A coordinate-independent characterization of a black hole shadow

Nature Astronomy , 2018

Our Galactic Center, Sagittarius A* (Sgr A*), is believed to harbour a supermassive black hole (BH), as suggested by observations tracking individual orbiting stars. Upcoming sub-millimetre very-long-baseline-interferometry (VLBI) images of Sgr A* carried out by the Event-Horizon-Telescope Collaboration (EHTC) are expected to provide critical evidence for the existence of this supermassive BH. We assess our present ability to use EHTC images to determine if they correspond to a Kerr BH as predicted by Einstein's theory of general relativity (GR) or to a BH in alternative theories of gravity. To this end, we perform general-relativistic magnetohydrodynamical (GRMHD) simulations and use general-relativistic radiative transfer (GRRT) calculations to generate synthetic shadow images of a magnetised accretion flow onto a Kerr BH. In addition, and for the first time, we perform GRMHD simulations and GRRT calculations for a dilaton BH, which we take as a representative solution of an alternative theory of gravity. Adopting the VLBI configuration from the 2017 EHTC campaign, we find that it could be extremely difficult to distinguish between BHs from different theories of gravity, thus highlighting that great caution is needed when interpreting BH images as tests of GR.

The Astrophysical Journal, 2020

The Event Horizon Telescope (EHT), a global submillimeter wavelength very long baseline interferometry array, unveiled event-horizon-scale images of the supermassive black hole M87 * as an asymmetric bright emission ring with a diameter of 42±3 μas, and it is consistent with the shadow of a Kerr black hole of general relativity. A Kerr black hole is also a solution of some alternative theories of gravity, while several modified theories of gravity admit non-Kerr black holes. While earlier estimates for the M87 * black hole mass, depending on the method used, fall in the range »´-Ḿ M 3 10 7 10 9 9   , the EHT data indicated a mass for the M87 * black hole of (6.5 ± 0.7)×10 9 M e. This offers another promising tool to estimate black hole parameters and to probe theories of gravity in its most extreme region near the event horizon. The important question arises: Is it possible by a simple technique to estimate black hole parameters from its shadow, for arbitrary models? In this paper, we present observables, expressed in terms of ordinary integrals, characterizing a haphazard shadow shape to estimate the parameters associated with black holes, and then illustrate its relevance to four different models: Kerr, Kerr-Newman, and two rotating regular models. Our method is robust, accurate, and consistent with the results obtained from existing formalism, and it is applicable to more general shadow shapes that may not be circular due to noisy data. Unified Astronomy Thesaurus concepts: Astrophysical black holes (98); Galactic center (565); Black hole physics (159); Gravitation (661); Gravitational lensing (670)

New Astronomy Reviews, 2012

Shadow formation around supermassive black holes were simulated. Due to enormous progress in observational facilities and techniques of data analysis researchers approach to opportunity to measure shapes and sizes of the shadows at least for the closest supermassive black hole at the Galactic Center. Measurements of the shadow sizes around the black holes can help to evaluate parameters of black hole metric. Theories with extra dimensions (Randall-Sundrum II braneworld approach, for instance) admit astrophysical objects (supermassive black holes, in particular) which are rather different from standard ones. Different tests were proposed to discover signatures of extra dimensions in supermassive black holes since the gravitational field may be different from the standard one in the general relativity (GR) approach. In particular, gravitational lensing features are different for alternative gravity theories with extra dimensions and general relativity. Therefore, there is an opportunity to find signatures of extra dimensions in supermassive black holes. We show how measurements of the shadow sizes can put constraints on parameters of black hole in spacetime with extra dimensions.

Dark Matter in Astro- and Particle Physics, 2006

Recently Holz & Wheeler [1] considered a very attracting possibility to detect retro-MACHOs, i.e. retro-images of the Sun by a Schwarzschild black hole. In this paper we discuss glories (mirages) formed near rapidly rotating Kerr black hole horizons and propose a procedure to measure masses and rotation parameters analyzing these forms of mirages. In some sense that is a manifestation of gravitational lens effect in the strong gravitational field near black hole horizon and a generalization of the retro-gravitational lens phenomenon. We analyze the case of a Kerr black hole rotating at arbitrary speed for some selected positions of a distant observer with respect to the equatorial plane of a Kerr black hole. We discuss glories (mirages) formed near rapidly rotating Kerr black hole horizons and propose a procedure to measure masses and rotation parameters analyzing these forms of mirages. Some time ago Falcke, Melia & Agol [2] suggested to search shadows at the Galactic Center. In this paper we present the boundaries for shadows calculated numerically. We also propose to use future radio interferometer RADIOASTRON facilities to measure shapes of mirages (glories) and to evaluate the black hole spin as a function of the position angle of a distant observer.

