Mass and spin of a Kerr black hole in modified gravity and a test of the Kerr black hole hypothesis (original) (raw)
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Mass and spin of a Kerr-MOG black hole and a test for the Kerr black hole hypothesis
2017
In this paper we compute the Arnowitt-Deser-Misner (ADM) mass, the angular momentum and the charge of the Kerr black hole solution in the scalar-tensor-vector gravity theory [known as the Kerr-MOG (modified-gravity) black hole configuration]; we study in detail as well several properties of this solution such as the stationary limit surface, the event horizon, and the ergosphere, and conclude that the new deformation parameter α affects the geometry of the Kerr-MOG black hole significantly in addition to the ADM mass and spin parameters. Moreover, the ADM mass and black hole event horizon definitions allow us to set a novel upper bound on the deformation parameter and to reveal the correct upper bound on the black hole spin. We further find the geodesics of motion of stars and photons around the Kerr-MOG black hole. By using them we reveal the expressions for the mass and the rotation parameter of the Kerr-MOG black hole in terms of the red-and blueshifts of photons emitted by geodesic particles, i.e., by stars. These calculations supply a new and simple method to further test the general theory of relativity in its strong field limit: If the measured redand blueshifts of photons exceed the bounds imposed by the general theory of relativity, then the black hole is not of Kerr type. It could also happen that the measurements are allowed by the Kerr-MOG metric, implying that the correct description of the dynamics of stars around a given black hole should be performed using MOG or another modified theory of gravity that correctly predicts the observations. In particular, this method can be applied to test the nature of the putative black hole hosted at the center of the Milky Way in the near future.
2022
In this work, we elaborate on the development of a general relativistic formalism that allows one to analytically express the mass and spin parameters of the Kerr black hole in terms of observational data: the total redshift and blueshift of photons emitted by geodesic massive particles revolving the black hole and their orbital parameters. Thus, we present concise closed formulas for the mass and spin parameters of the Kerr black hole in terms of few directly observed quantities in the case of equatorial circular orbits either when the black hole is static or is moving with respect to a distant observer. Furthermore, we incorporate the gravitational dragging effect generated by the rotating nature of the Kerr black hole into the analysis and elucidate its non-trivial contribution to the expression for the light bending parameter and the frequency shifts of photons emitted by orbiting particles that renders simple symmetric expressions for the kinematic redshift and blueshift. We also incorporate the dependency of the frequency shift on the azimuthal angle, a fact that allows one to express the total redshift/blueshift along any point of the orbit of the revolving particle for the cases when the black hole is both static or moving with respect to us. These formulas allow one to compute the Kerr black hole parameters by applying this general relativistic formalism to astrophysical systems like the megamaser accretion disks orbiting supermassive black holes at the core of active galactic nuclei. Our results open a new window to implement parameter estimation studies to constrain black hole variables, and they can be generalized to black hole solutions beyond Einstein gravity.
Physical Review D, 2015
We are motivated by the recently reported dynamical evidence of stars with short orbital periods moving around the center of the Milky Way and the corresponding hypothesis about the existence of a supermassive black hole hosted at its center. In this paper we show how the mass and rotation parameters of a Kerr black hole (assuming that the putative supermassive black hole is of this type), as well as the distance that separates the black hole from the Earth, can be estimated in a relativistic way in terms of i) the red and blue shifts of photons that are emitted by geodesic massive particles (stars and galactic gas) and travel along null geodesics towards a distant observer, and ii) the radius of these star/gas orbits. As a concrete example and as a first step towards a full relativistic analysis of the above mentioned star orbits around the center of our galaxy, we consider stable equatorial circular orbits of stars and express their corresponding red/blue shifts in terms of the metric parameters (mass and angular momentum per unit mass) and the orbital radii of both the emitter star (and/or galactic gas) and the distant observer. In principle, these expressions allow one to statistically estimate the mass and rotation parameters of the Kerr black hole, and the radius of our orbit, through a Bayesian fitting, i.e., with the aid of observational data: the red/blue shifts measured at certain points of stars' orbits and their radii, with their respective errors, a task that we hope to perform in the near future. We also point to several astrophysical phenomena, like accretion discs of rotating black holes, binary systems and active galactic nuclei, among others, to which this formalism can be applied.
