M. E. Gertsenshtein

About the singularity criterion in general relativity

The metric in vacuum is found for the case of a spherical charged dust source. It is shown that a “dead zone” occurs in the vacuum, impenetrable to light or test particles. All singularities resulting from theorems about geodesic lines, are located in the “dead zone” and do not represent a physical problem for the theory. The infinite-density type singularities may be absent inside matter-filled zone.

Is it necessary to abandon the ψ function in quantum gravitation

Hawkings conclusion that a pure state of an elementary particle converts into a mixed state as a result of a coupling with real and virtual black holes and that it is necessary to abandon the description of elementary particles by means of aψ function in quantum gravitation is subjected to a critical analysis. An examination of a specific example — the motion of particles of nonzero mass and of photons in the field of a charged black hole — does not support Hawkings conclusion. Elliss estimates of a lower (energy) limit on the applicability of quantum mechanics has been improved by 40 orders of magnitude.

Isotropic spherical coordinates

The method of using regularization to analyze singularities is applied to the Schwarzschild metric in isotropic spherical coordinates (3). It is found that there arises a singularity at the gravitational radius which does not satisfy the conditions of physical realizability (Tϕϕ=Tθθ,T00=Tθθ=0). Consequently, this metric cannot be considered as corresponding to pure vacuum.

Invariant and contracted actions of a physical system in the general theory of relativity

A study was made of the difference between the invariant action SR and the contracted action SG for the global problem: an isolated physical system as a whole. The actions are considered as functions of the upper limit; in the center-of-mass system their difference is distinct from zero (10). In an example from Newtonian mechanics this is shown to be related to the fact that the invariant Lagrangian contains second derivatives. The formulas for the energy-momentum vector as an action gradient (16) and their quantum generalizations (17) are valid only for the contracted action.

Physical effects which distort measurement of the rest mass of the neutrino from beta spectra

Various physical effects which distort the result at the 1-eV accuracy level are discussed in connection with the experimental possibility of raising the sensitivity to the neutrino rest mass mv2 to a value of the order of (1 eV)2 in measurements of the beta spectra of tritium decay. There is no contradiction in an integrated spectrometer between the accuracy, the resolution, and the statistics, which there is in a differential spectrometer, and the mass sensitivity range is significantly greater. The statistical reliability of the measurements on section A of the Curie curve — Fig. 1 — is discussed, in which the problem reduces to the determination of the coefficients of the expansion (4). It is necessary in a monolayer source at an accuracy level of the order of 1–3 eV to introduce correctionfor the formation of an excited helium atom. The remaining effects are at the 1-eV level. The possibility of measuring the Curie curve in region C — near the “cutoff” — is demonstrated.

Strong gravitational fields and geometry in the large

The problem of strong gravitational fields (μ∼1) can be neither formulated invariantly nor solved in a local manner; it belongs to geometry in the large and requires the discussion of a complete atlas of maps. At μ∼1 a complicated topology of space-time is possible. Requirements for a solution with a complete atlas of maps and a physical example, a rigorous discussion of which has led to new results, are discussed.

Limiting possibilities for measurement of the rest mass of the neutrino from beta spectra

The possibilities of an integrated spectrometer with a retarding electrostatic barrier in a longitudinal magnetic field with application to the problem of measurement of the rest mass of the neutrino mv formbeta-spectra of tritium are investigated. It is shown that one can obtain a sensitivity δMv2 of the order of (1 eV)2 with an exposure of ∼0.5 yr.

Metric inside collapsing matter

The metric within the matter is found for an exact self-similar solution: for a dusty sphere homogeneous over its volume. “Maps with a complex time” exist and show where the matter goes in the contraction stage and where it comes from in the expansion stage. The appearance of such a map is evidence of a complicated topology and contradicts the existence of trapping surfaces — a primary premise of topological theorems regarding singularities. The possibility of a replacement of a contraction by an expansion without an infinite-density singularity is discussed.

Equivalence principle, the general theory of relativity, ang “black holes”

The equivalence principle is necessary for the validity of Newtonian mechanics, since only in this case can one consider an isolated system, neglecting the attraction of distant bodies. The possibility of verifying the equivalence principle by observations of the structure of galaxies and the large-scale structure of the universe is discussed. It is pointed out that the existence of horizons with “valve” properties -a one-way exchange of information—contradicts the equivalence principle.

Two types of scenarios for the evolution of the universe

Scenarios for the evolution of the universe can be grouped into two classes: those in which the universe originates from a singularity at t = 0 and those in which the universe continues through a singularity. It is shown that the scenarios of this second type correspond well to the observed data. The entropy difficulties can be eliminated in a scenario which involves the condensation of extremely low-density matter, with a conversion into an open model due to the energy evolved during condensation of the matter into galaxies.