Constraints on the Size of Extra Dimensions from the Orbital Evolution of the Black-Hole X-Ray Binary XTE J1118+480

In a universe of the Randall-Sundrum type, black holes are unstable and emit gravitational modes in the extra dimension. This leads to dramatically shortened lifetimes of astrophysical black holes and to an observable change of the orbital period of black-hole binaries. I obtain an upper limit on the rate of change of the orbital period of the binary XTE J1118+480 and constrain the asymptotic curvature radius of the extra dimension to a value that is of the same order as the constraints from other astrophysical sources. A unique property of XTE J1118+480 is that the expected rate of change of the orbital period due to magnetic braking alone is so large that only one additional measurement of the orbital period would lead to the first detection of orbital evolution of a black-hole binary and impose the tightest constraint to date on the size of one extra dimension of the order of 35 microns.Comment: accepted for publication in A&

Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum: II. Black-Hole Images

According to the no-hair theorem, all astrophysical black holes are fully described by their masses and spins. This theorem can be tested observationally by measuring (at least) three different multipole moments of the spacetimes of black holes. In this paper, we analyze images of black holes within a framework that allows us to calculate observables in the electromagnetic spectrum as a function of the mass, spin, and, independently, the quadrupole moment of a black hole. We show that a deviation of the quadrupole moment from the expected Kerr value leads to images of black holes that are either prolate or oblate depending on the sign and magnitude of the deviation. In addition, there is a ring-like structure around the black-hole shadow with a diameter of about 10 black-hole masses that is substantially brighter than the image of the underlying accretion flow and that is independent of the astrophysical details of accretion flow models. We show that the shape of this ring depends directly on the mass, spin, and quadrupole moment of the black hole and can be used for an independent measurement of all three parameters. In particular, we demonstrate that this ring is highly circular for a Kerr black hole with a spin a<0.9M, independent of the observer's inclination, but becomes elliptical and asymmetric if the no-hair theorem is violated. Near-future very-long baseline interferometric observations of Sgr A* will image this ring and may allow for an observational test of the no-hair theorem.Comment: Accepted for publication in Ap

Tests of General Relativity in the Strong Gravity Regime Based on X-Ray Spectropolarimetric Observations of Black Holes in X-Ray Binaries

Although General Relativity (GR) has been tested extensively in the weak gravity regime, similar tests in the strong gravity regime are still missing. In this paper we explore the possibility to use X-ray spectropolarimetric observations of black holes in X-ray binaries to distinguish between the Kerr metric and the phenomenological metrics introduced by Johannsen and Psaltis (2011) (which are not vacuum solutions of Einstein's equation) and thus to test the no-hair theorem of GR. To this end, we have developed a numerical code that calculates the radial brightness profiles of accretion disks and parallel transports the wave vector and polarization vector of photons through the Kerr and non-GR spacetimes. We used the code to predict the observational appearance of GR and non-GR accreting black hole systems. We find that the predicted energy spectra and energy dependent polarization degree and polarization direction do depend strongly on the underlying spacetime. However, for large regions of the parameter space, the GR and non-GR metrics lead to very similar observational signatures, making it difficult to observationally distinguish between the two types of models.Comment: 27 pages, 8 figures, accepted for publication in the Astrophysical Journa

Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum: I. Properties of a Quasi-Kerr Spacetime

According to the no-hair theorem, an astrophysical black hole is uniquely described by only two quantities, the mass and the spin. In this series of papers, we investigate a framework for testing the no-hair theorem with observations of black holes in the electromagnetic spectrum. We formulate our approach in terms of a parametric spacetime which contains a quadrupole moment that is independent of both mass and spin. If the no-hair theorem is correct, then any deviation of the black-hole quadrupole moment from its Kerr value has to be zero. We analyze in detail the properties of this quasi-Kerr spacetime that are critical to interpreting observations of black holes and demonstrate their dependence on the spin and quadrupole moment. In particular, we show that the location of the innermost stable circular orbit and the gravitational lensing experienced by photons are affected significantly at even modest deviations of the quadrupole moment from the value predicted by the no-hair theorem. We argue that observations of black-hole images, of relativistically broadened iron lines, as well as of thermal X-ray spectra from accreting black holes will lead in the near future to an experimental test of the no-hair theorem.Comment: Accepted for publication in Ap

Theory of Alike Selectivity in Biological Channels

We introduce a statistical mechanical model of the selectivity filter that accounts for the interaction between ions within the channel and derive Eisenman equation of the filter selectivity directly from the condition of barrier-less conduction

Black hole solutions in massive gravity

The static vacuum spherically symmetric solutions in massive gravity are obtained both analytically and numerically. The solutions depend on two parameters (integration constants): the mass M (or, equivalently, the Schwarzschild radius), and an additional parameter, the "scalar charge" S. At zero value of S and positive mass the standard Schwarzschild black hole solutions are recovered. Depending on the parameters of the model and the signs of M and S, the solutions may or may not have horizon. Those with the horizon describe modified black holes provided they are stable against small perturbations. In the analytically solvable example, the modified black hole solutions may have both attractive and repulsive (anti-gravitating) behavior at large distances. At intermediate distances the gravitational potential of a modified black hole may mimics the presence of dark matter. Modified black hole solutions are also found numerically in more realistic massive gravity models which are attractors of the cosmological evolution.Comment: Original version + erratu

