Decoupled, separable wave equations describing neutrino, electromagnetic and gravitational perturbations have been derived (Teukolsky, 1972, 1973). A number of applications have been made (Press and Teukolsky, 1973; Starobinsky and Churilov, 1973).

As a stopgap measure until a rigorous analytic determination is made, Teukolsky and I have tested the dynamical stability of the Kerr metric under small perturbations numerically (Press and Teukolsky, 1973). We find that it is stable for all a ≤ M. We have also computed the magnitude of electromagnetic and gravitational-wave amplification in superradiant scattering, and Bardeen has independently obtained identical results (Teukolsky, 1973; Teukolsky et al., 1974). The amplification ranges up to ~2% for electromagnetism (l=m=1) and up to 140% for gravitation (l=m=2); these values are also consistent with Starobinsky's (1973) results for the value of critical frequencies.

The effect of amplification of electromagnetic and gravitational waves reflected from a rotating black hole (‘superradiance scattering’) is investigated. This effect was proposed by Zel'dovich (1971). It leads, as well as the Penrose process, to the energy extraction from a Kerr black hole at the expense of its rotational energy and momentum decrease. The coefficient of wave reflection R>1 if ω<nω, where ω is the wave frequency, n - its angular momentum and ω is the black hole angular velocity. The value of this effect is not small in the case of gravitational waves, for example, if l=n = 2, ω →nω and a = M, then R≈2.38.

There also exists a quantum version of the effect, namely, the one of spontaneous pair creation in the Kerr metric, but this quantum effect is exceedingly small in real astrophysical conditions, because its characteristic time is of the order G2M3/hc4, where M is the black hole mass.

Fourier and Laplace transforms are used to study rigorously the properties of a test scalar field PS in the exterior of a Schwarzschild black hole of the mass m. In the Fourier analysis we examine the properties of the solutions of the radial wave equation and the relations of the exterior and interior solutions of the following four cases: (i) ω ≠ 0, m≠0, (ii) ω=0, m≠0, (iii) ω≠0, m=0, (iv) ω=0, m=0.

In the Laplace analysis we show rigorously the following theorem: If ψ(t, r, τ, ϕ) is the field of a point test particle falling into the black hole, and lim Ψ exists, then lim Ψ = 0. The proof of this theorem is based on the facts that (a)t+2m ln (r − 2m) is finite for the particle even on the horizon, and (b) the behavior of Ψ as t → + ∞ is related to its Laplace transform near the origin of the complex plane.

Using the technique of Debye potentials, the regular (nonstatic) EM fields are found to behave at r = M either as purely ingoing or as purely outgoing waves. After separation the radial equation is treated in the short wavelength approximation.

Mechanisms promoting mass transfer include (i) envelope instability or (ii) nuclear evolution of the red star and (iii) gravitational radiation of orbital angular momentum. Growing observational evidence against (i) is supported by recent theoretical work on the medium and long-term response of stellar radii to mass-loss (Eggleton, Faulkner and Webbink, in progress). Since (ii) is in most cases too slow a process, (iii) is left as the best surviving explanation.

Taub and I have used the ‘Average Lagrangian’ method (Whitham, 1971; Dougherty, 1970) for the case of gravitational waves (MacCallum and Taub, 1973; Taub, 1973). A difficulty arises in going beyond first-order effects as gauge waves and physical waves appear to interact (MacCallum, 1973). The source of this difficulty is not yet known, but doubt is cast on the usual conceptual framework.

Following Penrose's construction of space-time infinity by means of a conformal construction, in which null-infinity is a three-dimensional domain, whereas time- and space-infinities are points, Geroch has recently endowed space-infinity with a somewhat richer structure. An approach that might work with a large class of pseudo-Riemannian manifolds is to induce a topology on the set of all geodesics (whether complete or incomplete) by subjecting their Cauchy data to (small) displacements in space-time and Lorentz rotations, and to group the geodesics all of whose neighborhoods intersect into equivalence classes. The quotient space of geodesics over equivalence classes is to represent infinity. In the case of Minkowski, null-infinity has the usual structure, but I0, I+, and I- each become three-dimensional as well.

