Schwarzschild Field Research Articles

Schwarzschild field with maximal acceleration corrections

We consider a model in which accelerated particles experience line-elements with maximal acceleration corrections. When applied to the Schwarzschild metric, the effective field experienced by accelerated test particles contains corrections that vanish in the limit ℏ→0, but otherwise affect the behaviour of matter greatly. A new effect appears in the form of a spherical shell, external to the Schwarzschild sphere, impenetrable to classical particles.

The effect of Schwarzschild field on spin [formula omitted] particles compared to the effect of a uniformly accelerating frame

The Dirac Hamiltonian is calculated in the Schwarzschild space and compared to the analogous one in a uniformly accelerating Minkowski frame yielding a test of the equivalence principle. Comparing these Hamiltonians, we see that the flat-space energy-mass terms and their redshifted forms are the same in the two cases, but the coefficient of the spin-orbit coupling term is different and an additional term appears in the gravitational case.

Doublevaluedness in Cosmology

In a Schwarzschild field, the use of an isotropic radial coordinate r produces a doublevalued description of space in that at a given time two values of r correspond to the same spatial point. We show that a similar doublevaluedness is present in a bound or unbound Friedmann-Robertson-Walker universe when it is described with an isotropic radial coordinate. This has important implications in cosmology when isotropic coordinates are used for describing distant galaxies in bound and unbound universe models.

Behavior of a charged particle in a schwarzschild field

The influence of the De Witt self-action force on the motion of and electromagnetic emission from a charged particle in a Schwarzschild field is considered. It is shown that a charged particle in a Schwarzschild field is equivalent to a neutral particle of the same mass in a certain Reissner-Nordstrom field. A relationship is found between the power of the electromagnetic emission from an accelerated charge and the power of the thermal emission generated in a reference frame with the same acceleration at the event horizon. The quantum-mechanical problem of the motion of and emission from a charge in the field of a minihole is considered. Wave functions, the energy spectrum, and the widths of quasi-stationary levels are found with allowance for the De Witt self-action force. It is shown that the latter is important for large charges, when the solution becomes oscillatory.

Schwarzschild black hole with global monopole charge

We derive the metric for a Schwarzschild black hole with global monopole charge by relaxing asymptotic flatness of the Schwarzschild field. We then study the effect of global monopole charge on particle orbits and the Hawking radiation. It turns out that existence, boundedness and stability of circular orbits scale up by $(1-8 \pi\eta^2)^{-1}$, and the perihelion shift and the light bending by $(1-8 \pi\eta^2)^{-3/2}$, while the Hawking temperature scales down by $(1 - 8 \pi \eta^2)^2$ the Schwarzschild values. Here $\eta$ is the global charge.

Induced Quantum Fluctuations in the Spherically Symmetric Space–Time

In the Schwarzschild field due to a mass moving with velocity v → c0, where c0 is the speed of light in vacuum, the source-induced quantum fluctuation in the light cone exhibits consistency with the Aichelburg–Sexl solution while that in the metric dynamical variable does not. At the horizon, none of the fluctuations is proportional to anything finite. However, in the nonrelativistic limit (v → 0), known expressions follow.

On the orbital motion description with a proper reference frame in a complete Schwarzschild field

It is a fact that, none of the diverse coordinate systems unified in the Post-Newtonian formalism used to describe the exterior Schwarzschild field can be regarded as being materialized by a reference frame. Only the polar Gaussian coordinates (ρ, ϑ, ϕ, t), or their naturally associated Fermi coordinates, can be shown to have this property (Synge, 1960).

Privileged coordinate system in a Schwarzschild field

A basis is given for the idea that a Gaussian coordinate system is the most rational outside a singular sphere in a Schwarzschild field. It can also be extended into the matter below the singular sphere, describing a stationary distribution of matter with a density ρ=A/r2 at r R, where R≤rg.

On the optical–mechanical analogy in general relativity

We demonstrate that the Evans–Rosenquist formulation of the optical–mechanical analogy, so successful in the application to classical problems, also describes the motion of massless particles in the Schwarzschild field of general relativity. It is possible to obtain the well-known equations for light orbit and radar echo delay which account for two exclusive tests of Einstein’s field equations. Some remarks including suggestions for future work are also added.

Model of a gravitational wave in Schwarzschild space-time.

A model of a spherical impulsive gravitational wave propagating through the Schwarzschild field is constructed. The vacuum part of the space-time to the future of the history of the wave is calculated approximately as a Bondi-Sachs space-time, providing a model of the reaction of the Schwarzschild field to the passage of the wave through it and implying the existence of backscattered radiation due to the presence of the isolated matter distribution.

