical value of the impact parameter, characterizing the capture cross section for a Reissner -Nordsröm black hole, is determined by the equation (3), since ξ = √ l. As it was shown by Zakharov et al (2005b); Zakharov (2014Zakharov ( , 2022 we can calculate the radius of the unstable circular photon orbit (which is the same as the minimum periastron distance for all orbits which are scattered). Namely,…”

“…Based on estimates of shadow size for M87* done by Event Horizon Telescope Collaboration: Kocherlakota et al (2021) in paper by Zakharov (2022) it was estimated a tidal charge using analytical expressions done Zakharov (2014), namely q ∈ [−1.22, 0.814] at 68% C. L. and the upper bound (q upp = 0.814) of the interval corresponds to the upper limit Q upp = √ q upp ≈ 0.902 which corresponds to the value shown by blue curve in Fig. 2 of paper by Event Horizon Telescope Collaboration: Kocherlakota et al (2021).…”

“…2 of paper by Event Horizon Telescope Collaboration: Kocherlakota et al (2021). Zakharov (2022) found constraints on a tidal charge −0.25 < q for Sgr A* based on preliminary estimates of a ring width done by Lu et al (2018). Below we improve an upper limit estimate for tidal charge using new EHT estimates for shadow size in Sgr A*.…”

Testing Strong Gravitational Lensing Effects of Supermassive Compact Objects with Regular Spacetimes

“…The EHT result for Sgr A * also only calculated the emission ring angular diameter θ d = (51.8 ± 2.3) μas with the prior perceived estimates M mentioned above and D LS = 8.15 ± 0.15 kpc (Akiyama et al 2022a). The horizon-scale images of supermassive black holes furnish a theoretically fresh avenue for testing the theories of gravity and use the EHT results of the Sgr A * and M87 * shadow size to infer constraints on the additional parameter of the underlying theory for a wide variety of black holes (Kumar et al 2020d;Afrin et al 2021;Kocherlakota et al 2021;Akiyama et al 2022a;Islam et al 2022;Kumar Walia et al 2022;Zakharov 2022). We use the EHT observation results of M87 * and Sgr A * black hole shadows to constrain the deviation parameter b associated with REC black hole spacetime.…”