Testing the Kerr Paradigm with the Black Hole Shadow

Within 5-10 years, submillimeter VLBI facilities will be hopefully able to image the "shadow" of SgrA$^*$. When a black hole is surrounded by an optically thin emitting medium, the boundary of the shadow corresponds to the apparent photon capture sphere and only depends on the background metric. An accurate determination of the shape of the shadow of SgrA$^*$ could constrain possible deviations from the Kerr solution. In combination with other measurements, these observations could test the Kerr black hole paradigm.Comment: 6 pages, 3 figures. Talk given at the "14th Marcel Grossmann Meeting" (12-18 July 2015, Rome, Italy). To appear in the conference proceeding

Testing the space-time geometry around black hole candidates with the analysis of the broad Kα\alpha iron line

Astrophysical black hole candidates are thought to be the Kerr black holes predicted by General Relativity, but there is not yet clear evidence that the geometry of the space-time around these objects is really described by the Kerr metric. In order to confirm the Kerr black hole hypothesis, we have to observe strong gravity features and check that they are in agreement with the ones predicted by General Relativity. In this paper, I study the broad K$\alpha$ iron line, which is often seen in the X-ray spectrum of both stellar-mass and super-massive black hole candidates and whose shape is supposed to be strongly affected by the space-time geometry. As found in previous studies in the literature, there is a strong correlation between the spin parameter and the deformation parameter; that is, the line emitted around a Kerr black hole with a certain spin can be very similar to the one coming from the space-time around a non-Kerr object with a quite different spin. Despite that, the analysis of the broad K$\alpha$ iron line is potentially more powerful than the continuum-fitting method, as it can put an interesting bound on possible deviations from the Kerr geometry independently of the value of the spin parameter and without additional measurements.Comment: 14 pages, 9 figures. v2: refereed version covering a wider range of spins and inclination

Testing the Kerr black hole hypothesis with RELXILL_NK

Astrophysical black hole candidates are thought to be the Kerr black holes of general relativity. However, macroscopic deviations from the Kerr background are predicted by a number of scenarios beyond Einstein's gravity. X-ray reflection spectroscopy can be a powerful tool to probe the strong gravity region of these objects and test the Kerr black hole hypothesis. Here I briefly review the state of the art of this line of research and I present some constraints on possible deviations from the Kerr metric obtained with the new X-ray reflection model relxill_nk and XMM-Newton, NuSTAR, and Swift data of the supermassive black hole in 1H0707-495.Comment: 6 pages, 5 figures. Talk given at the "3rd Karl Schwarzschild Meeting" (Frankfurt am Main, Germany, 24-28 July 2017). v2: refereed versio

Testing the Kerr-nature of stellar-mass black hole candidates by combining the continuum-fitting method and the power estimate of transient ballistic jets

Astrophysical black hole candidates are thought to be the Kerr black holes predicted by General Relativity, as these objects cannot be explained otherwise without introducing new physics. However, there is no observational evidence that the space-time around them is really described by the Kerr solution. The Kerr black hole hypothesis can be tested with the already available X-ray data by extending the continuum-fitting method, a technique currently used by astronomers to estimate the spins of stellar-mass black hole candidates. In general, we cannot put a constraint on possible deviations from the Kerr geometry, but only on some combination between these deviations and the spin. The measurement of the radio power of transient jets in black hole binaries can potentially break this degeneracy, thus allowing for testing the Kerr-nature of these objects.Comment: 8 pages, 6 figures. v2: some typos correcte

Can the supermassive objects at the centers of galaxies be traversable wormholes? The first test of strong gravity for mm/sub-mm VLBI facilities

The near future mm/sub-mm VLBI experiments are ambitious projects aiming at imaging the "shadow" of the supermassive black hole candidate at the center of the Milky Way and of the ones in nearby galaxies. An accurate observation of the shape of the shadow can potentially test the nature of these objects and verify if they are Kerr black holes, as predicted by general relativity. However, previous work on the subject has shown that the shadows produced in other spacetimes are very similar to the one of the Kerr background, suggesting that tests of strong gravity are not really possible with these facilities in the near future. In this work, I instead point out that it will be relatively easy to distinguish black holes from wormholes, topologically non-trivial structures of the spacetime that might have been formed in the early Universe and might connect our Universe with other universes.Comment: 5 pages, 2 figures. v2: some typos correcte

Constraining possible variations of the fine structure constant in strong gravitational fields with the Kα\alpha iron line