Measuring the spin of the primary black hole in OJ287

The compact binary system in OJ287 is modelled to contain a spinning primary black hole with an accretion disk and a non-spinning secondary black hole. Using Post Newtonian (PN) accurate equations that include 2.5PN accurate non-spinning contributions, the leading order general relativistic and classical spin-orbit terms, the orbit of the binary black hole in OJ287 is calculated and as expected it depends on the spin of the primary black hole. Using the orbital solution, the specific times when the orbit of the secondary crosses the accretion disk of the primary are evaluated such that the record of observed outbursts from 1913 up to 2007 is reproduced. The timings of the outbursts are quite sensitive to the spin value. In order to reproduce all the known outbursts, including a newly discovered one in 1957, the Kerr parameter of the primary has to be $0.28 \pm 0.08$. The quadrupole-moment contributions to the equations of motion allow us to constrain the `no-hair' parameter to be $1.0\:\pm\:0.3$ where 0.3 is the one sigma error. This supports the `black hole no-hair theorem' within the achievable precision. It should be possible to test the present estimate in 2015 when the next outburst is due. The timing of the 2015 outburst is a strong function of the spin: if the spin is 0.36 of the maximal value allowed in general relativity, the outburst begins in early November 2015, while the same event starts in the end of January 2016 if the spin is 0.2Comment: 12 pages, 6 figure

Testing the No-Hair Theorem with Observations of Black Holes in the Electromagnetic Spectrum

According to the no-hair theorem, astrophysical black holes are uniquely described by their mass and spin. In this paper, we review a new framework for testing the no-hair hypothesis with observations in the electromagnetic spectrum. The approach is formulated in terms of a Kerr-like spacetime containing a quadrupole moment that is independent of both mass and spin. If the no-hair theorem is correct, then any deviation from the Kerr metric quadrupole has to be zero. We show how upcoming VLBI imaging observations of Sgr A* as well as spectroscopic observations of iron lines from accreting black holes with IXO may lead to the first astrophysical test of the no-hair theorem.Comment: 5 pages, 3 figures, to appear in Adv. Space Res., Proc. COSPAR 201

Formation of the black-hole binary M33 X-7 via mass-exchange in a tight massive system

M33 X-7 is among the most massive X-Ray binary stellar systems known, hosting a rapidly spinning 15.65 Msun black hole orbiting an underluminous 70 Msun Main Sequence companion in a slightly eccentric 3.45 day orbit. Although post-main-sequence mass transfer explains the masses and tight orbit, it leaves unexplained the observed X-Ray luminosity, star's underluminosity, black hole's spin, and eccentricity. A common envelope phase, or rotational mixing, could explain the orbit, but the former would lead to a merger and the latter to an overluminous companion. A merger would also ensue if mass transfer to the black hole were invoked for its spin-up. Here we report that, if M33 X-7 started as a primary of 85-99 Msun and a secondary of 28-32 Msun, in a 2.8-3.1 day orbit, its observed properties can be consistently explained. In this model, the Main Sequence primary transferred part of its envelope to the secondary and lost the rest in a wind; it ended its life as a ~16 Msun He star with a Fe-Ni core which collapsed to a black hole (with or without an accompanying supernova). The release of binding energy and, possibly, collapse asymmetries "kicked" the nascent black hole into an eccentric orbit. Wind accretion explains the X-Ray luminosity, while the black hole spin can be natal.Comment: Manuscript: 18 pages, 2 tables, 2 figure. Supplementary Information: 34 pages, 6 figures. Advance Online Publication (AOP) on http://www.nature.com/nature on October 20, 2010. To Appear in Nature on November 4, 201

Measuring Black Hole Spin in OJ287

We model the binary black hole system OJ287 as a spinning primary and a non-spinning secondary. It is assumed that the primary has an accretion disk which is impacted by the secondary at specific times. These times are identified as major outbursts in the light curve of OJ287. This identification allows an exact solution of the orbit, with very tight error limits. Nine outbursts from both the historical photographic records as well as from recent photometric measurements have been used as fixed points of the solution: 1913, 1947, 1957, 1973, 1983, 1984, 1995, 2005 and 2007 outbursts. This allows the determination of eight parameters of the orbit. Most interesting of these are the primary mass of $1.84\cdot 10^{10} M_\odot$, the secondary mass $1.46\cdot 10^{8} M_\odot$, major axis precession rate $39^\circ.1$ per period, and the eccentricity of the orbit 0.70. The dimensionless spin parameter is $0.28\:\pm\:0.01$ (1 sigma). The last parameter will be more tightly constrained in 2015 when the next outburst is due. The outburst should begin on 15 December 2015 if the spin value is in the middle of this range, on 3 January 2016 if the spin is 0.25, and on 26 November 2015 if the spin is 0.31. We have also tested the possibility that the quadrupole term in the Post Newtonian equations of motion does not exactly follow Einstein's theory: a parameter $q$ is introduced as one of the 8 parameters. Its value is within 30% (1 sigma) of the Einstein's value $q = 1$. This supports the $no-hair theorem$ of black holes within the achievable precision. We have also measured the loss of orbital energy due to gravitational waves. The loss rate is found to agree with Einstein's value with the accuracy of 2% (1 sigma).Comment: 12 pages, 4 figures, IAU26