Constraining spherically symmetric metrics by the gap between photon rings

Abstract

Gravitational lensing of luminous matter that surrounds a black hole or some other sufficiently compact object produces an infinite sequence of images. Besides the direct (or primary) image, it comprises demagnified and deformed replicas of the original known as photon rings which are progressively nearing the boundary of the socalled shadow. In the present paper, we present analytical approximation formulas for higher-order photon rings for an asymptotically flat, static, spherically symmetric spacetime that admits a photon sphere. We consider a geometrically thin disk of light sources in the equatorial plane and an observer at arbitrary inclination far away from the center. Fixing the emission radius and leveraging the strong deflection limit, which provides an analytical logarithmic approximation for the deflection angle, we find the deformed shape of higher-order photon rings in the form of a polar equation on the observer's screen. It has been suggested by other authors to use the relative size of photon rings for characterizing the underlying spacetime. In particular, the relative separation between two neighboring photon rings, which we call "gap parameter", was considered. We analytically calculate the gap parameter of higher-order photon rings for metrics of the considered class that may depend on multiple parameters. The advantage of using this quantity is in the fact that, to within the assumed approximations, it is independent of the mass of the central object (or of some other characteristic parameter if the mass is zero) and of the distance of the observer. Measurements of the gap parameter, which may become possible in the near future, will restrict the spacetime models that are in agreement with the observations. Even without knowing the inner and outer radii of the shining disk, it will conclusively rule out some metrics. Some examples are provided.

arXiv comment15 pages, 5 figures, 1 table

References in corpus (70)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole
• First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring
• Viewing the Shadow of the Black Hole at the Galactic Center
• First M87 Event Horizon Telescope Results. II. Array and Instrumentation
• Schwarzschild black hole lensing
• First M87 Event Horizon Telescope Results. III. Data Processing and Calibration
• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Gravitational lensing in the strong field limit
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• Black Hole Shadows, Photon Rings, and Lensing Rings
• Calculating black hole shadows: Review of analytical studies
• The geometry of photon surfaces
• Shadows and strong gravitational lensing: a brief review
• First Sagittarius A* Event Horizon Telescope Results. V. Testing Astrophysical Models of the Galactic Center Black Hole
• First Sagittarius A* Event Horizon Telescope Results. III: Imaging of the Galactic Center Supermassive Black Hole
• Strong field limit of black hole gravitational lensing
• First Sagittarius A* Event Horizon Telescope Results. II. EHT and Multi-wavelength Observations, Data Processing, and Calibration
• Universal Interferometric Signatures of a Black Hole's Photon Ring
• First Sagittarius A* Event Horizon Telescope Results. IV. Variability, Morphology, and Black Hole Mass
• Reissner-Nordstrom black hole lensing
• Gravitational Lensing by Black Holes
• Constraints on black-hole charges with the 2017 EHT observations of M87*
• On the exact gravitational lens equation in spherically symmetric and static spacetimes
• The Shape of the Black Hole Photon Ring: A Precise Test of Strong-Field General Relativity
• Quasi-Equatorial Gravitational Lensing by Spinning Black Holes in the Strong Field Limit
• Strong deflection limit analysis and gravitational lensing of an Ellis wormhole
• Analytic Kerr black hole lensing for equatorial observers in the strong deflection limit
• Janis-Newman-Winicour and Wyman solutions are the same
• Constraints on a charge in the Reissner--Nordström metric for the black hole at the Galactic Center
• Kerr black hole lensing for generic observers in the strong deflection limit
• Gravitational Lensing in presence of Plasma: Strong Lens Systems, Black Hole Lensing and Shadow
• Concerns regarding the use of black hole shadows as standard rulers
• Strong deflection limit of black hole gravitational lensing with arbitrary source distances
• Photon Ring and Observational Appearance of a Hairy Black Hole
• Key Science Goals for the Next-Generation Event Horizon Telescope
• Strong field limit analysis of gravitational retro-lensing
• Braneworld black hole gravitational lens: Strong field limit analysis
• Kerr-Sen dilaton-axion black hole lensing in the strong deflection limit
• Can different black holes cast the same shadow?
• Image of the Janis-Newman-Winicour naked singularity with a thin accretion disk
• Gravitational lensing in the Simpson-Visser black-bounce spacetime in a strong deflection limit
• Gravitational lensing in plasma: Relativistic images at homogeneous plasma
• Photon rings of spherically symmetric black holes and robust tests of non-Kerr metrics
• Photon Ring Autocorrelations
• On the Observable Shape of Black Hole Photon Rings
• Toward determining the number of observable supermassive black hole shadows
• The Photon Ring in M87*
• Black hole shadow as a standard ruler in cosmology
• Analytical study of higher-order ring images of accretion disk around black hole
• Strong Gravitational Lensing by Schwarzschild Black Holes
• Photon ring test of the Kerr hypothesis: Variation in the ring shape
• Nature of singularity in Einstein-massless scalar theory
• Shape of higher-order images of equatorial emission rings around a Schwarzschild black hole: Analytical description with polar curves
• The weakly perturbed Schwarzschild lens in the strong deflection limit
• Photon rings as tests for alternative spherically symmetric geometries with thin accretion disks
• Unbound motion of massive particles in the Schwarzschild metric: Analytical description in case of strong deflection
• Universal signatures of singularity-resolving physics in photon rings of black holes and horizonless objects
• Black Hole Photon Rings Beyond General Relativity
• Testing Gravity with Black Hole Shadow Subrings
• The Fingerprints of Black Holes - Shadows and their Degeneracies
• A new cosmological probe using super-massive black hole shadows
• Relativistic iron lines in accretion disks: the contribution of higher order images in the strong deflection limit
• The Unsettled Number: Hubble's Tension
• Flares and their echoes can help distinguish photon rings from black holes with space-Earth very long baseline interferometry
• Jets and Rings in Images of Spinning Black Holes
• $H_0$ Tension on the Light of Supermassive Black Hole Shadows Data
• Climbing out of the shadows: building the distance ladder with black hole images

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• Strong deflection of massive particles in spherically symmetric spacetimes
• Constraints on the black-hole charges of M87* and Sagittarius A* by changing rates of photon spheres can be relaxed
• Interferometric signature of higher-order images in a parametrized framework
• Analyzing the Influence of Geometrical Deformation on Photon Sphere and Shadow Radius: A New Analytical Approach -Stationary, and Axisymmetric Spacetime
• Overlapping of photon rings in black hole imaging
• Gauss-Bonnet lensing of spinning massive particles in static spherically symmetric spacetimes
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• Gravitational lensing inside and outside of a marginally unstable photon sphere in a general, static, spherically symmetric, and asymptotically-flat spacetime in strong deflection limits
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• Fast and accurate analytical formulas for light propagation in general static, spherically symmetric spacetimes
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