List of Figures

View Image Figure 1:
A parameter space for quantifying the strength of a gravitational field. The x-axis measures the potential ε ≡ GM ∕rc2 and the y-axis measures the spacetime curvature ξ ≡ GM ∕r3c2 of the gravitational field at a radius r away from a central object of mass M. These two parameters provide two different quantitative measures of the strength of the gravitational fields. The various curves, points, and legends are described in the text.
View Image Figure 2:
Tests of general relativity placed on an appropriate parameter space. The long-dashed line represents the event horizon of Schwarzschild black holes.
View Image Figure 3:
The scalar curvature of our universe, as a function of redshift. The curve corresponds to a flat universe with the best-fit values of the cosmological parameters obtained by the WMAP mission [156]. The arrows point to the curvature and redshift of the universe during various epochs.
View Image Figure 4:
The opening angles, as viewed by an observer on Earth, of the horizons of a number of supermassive black holes in distant galaxies with a secure dynamical mass measurement (sample of [169]). The opening angle of the black-hole horizon in the center of the Milky Way (Sgr A*) is also shown for comparison.
View Image Figure 5:
The major axis of the accretion flow around the black hole in the center of the Milky Way, as measured at different wavelengths, in units of the Schwarzschild radius (left axis) and in milliarcsec (right axis; adapted from [148]). Even with current technology, the innermost radii of the accretion flow can be readily observed.
View Image Figure 6:
The 2 – 20 keV quiescent luminosities of black-hole candidates (filled circles) and neutron stars (open circles) in units of the Eddington luminosity for different galactic binary systems, as a function of their orbital periods, which are thought to determine the mass transfer rate between the two stars. The systematically lower luminosities of the black-hole systems have been attributed to the presence of the event horizon [10691].
View Image Figure 7:
The spectra emerging from geometrically thin accretion disks around black holes with different spins, but with the same accretion luminosity [41].From left to right, the curves correspond to spins (a ∕M) of 0, 0.2, 0.4, 0.6, 0.78, 0.881, 0.936, 0.966, and 0.99. The spin values were chosen to give roughly equal variation in the position of the spectral peak for spins > 0.8. The other parameters that determine the model are the viscosity parameter, α = 0.01, the inclination of the observer, cosi = 0.5, the mass of the black hole, M = 10M ⊙, and the accretion luminosity, L = 0.1LEdd. The peak energies of the spectra increase with increasing spin, as a consequence of the fact that the ISCO radius decreases with spin.
View Image Figure 8:
Theoretical models of relativistically-broadened iron line profiles from accretion flows around black holes. The left panel shows the dependence of the line profile on the spin parameter of the black hole, whereas the right panel shows its dependence on the emissivity index (see text). All calculations were performed for an inclination angle of 40 ∘ [23].
View Image Figure 9:
The 0.5 – 10 keV spectrum of the supermassive black hole in the center of the galaxy MCG-6-15-30 as observed with XMM-EPIC. Panel (a) shows the ratio of the observed spectrum to a power-law model and reveals the complicated structure of the residuals. Panel (b) shows the ratio of the observed spectrum to a model of the warm absorber, which accounts for the low-energy residuals. Panel (c) shows the 2 – 9 keV spectrum of the source together with a model of the relativistically-broadened iron line [183].
View Image Figure 10:
The dependence of the twin QPO frequencies on the X-ray count rate observed by the PCA instrument onboard RXTE, for the neutron-star source 4U 1820–30 [188]. The flattening of the correlation at high frequencies has been discussed as a signature of the innermost stable circular orbit.
View Image Figure 11:
The dependence of the amplitude and quality factor of the lower kHz QPO on its frequency for the neutron-star source 4U 1636–56 [10]. The drop of the QPO amplitude and coherence at high frequencies have been discussed as signatures of the innermost stable circular orbit.
View Image Figure 12:
(Left Panel) The intersection of the two solid lines shows the black-hole mass and spin for the source GRO J1655–40 for which the observed 300 Hz and 450 Hz oscillations can be explained as the lowest-order c and g-modes, respectively. The intersection of the dotted lines makes the opposite identification of disk modes to the observed oscillatory frequencies (after [177]). (Right Panel) Each solid line traces pairs of black-hole mass and spin for which the observed frequencies correspond to different resonances between the Keplerian and periastron precession frequencies (after [1]). In both panels, the horizontal dashed lines show the uncertainty in the dynamically-measured mass of the black hole.
View Image Figure 13:
Mass-radius relations of neutron stars in general relativity (GR), scalar-tensor gravity (ST), and Rosen’s bimetric theory of gravity [43]. The shaded areas represent the range of mass-radius relations predicted in each case by neutron-star equations of state without unconfined quarks or condensates. All gravity theories shown in the figure are consistent with solar-system tests but introduce variations in the predicted sizes of neutron stars that are significantly larger than the uncertainty caused by the unknown equation of state.
View Image Figure 14:
The limiting rate for the evolution of the orbital periods (τ−P1 ≡ P˙∕P) of five known millisecond, accreting pulsars as a function of the Brans–Dicke parameter ω BD. The lower half of the plot corresponds to an orbital period that decreases with time (˙ P∕P < 0), whereas the upper half corresponds to an orbital period that increases with time (P˙∕P > 0). Only the area outside the two curves for each system is physically allowed [125].
View Image Figure 15:
Constraints on the two parameters of a second-order scalar-tensor theory placed by the timing properties of binary stellar systems that harbor neutron stars (SEP stands for tests of the strong equivalence principle). The constraints imposed by solar system tests, including the Cassini mission, are also shown for comparison [38]. In all cases, the allowed part of the parameter space is under the corresponding curve.
View Image Figure 16:
Contours of constant gravitational redshift measured at infinity for an atomic line originating at the surface of a neutron star in a scalar-tensor gravity theory, for different values of the parameter β0 that measures the relative contribution of the scalar field. The thick curve separates the scalarized stars from their general-relativistic counterparts. The measurements of a redshift of z = 0.35 from a burster [37] and the astrophysical constraint of a baryonic mass of at least 1.4M ⊙ (dashed lines) result in a bound on the parameter β of − β < 9 [43].
View Image Figure 17:
The maximum orbital frequency outside a neutron star of mass MADM for different scalar-tensor theories identified by the parameter β. The dashed line shows the maximum observed frequency of a quasi-periodic oscillation from an accreting neutron star [44].
View Image Figure 18:
The spectral (redshift) and timing capabilities required for an observatory to probe different strengths of gravitational fields. Phenomena that occur in the vicinities of neutron stars and stellar-mass black holes experience large redshift and occur over sub-millisecond timescales.
View Image Figure 19:
The parameter space that will be probed by an experiment based on gravitational wave detection with LIGO and LISA, for an assumed source at a distance of 1 Mpc.