The knowledge of the geodetic interval between two points in a Riemannian space-time with the metric gab is essential for statements on the time delay in a gravitational field represented by gab and makes possible to derive explicit criteria for clear-cut wave propagation. The nonlinear differential equation for the geodetic interval is integrated via perturbation expansion in the second post-Minkowskian approximation.

It is shown that the universal magnetic field, or sufficiently extended intergalactic fields, of magnitude ≳ 10-9 G would have aligned the magnetic moments of all leptons at an early time. Unless an upper limit to temperature exists, the alignment of all nucleons would also have occurred at an earlier time when the temperature was mN/me~2000 times higher. Possible inferences of this early magnetization of the matter in the universe for observation are discussed. The one selected for particular analysis is the parameter expressing the inverse ‘hotness’ of the universe. The matter-anti-matter symmetric theory of η given by Omnes, amended by Steigman and Kundt is reviewed. The effect of the large scale magnetic alignment on the value of η resulting from the annihilation era is then discussed by means of a model in which matter and antimatter droplets or filaments are in quasi-equilibrium under magnetization and effective surface forces. The magnetized droplets affect the diffusion of neutrons, which is dominant in the annihilation era.

A new general covariant approach to the general relativistic equations of motion is presented. It is stressed that our present understanding of the development of binaries due to general relativistic effects and of the power emitted by these systems in the form of gravitational radiation is highly unsatisfactory.

A gravitational radiation reaction tensor is calculated for a point quadrupole source in the fast motion approximation. The calculation is in direct analogy with Dirac's original calculation of electromagnetic radiation reaction. In the gravitational case a tidal deviation reaction tensor results which is linear in the fifth derivatives of the source quadrupole moments.

The absorption and emission of gravitational radiation can be calculated in the long wavelength limit by use of the tidal tensor, defined as the gradient of the gravitational pseudoforce, thus where ηb is orthogonal to the 4-velocity ua, and normal coordinates are understood.

The exchange of energy and momentum between an extended body and the gravitational field is governed by appropriate integrals of the tidal tensor over space and time.

The tidal tensor is the trace Tabdb of the Bel-Robinson tensor Tabcd. In emty space this trace is zero and the tidal tensor vanishes; there is no local exchange of energy.

We consider the class of regular (in a certain precise sense) null vector fields, lμ which have the following properties; they are (1) tangent to geodesics, (2) diverging, (3) shear free, (4) twist (or curl) free. It is well known that the vacuum Einstein fields whose principle null vector field (pnvf) satisfies (1)–(4) are the Robinson-Trautman (1962) (RT) metrics and those which satisfy (1)–(3) are the algebraically special twisting metrics, (Kerr, 1963). To understand these metrics better we ask for those Maxwell fields (in flat space) whose pnvf also satisfy conditions (1)–(4) and (1)–(3). It can be shown that (1)–(4) imply (and are implied by) that the Maxwell field is a Lienard-Wiechart (LW) field. (This establishes the analogy between the RT metrics and the LW fields.) Conditions (1)–(3) imply that the Maxwell field is a complex LW field. (We mean by this that if the Maxwell equations are complexified (Newman, 1973) (in complex Minkowski space) then the real solution in question is induced from the complex solution which is associated with a charged particle moving along an arbitrary complex world line.) Finally it can be shown that the Einstein equations can be complexified and that the algebraically special twisting metrics can be interpreted as if they had a point source moving in the complex manifold and are thus analogous to the complex LW fields.

Various possible cases of spherically systems the matter of which is localized in a domain smaller than the corresponding gravitational radius is considered.

The metic of the Friedmann closed world or of a part of it with an external continuation is suggested as a model of these systems.

There can exist black holes which are described by semi-closed metrics (black holes of the second kind). The class of systems in question may be both in the state of collapse and in the state of anti-collapse (including the state of ‘white holes’).

There are some grounds to suppose that collapse of celestial bodies should stop in the domain h/mvc, where mv is the mass of the vector meson, and that the pair production effect due to collapse of a charged sphere should conserve the Laplace determinism of the process.

The role of the charges of sources of different fields (electromagnetic, meson vector, scalar long-range, scalar meson, various versions of neutrino fields) in the deformation of the external and internal metric of black and white holes is analysed.

