## Black hole shadows

### Project Overview

Evidence supporting the existence of black holes has come in the form of spectroscopic and proper motion studies of galactic nuclei [1,2,3]. These studies indicate that there are dark objects at the center of galaxies with parameters, mass and angular momentum, that make it difficult to imagine viable alternatives to a black hole. Nevertheless, alternative solutions have been proposed, and unambiguous proof that the central object is a black hole has been lacking. Given that the defining characteristic of a black hole is the existence of an event horizon, a direct observation - or lack thereof - of such a structure could fill this gap. This would require a probe of the horizon-scale structure of the dark central object.

One option is to make use of gravitational wave (GW) astronomy [4]. In this case we are primarily interested in observing the gravitational waves emitted during and after the merger of two compact massive objects. There will be GW emission throughout this process as the objects inspiral and merge, and also by the remnant object as it relaxes towards an equilibrium. These final waves are known as the ringdown signal and their spectrum is believed to coincide with the characteristic oscillation modes of the remnant [5]. These characteristic modes are modeled using perturbation theory in General Relativity, and their structure encodes properties of the solution - including the (non)existence of a horizon. Hence an observation of the GW radiation from the end stages of a merger process is expected to provide a 'smoking gun' for the existence of black holes. Remarkably, an observation of just this kind was managed by the aLIGO team in their detection of a GW signal from the merger of compact binary GW150914 [6].

A second option, and the focus of this project, makes use of radio astronomy to get an image of the galactic center; as the processes that lead to electromagnetic radiation are different to those that drive gravitational radiation these two approaches are, in a sense, complementary. The objective with this option is to resolve the 'shadow' that the event horizon of a black hole - should there be one - casts due to the strong bending of light by its gravitational field [7,8,9]. This black hole shadow has been shown to encode the parameters of the solution, much as the ringdown signal does in GW observations, and shadow templates have been generated for a number of different black holes [7-16]. As a result, an observation of the galactic core which reveals a shadow will signal the existence of a black hole, and then the precise form of the shadow can be matched against templates to discriminate between different candidate black hole solutions [17-20].

### Project Goals and Methodology

An initial goal of this project is to study the shadows of a recently discovered class of black hole solutions, referred to as Kerr Black Holes with Scalar Hair (KBHsSH) [21,22], with a view towards developing templates for use in experiments such as the Event Horizon Telescope [7]. KBHsSH are rotating black hole solutions to GR coupled to a massive, complex, scalar field that satisfies a certain synchronicity condition; this framework permits non-trivial, long-lived, configurations of fields around black holes that break black hole uniqueness without invoking higher dimensions or different asymptotics. In such cases the black hole solution will be characterised by additional parameters and one may ask whether, again, through direct observations of the black hole, one can measure its parameters and thereby discern a departure from the Kerr class of solutions.

To address this problem we have developed a GR ray-tracing code, PyHole , that can simulate the motion of light on the curved KBHSH background. Conceptually, we are studying the motion of light rays that are emitted from a distant source and which eventually reach the position of an observer(or camera), perhaps having passed near the black hole along the way. In practice with PyHole light rays are traced backwards in time, starting at the camera, along null geodesics of the black hole metric. Each pixel on the camera image corresponds to a light ray with a different initial momentum vector, which will, as a result, follow a different trajectory; some rays will reach a distant light source, and some will not, having fallen instead behind the event horizon. The former will appear as bright pixels on the camera image and the latter as dark pixels. There is also a set of marginal trajectories that enter into null orbits of the black hole and delimit the region of space that appears dark on the image plane, corresponding to the black hole’s shadow. To get a sense of how all this comes together we have set up a visualisation tool.

Together with researchers from the gravitional physics group at the University of Aveiro, we have studied the emergence of chaotic behaviour in the lensing of light by KBHsSH and rotating boson stars [23].

### References

[1] J. H. Krolik, Active Galactic Nuclei, Princeton University Press, ISBN 0-691-01151-6 (1999).[2] J. Kormendy, and D. Richstone," Inward Bound---The Search For Supermassive Black Holes In Galactic Nuclei", ARA&A, 33, 581, (1995).