The spherically-symmetrical trajectories of spin particles in the Schwarzschild field

The motion of spin particles in the Schwarzschild field is examined in this paper. It is shown that Mathisson-Papapetrou equations under additional conditions\(\mathop L\limits_j {\text{ }}S^{\alpha \beta } {\text{ = }}0\), where\(\mathop L\limits_j\) is the Lie derivative of the Killing vector ξj, permit only radial motion, motion in the equatorial plane and in the equilibrium points. All these types of motion are considered more in detail.

McVittie's mass particle in an expanding universe and related solutions of Einstein's equations

Three alternative forms are presented for the Robertson-Walker line element of the k = -1 Riemannian curvature isotropic cosmological models, as well as two alternative forms for the k = 0 model and one form for the k = +1 model; these forms are directly derived by solving Einstein's field equations. It is then noted that McVittie's (1933) embedding of a Schwarzschild field in the Robertson-Walker spacetimes fits naturally into one each of the alternative line elements. Related solutions of Einstein's equations are derived with a perfect fluid source which fit naturally in the remaining two forms of the k = -1 universe and the one remaining form of the k = 0 universe. Three additional perfect fluid solutions of Einstein's equations that are in a different sense analogous to McVittie's original solutions are also presented. 12 refs.

Quantum radiation of a charged particle in a Schwarzschild field

AbstractWithin the framework of quantum mechanics in a curved space‐time the transitions between energy levels of a charged particle (elementary particle, atomic nucleus) being in a Schwarzschild field are considered. The DeWitt conservative self‐force acting on the charge is taken into account. Energy and intensity of the electric dipole radiation are calculated for charged particles in the field of miniholes with masses ranging from 1014 to 10−5 g.

Relativistic theory of direct interactions and gravitational two-body problem in the second post-Newtonian approximation

The three-dimensional Lagrangian of the formulation of relativistic theory of direct interactions is applied to the problem of two-body motion in the second post-Newtonian approximation. On the basis of the conditions of Poincare invariance, taking account of the requirement of consistency with scalar-tensor theory in the linear approximation with respect to the gravitational constant and with the trial-particle Lagrangian in a Schwarzschild field in the approximation of the single-body problem, the Lagrangian function of a system of two gravitating point particles is constructed. The effectiveness of using both methods of directinteraction theory is shown, permitting, in particular, transition to the Hamiltonian description of the given system.

Spin interference effects in the earth's field

The spin interference effects in the earth's field is investigated. It is shown that there exist three effects, which are induced by (a) the Schwarzschild field, (b) the earth's spin and (c) the frame rotation respectively, affecting the resulting spin polarization after interference.

Stability of noncircular and infinite motions of test bodies in general relativity

The stability of finite noncircular and infinite motions of nonspinning and spinning test bodies in the Schwarzschild field has been investigated. It is shown that these motions are unstable by Lyapunov relative to variables\(r,\dot r,\theta ,\dot \theta \). The conditions of the stability in a finite interval of time for these motions have been found. The time interval of the motion stability has been numerically estimated.

The Influence of Supplementary Conditions for Papapetrou Equations on the Lyapunov Stability of Motion

AbstractThe Lyapunov stability of circular motions of spinning test bodies in the Schwarzschild field has been considered. For Papapetrou equations the generalized supplementary conditions S0iu0 = kSijuj = k const, i, j = 1, 2, 3, have been chosen. Four of the first integrals of motion have been indicated. With the aid of Lyapunov functions the domains of stable motions have been found.

The plane trajectories of spin particles in the Schwarzschild field

Plane motions of spin particles in the Schwarzschild field are investigated. Cases of parallel transport of spin tensor (PTS) and of geodesic motion (GM) as well as of the motion under additional Pirani (PC) and Dixon (DC) conditions are considered. Using these assumptions analogues of the Binnet formula are obtained. In the case of PTS and PS the stability of circular orbits the way Liapunov interprets it is examined.

Analytical derivation of the embedding of the Schwarzschild solution in a flat space-time

The embedding of the Schwarzschild line element in a flat space-time of six dimensions is univocally worked out on the basis of i) the static nature of the Schwarzschild field, ii) the Minkowski structure of the flat space-time and iii) the requirement that the embedding itself be analytic on the whole interval 0<r<∞. We arrive then at Fronsdal's embedding, which is therefore the sole possible complete embedding of the Schwarzschild solution in the six-dimensional Minkowski space-time.

Evolution of electromagnetic waves of a point source in the Schwarzschild field

The problem of electromagnetic radiation of a source in the gravity field of a nearby black hole is considered. A complete class of exact axial-symmetric solutions of the eikonal equations is found. The components of the field tensor are obtained in the large frequency approximation. An expression is found for the strength of the observed radiation as a function of the distance between the black hole and the source, and of the angle between the directions black hole-observer and black hole-source. It is shown that the system consisting of a black hole and a normal star in rotation around the common center of gravity must look like an object of variable brightness.