In this consideration a number of problems arises (the absence of horizon in the case of any small charges of scalar fields, the presence of the generalized Gauss theorem for vector meson field etc.), which provide evidence that the assertion ‘Black hole has no hair’ needs further investigations. In particular, the inverse process of formation of hair (e.g. vector-meson, scalar fields) in the process of anti-collopose has not been studied yet.

For the limiting case of the Nordström-Reissner metric m = e (more correctly m → e) two essentially different possibilities of continuing to the internal metric are considered (the Papapetrou case and the case which we called ‘friedmon metric’ describing charged black holes of the second kind (friedmons)).

In the case of charged holes of the second kind (friedmons) the occurance of quantum effects (pair productions) can reduce the horizon surface and violate the Hawking theorem.

The notion of black holes may turn out to be essential in elementary particle theory: among the intermediate states in elementary particle theory there are states the characteristic feature of which is the localization of arbitrary large energies (masses) in a domain smaller than the gravitational radius.

Black holes are very small objects by astronomical standards, so in many circumstances they interact with their surroundings like a Newtonian mass point. However, if black holes are present in X-ray binary systems, the X-rays emitted in the inner part of the accretion disk probe the highly curved spacetime geometry near the horizon, particularly if the black hole is rapidly rotating. Some of the properties of circular orbits near the black hole are quite sensitive to the amount of angular momentum. The relativistic corrections remove a Newtonian degeneracy between several of the characteristic frequencies associated with perturbations of the circular orbits.

Hot spots in the inner part of the disk can produce dramatic fluctuations in intensity, since the frequency shifts of photons emitted by a given point on the disk are strongly time-dependent. The bending of the photon trajectories by the strong gravitational field can drastically affect the energy balance of the disk; much of the radiation emitted by the inner part of the disk is reabsorbed. The dragging of inertial frames by the angular momentum of the black hole can have striking consequences for the structure of the disk at quite large radii if the angular momentum of the accreting matter is not in the same direction as the angular momentum of the black hole.

Dynamic perturbations of black holes are now being intensively studied to see if there are any surprising physical effects associated with the rotation of the black hole. Unfortunately, though quite interesting methods of extracting energy from the black hole exist in principle most of them are unlikely to be realized to an important extent in the real astrophysical world.

The observational data concerning binary X-ray sources is reviewed, with emphasis placed on Her X-1, Cen X-3 and Cyg X-1. In particular, the evidence for the identification of Cyg X-1 as a black hole is discussed.

From U, B, V photometry of 104 stars in a field of radius ~ 30′ centered on the X-ray binary star Cyg X-1 (HDE 226868), we have studied the color excess E(B–V) as a function of distance. Spectral types were observed de novo for 42 of these stars. We conclude that HDE 226868 cannot be nearer than 1 kpc, and is probably at a distance of 2.5 kpc or more. The primary component is therefore a luminous OB star of mass ~30 M⊙, and the X-ray component has a minimum mass ~6 M⊙.

Explosions of massive stars (8 ≲ M/M⊙ ≲ 70) are examined as the source of galactic cosmic rays. Detailed nucleosynthetic and evolutionary calculations suggest that these massive stars produce the heavy elements (carbon and above) in their proper relative abundances. This is particularly significant because lower mass stars (in particular the 4–8 M⊙ range) are not able to produce the observed abundances of C and O relative to the iron peak. A small (~ 1.4 M⊙) dense remnant star (a neutron star) left after the explosion may provide a location for an electromagnetic acceleration mechanism. Those abundance ratios which can now be predicted (He, C, O, Ne, Mg) for the material to be accelerated by the pulsar give a reasonable match to the observed cosmic ray data. The conditions at the outer edge of the remnant and the inner edge of the ejected material may be appropriate for an r-process to occur; the high Z cosmic rays seem to show an enrichment of r-process material. It appears that these stars may be the astrophysical source for the galactic cosmic rays. The questions of rotation and black hole formation were discussed. It appears that the most straight-forward result of evolution of a close massive binary is a massive star and a neutron star in a low eccentricity orbit, in agreement with observation.

The interstellar plasma accreted by isolated black holes should be heated during the infall process and radiate in the magnetic fields connected with the infalling material. A portion of the radiation in the optical range is likely to have a luminosity of order 1027–1030 erg s-1. In SAO U.S.S.R. AS an experiment is being carried out to observe isolated black holes as faint optical stars without spectral lines. So far the results of the experiment are negative.