[3] M. Miyoshi et al, "Evidence for a black hole from high rotation velocities in a sub-parsec region of NGC4258", Nature 373, 127 (1995). .

[4] B.S. Sathyaprakash and Bernard F. Schutz, "Physics, Astrophysics and Cosmology with Gravitational Waves", Living Rev. Relativity 12 (2009).

[5] E. Berti, V. Cardoso, and C. M. Will, "On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA", Physical Review D 73, 064030 (2006); [gr-qc /0512160].

[6] B. P. Abbott et al, "Observation of Gravitational Waves from a Binary Black Hole Merger", Physical Review Letters 116, 6, (2016).

[7] Event Horizon Telescope project, www.eventhorizontelescope.org.

[8] J. M. Bardeen, "Timelike and null geodesics of the Kerr metric" in Black Holes (Les Astres Occlus), edited by C. DeWitt and B. S. DeWitt (1973), pp. 215.

[9] H. Falcke, F. Melia, and E. Agol, "Viewing the shadow of the black hole at the galactic center", Astrophysical Journal Letters 528, L13 (2000); [astro-ph/9912263].

[10] V. Perlick, "Gravitational Lensing from a Spacetime Perspective", Living Rev. Relativity 7, 9 (2004).

[11] R. Takahashi, "Shapes and positions of black hole shadows in accretion disks and spin parameters of black holes", Astrophys.J. 611 996-1004 (2004) ; [astro-ph/0405099].

[12] A. Grenzebach, V. Perlick, and C. Lammerzahl, "Photon regions and shadows of Kerr-Newman-NUT black holes with a cosmological constant", Physical Review D 89, 12 (2014).

[13] A. Bohn, W. Throwe, F. Hebert, K. Henriksson, D. Bunandar, N. W. Taylor, M. A. Scheel, "What does a binary black hole merger look like?", Class. Quantum Grav. 32, 065002 (2015); [arXiv:1410.7775].

[14] A. A. Abdujabbarov, L. Rezzolla, B. J. Ahmedov, "A coordinate independent characterisation of a black-hole shadow"; [arXiv:1503.09054].

[15] P. Franklin, K.S. Thorne and E. von Tunzelmann, and O. James, "Gravitational Lensing by Spinning Black Holes in Astrophysics, and in the Movie Interstellar", Class. Quantum Grav. 32, 065001 (2015); [arXiv:1502.03808v1].

[16] GYOTO, relativistic ray tracing code, https://gyoto.obspm.fr/.

[17] C. Bambi, "Testing the Kerr paradigm with the black hole shadow"; [arXiv:1507.05257].

[18] A. E. Broderick , T. Johannsen, A. Loeb, D. Psaltis, "Testing the No-Hair Theorem with Event Horizon Telescope Observations of Sagittarius A*, Astrophys.J. 784 (2014) 7; [arXiv:1311.5564].

[19] A.E. Broderick, A. Loeb, R. Narayan, "The Event Horizon of Sagittarius A*", The Astrophysical Journal 701: 1357 (2009); [arXiv:0903.1105].

[20] M. D. Johnson et al, "Resolved magnetic-field structure and variability near the event horizon of Sagittarius A*", Science 350 (6265): 1242–1245, (2015); [arXiv:1512.0122].

[21] C. A. R. Herdeiro, E. Radu, "Kerr black holes with scalar hair", Physical Review Letters 112, 221101 (2014); [arXiv:1403.2757].

[22] Pedro V. P. Cunha, Carlos A. R. Herdeiro, Eugen Radu, Helgi F. Runarsson, "Shadows of Kerr black holes with scalar hair", Physical Review Letters 115, 211102 (2015); [arXiv:1509.00021].

[23] P. V. P. Cunha, J. Grover, C. Herdeiro, E. Radu, H. Runarsson, A. Wittig "Chaotic lensing around boson stars and Kerr black holes with scalar hair", Physical Review D 94, 104023 (2016); [arXiv:1609.01340].

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