Testing the no-hair theorem with observations of black holes in the electromagnetic spectrum

Abstract

According to the general-relativistic no-hair theorem, astrophysical black holes depend only on their masses and spins and are uniquely described by the Kerr metric. Mass and spin are the first two multipole moments of the Kerr spacetime and completely determine all other moments. The no-hair theorem can be tested by measuring potential deviations from the Kerr metric which alter such higher-order moments. In this review, I discuss tests of the no-hair theorem with current and future observations of such black holes across the electromagnetic spectrum, focusing on near-infrared observations of the supermassive black hole at the Galactic center, pulsar-timing and very-long baseline interferometric observations, as well as X-ray observations of fluorescent iron lines, thermal continuum spectra, variability, and polarization. arXiv:1602.07694v3 [astro-ph.HE] 20 May 2016According to the no-hair theorem, isolated and stationary black holes in general relativity are uniquely characterized by their masses M , spins J, and electric charges Q and are described by the Kerr-Newman metric [29], which reduces to the Kerr metric [30] in the case of electrically neutral black holes (which should be the case for astrophysical black holes, because any residual electric charge would quickly neutralize) [31][32][33][34][35][36][37]. This metric, then, is the unique stationary, axisymmetric, asymptotically flat, vacuum solution of the Einstein field equations which contains an event horizon but no closed timelike curves in the exterior domain. The no-hair theorem relies on the cosmic censorship conjecture [38] as well as on the physically reasonable assumption that the exterior metric is free of closed timelike curves. See Refs. [39,40] for reviews. Note, however, that the mathematical status of the no-hair theorem is not without controversy, principally in relation to the assumption (in the classical proof) of analyticity; see Sec. 3.4 in Ref.[39] for a discussion. Other no-hair theorems exist for different extensions of general relativity; see Refs. [39,52] for reviews.Consequently, general relativity predicts that all astrophysical black holes are described by the Kerr metric. Nonetheless, such black holes will not be perfectly stationary in practice nor exist in perfect vacuum, because the presence of other objects or fields such as stars, accretion disks, or dark matter could alter the Kerr nature of the black hole (see, e.g., Ref. [41]). However, under the assumption that such perturbations are so small to be practically unobservable, one can argue that astrophysical black holes are indeed described by the Kerr metric.In Boyer-Lindquist coordinates, then, the Kerr metric g K µν has the nonzero metric elements (setting G = c = 1)

Investigating the Binarity of S0-2: Implications for Its Origins and Robustness as a Probe of the Laws of Gravity around a Supermassive Black Hole

“…As anticipated by many theorists, observations of shortperiod stars orbiting the SMBH in our Galactic center are currently opening a new window into testing the gravitational theory and to measure relativistic effects (see, e.g., Rubilar & Eckart 2001;Zucker et al 2006;Will 2008;Borka et al 2013;Johannsen 2016aJohannsen , 2016bPsaltis et al 2016;Zakharov et al 2016;Iorio 2017 and references therein). The relativistic redshift on S0-2′s RV is the first relativistic effect expected to be detected with S0-2′s closest approach in 2018 (Zucker et al 2006;Angélil & Saha 2010, 2011.…”

On the shadow of rotating traversable wormholes

“…The specific features of the images can be used to extract information about the physical properties of the compact objects, and to a e-mail: gyulchev@phys.uni-sofia.bg b e-mail: pnedkova@phys.uni-sofia.bg c e-mail: yazad@phys.uni-sofia.bg differentiate between gravitational theories [17][18][19]. Using the deformation of the shadow shape of an isolated black hole we can evaluate its spin and multipole moments [20][21][22][23].…”

Innermost stable circular orbit of Kerr-MOG black hole

“…ISCO is believed to be the inner edge of an accretion disc orbiting a black hole. Iron line profiles for black holes are determined by the photons that are emitted near the ISCO [16]. The radius of the ISCO is 6M (M is the total mass of a black hole) in the case of the Schwarzschild black hole, while the radius of ISCO for a Kerr black hole depends on the intrinsic angular momentum a, the well-known Kerr parameter.…”