In extensions of general relativity and in theories aiming at unifying gravity with the forces of the Standard Model, the value of the "fundamental constants" is often determined by the vacuum expectation value of new fields, which may thus change in different backgrounds. Variations of fundamental constants with respect to the values measured today in laboratories on Earth are expected to be more evident on cosmological timescales and/or in strong gravitational fields. In this paper, I show that the analysis of the K$\alpha$ iron line observed in the X-ray spectrum of black holes can potentially be used to probe the fine structure constant $\alpha$ in gravitational potentials relative to Earth of $\Delta \phi \approx 0.1$. At present, systematic effects not fully under control prevent to get robust and stringent bounds on possible variations of the value of $\alpha$ with this technique, but the fact that current data can be fitted with models based on standard physics already rules out variations of the fine structure constant larger than some percent.Comment: 1+15 pages, 6 figures. v2: refereed versio

Measuring the Kerr spin parameter of a non-Kerr compact object with the continuum-fitting and the iron line methods

Under the assumption that astrophysical black hole candidates are the Kerr black holes of general relativity, the continuum-fitting method and the analysis of the K$\alpha$ iron line are today the only available techniques capable of providing a relatively reliable estimate of the spin parameter of these objects. If we relax the Kerr black hole hypothesis and we try to test the nature of black hole candidates, we find that there is a strong correlation between the measurement of the spin and possible deviations from the Kerr solution. The properties of the radiation emitted in a Kerr spacetime with spin parameter $a_*$ are indeed very similar, and practically indistinguishable, from the ones of the radiation emitted around a non-Kerr object with different spin. In this paper, I address the question whether measuring the Kerr spin with both the continuum-fitting method and the K$\alpha$ iron line analysis of the same object can be used to claim the Kerr nature of the black hole candidate in the case of consistent results. In this work, I consider two non-Kerr metrics and it seems that the answer does depend on the specific background. The two techniques may either provide a very similar result (the case of the Bardeen metric) or show a discrepancy (Johannsen-Psaltis background).Comment: 1+14 pages, 5 figures. v2: refereed versio

Note on the Cardoso-Pani-Rico parametrization to test the Kerr black hole hypothesis

The construction of a generic parametrization to describe the spacetime geometry around astrophysical black hole candidates is an important step to test the Kerr black hole hypothesis. In the last few years, the Johannsen-Psaltis metric has been the most common framework to study possible deviations from the Kerr solution with present and near future observations. Recently, Cardoso, Pani and Rico have proposed a more general parametrization. The aim of the present paper is to study this new metric in a specific context, namely the thermal spectrum of geometrically thin and optically thick accretion disks. The most relevant finding is that the spacetime geometry around objects that look like very fast-rotating Kerr black holes may still have large deviations from the Kerr solution. This was not the case with the Johannsen-Psaltis metric, which means the latter was missing an important class of non-Kerr spacetimes.Comment: 5 pages, 3 figures. v2: a few typos correcte

Testing the Kerr Paradigm with X-ray Observations

Astrophysical black hole candidates are thought to be the Kerr black holes of general relativity, but the actual nature of these objects has still to be confirmed. The continuum-fitting and the iron line methods are currently the only available techniques to probe the spacetime geometry around these bodies and test the Kerr black hole paradigm. The continuum-fitting method is a robust approach, but the shape of the disk's thermal spectrum is in general too simple to measure the spin and to constrain possible deviations from the Kerr solution at the same time. The iron line analysis is potentially a powerful technique, but at the moment we do not have high quality data and a robust astrophysical model.Comment: 6 pages, 3 figures. Talk given at the "14th Marcel Grossmann Meeting" (12-18 July 2015, Rome, Italy). To appear in the conference proceeding

Evolution of the spin parameter of accreting compact objects with non-Kerr quadrupole moment

There is robust observational evidence supporting the existence of $5 - 20$ $M_\odot$ compact bodies in X-ray binary systems and of $10^5 - 10^9$ $M_\odot$ bodies at the center of many galaxies. All these objects are commonly interpreted as black holes, even is there is no direct evidence that they have an event horizon. A fundamental limit for a black hole in 4-dimensional general relativity is the Kerr bound $|a_*| \le 1$, where $a_*$ is the spin parameter. This is just the condition for the existence of the event horizon. The accretion process can spin a black hole up to $a_* \approx 0.998$ and some super-massive objects in galactic nuclei could be rapidly rotating black holes with spin parameter close to this limit. However, if these super-massive objects are not black holes, the Kerr bound does not hold and the accretion process can spin them up to $a_* > 1$. In this paper, I consider compact bodies with non-Kerr quadrupole moment. I study the evolution of the spin parameter due to accretion and I find its equilibrium value. Future experiments like the gravitational wave detector LISA will be able to test if the super-massive objects at the center of galaxies are the black holes predicted by general relativity. If they are not black holes, some of them may be super-spinning objects with $a_* > 1$.Comment: 20 pages, 16 figures. v2: published version with a few typos correcte