Measuring Parameters of Supermassive Black Holes with Space Missions
Mathematical physics: proceedings of the 12th …, 2007
To describe black hole in astrophysics typically astronomers use Newtonian approaches for gravitational field because usually one analyzes processes acting far enough (in Schwarzschild radius units) from black hole horizons. Here we discuss phenomena where we have to use general relativistic approaches to explain present and future observational data like Fe K α line profiles and shapes of shadows around black holes. Different X-ray missions such as ASCA, XMM-Newton, Chandra etc. discovered features of Fe K α lines and other X-ray lines as well. Attempts to fit spectral line shapes lead to conclusions that sometimes the profiles line shapes should correspond to radiating regions which are located in the innermost parts of accretion disks where contributions of general relativistic phenomena are extremely important. As an illustration we consider a radiating annulus model to clarify claims given recently by Müller & Camenzind (2004). We discuss properties of highly inclined disks and analyze a possibility to evaluate magnetic fields near black hole horizons. We mention also that shadows could give us another case when one could evaluate black hole parameters (namely, spins, charges and inclination angles) analyzing sizes and shapes shadows around black holes. We discuss glories (mirages) formed near rapidly rotating Kerr black hole horizons and propose a procedure to measure masses, charges and rotation parameters analyzing these forms of mirages. We also propose to use future radio interferometer RADIOASTRON (Millimetron or MAXIM) 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. We propose also a procedure to measure a black hole charge with future space missions.
Testing general relativity with the Event Horizon Telescope
General Relativity and Gravitation
The Event Horizon Telescope is a millimeter VLBI array that aims to take the first pictures of the black holes in the center of the Milky Way and of the M87 galaxy, with horizon scale resolution. Measurements of the shape and size of the shadows cast by the black holes on the surrounding emission can test the cosmic censorship conjecture and the no-hair theorem and may find evidence for classical effects of the quantum structure of black holes. Observations of coherent structures in the accretion flows may lead to accurate measurements of the spins of the black holes and of other properties of their spacetimes. For Sgr A * , the black hole in the center of the Milky Way, measurements of the precession of stellar orbits and timing monitoring of orbiting pulsars offer complementary avenues to the gravitational tests with the Event Horizon Telescope.
Observational features of black holes
Arxiv preprint gr-qc/ …, 2005
Recently Holz & Wheeler [59] considered a very attracting possibility to detect retro-MACHOs, i.e. retroimages 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 [60] 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.
Testing General Relativity with NuSTAR Data of Galactic Black Holes
The Astrophysical Journal, 2021
Einstein’s theory of General Relativity predicts that the spacetime metric around astrophysical black holes is described by the Kerr solution. In this work, we employ state-of-the-art relativistic reflection modeling to analyze a selected set of NuSTAR spectra of Galactic black holes to obtain the most robust and precise constraints on the Kerr black hole hypothesis possible today. Our constraints are much more stringent than those from other electromagnetic techniques and, with some sources, we find stronger constraints than those currently available from gravitational waves.
Constraining Kerr-like black holes with Event Horizon Telescope results of Sgr A*
Cornell University - arXiv, 2022
The Event Horizon Telescope (EHT), recently released the image of supermassive black hole Sgr A* showing an angular shadow diameter d sh = 48.7 ± 7 µas, with an inferred black hole mass M = 4.0 +1.1 −0.6 × 10 6 M ⊙ and Schwarzschild shadow deviation δ = −0.08 +0.09 −0.09 (VLTI), −0.04 +0.09 −0.10 (Keck). The EHT image of Sgr A* is consistent with a Kerr black hole's expected appearance and the results directly prove a supermassive black hole in the center of the Milky Way. The Kerr hypothesis, a strong-field prediction of general relativity (GR), may not hold in the theories of gravity that admit Kerr-like black holes having an additional deviation parameter arising from the underlying theory. Here, we use the EHT observational results of Sgr A* to investigate the constraints on the deviation parameter whereby, such a rotating Kerr-like black hole can be an astrophysical black hole candidate, paying attention to three leading models. Modelling Kerr-like black holes as supermassive black hole Sgr A*, we observe that for it to be a viable astrophysical black hole candidate, the EHT results of Sgr A* put more stringent constraints on the parameter space than those put by the EHT results of M87*. However, a systematic bias analysis shows Kerr-like black hole shadows may capture Kerr black hole shadows over a good part of the constrained parameter space, making Kerr-like and Kerr black holes indistinguishable and one can't rule out a possibility of potential modifications of the Kerr metric or GR.