Physical review letters, 2016

In general relativity, the angular radius of the shadow of a black hole is primarily determined by its mass-to-distance ratio and depends only weakly on its spin and inclination. If general relativity is violated, however, the shadow size may also depend strongly on parametric deviations from the Kerr metric. Based on a reconstructed image of Sagittarius A^{*} (Sgr A^{*}) from a simulated one-day observing run of a seven-station Event Horizon Telescope (EHT) array, we employ a Markov chain Monte Carlo algorithm to demonstrate that such an observation can measure the angular radius of the shadow of Sgr A^{*} with an uncertainty of ∼1.5 μas (6%). We show that existing mass and distance measurements can be improved significantly when combined with upcoming EHT measurements of the shadow size and that tight constraints on potential deviations from the Kerr metric can be obtained.

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, allowing us to test whether the Kerr metric provides a good description of the space-time in the vicinity of the event horizons of supermassive BHs. We consider a wide range of well-motivated deviations from classical General Relativity solutions, and constrain them using the Event Horizon Telescope (EHT) observations of Sagittarius A * (SgrA *), connecting the size of the bright ring of emission to that of the underlying BH shadow and exploiting high-precision measurements of SgrA * 's mass-to-distance ratio. The scenarios we consider, and whose fundamental parameters we constrain, include various regular BH models, string-and non-linear electrodynamics-inspired space-times, scalar field-driven violations of the no-hair theorem, alternative theories of gravity, new ingredients such as the generalized uncertainty principle and Barrow entropy, and BH mimickers including examples of wormholes and naked singularities. We demonstrate that SgrA * 's image places particularly stringent constraints on models predicting a shadow size which is larger than that of a Schwarzschild BH of a given mass: for instance, in the case of Barrow entropy we derive constraints which are significantly tighter than the cosmological ones. Our results are among the first tests of fundamental physics from the shadow of SgrA * and, while the latter appears to be in excellent agreement with the predictions of General Relativity, we have shown that various well-motivated alternative scenarios (including BH mimickers) are far from being ruled out at present.

The Astrophysical Journal, 2000

In recent years, the evidence for the existence of an ultra-compact concentration of dark mass associated with the radio source Sgr A* in the Galactic Center has become very strong. However, an unambiguous proof that this object is indeed a black hole is still lacking. A defining characteristic of a black hole is the event horizon. To a distant observer, the event horizon casts a relatively large "shadow" with an apparent diameter of ∼ 10 gravitational radii due to bending of light by the black hole, nearly independent of the black hole spin or orientation. The predicted size (∼ 30µarcseconds) of this shadow for Sgr A* approaches the resolution of current radio-interferometers. If the black hole is maximally spinning and viewed edge-on, then the shadow will be offset by ∼ 8 µarcseconds from the center of mass, and will be slightly flattened on one side. Taking into account scatter-broadening of the image in the interstellar medium and the finite achievable telescope resolution, we show that the shadow of Sgr A* may be observable with very long-baseline interferometry at sub-millimeter wavelengths, assuming that the accretion flow is optically thin in this region of the spectrum. Hence, there exists a realistic expectation of imaging the event horizon of a black hole within the next few years.

arXiv (Cornell University), 2022

We consider a black hole mimicker given by an exact solution of the stationary and axially symmetric field equations in vacuum known as the δ-Kerr metric. We study its optical properties based on a ray-tracing code for photon motion and characterize the apparent shape of the shadow of the compact object and compare it with the Kerr black hole. For the purpose of obtaining qualitative estimates related to the observed shadow of the supermassive compact object in the galaxy M87 we focus on values of the object's spin a and inclination angle of observation θ0 close to the measured values. We then apply the model to the shadow of the δ-Kerr metric to obtain constraints on the allowed values of the deformation parameter. We show that based uniquely on one set of observations of the shadow's boundary it is not possible to exclude the δ-Kerr solution as a viable source for the geometry in the exterior of the compact object.

Physical Review D

We consider a black hole mimicker given by an exact solution of the stationary and axially-symmetric field equations in vacuum known as the δ-Kerr metric. We study its optical properties based on a ray-tracing code for photon motion and characterize the apparent shape of the shadow of the compact object and compare it with the Kerr black hole. For the purpose of obtaining qualitative estimates related to the observed shadow of the supermassive compact object in the galaxy M87 we focus on values of the object's spin a and inclination angle of observation θ 0 close to the measured values. We then apply the model to the shadow of the δ-Kerr metric to obtain constraints on the allowed values of the deformation parameter. We show that based uniquely on one set of observations of the shadow's boundary it is not possible to exclude the δ-Kerr solution as a viable source for the geometry in the exterior of the compact object.

Classical and Quantum Gravity

Recently, Tsupko et al. have put forward the very interesting proposal to use the shadows of highredshift supermassive black holes (SMBHs) as standard rulers. This would in principle allow us to probe the expansion history within a redshift range which would otherwise be challenging to access. In this note, we critically examine this proposal, and identify a number of important issues which had been previously overlooked. These include difficulties in obtaining reliable SMBH mass estimates and reaching the required angular resolution, and an insufficient knowledge of the accretion dynamics of high-redshift SMBHs. While these issues currently appear to prevent high-redshift SMBH shadows from being used as robust standard rulers, we hope that our flagging them early will help in making this probe theoretically mature by the time it will be experimentally feasible.