Three main areas of relativistic stellar dynamics are reviewed: (a) Relativistic clusters, (b) Systems containing a massive black hole, and (c) Perturbed expanding Universes. The emphasis is on the use of orbit perturbations.

The local black holes describe physical situations involving a black hole surrounded by a finite vacuum region and then by matter and fields. The stationary and axisymmetric local black holes belong into two classes, the spherical and the toroidal ones, depending on the topology of their horizon. For the static black holes their metric tensors are given explicitly in terms of Legendre polynomials. For the stationary local black holes the problem is formulated interms of the Ernst potential of the rotational Killing field and the appropriate asymptotic conditions on the horizon are determined.

It is proposed that the small difference between the observed and the theoretically predicted decrease of the orbital period of the Binary Pulsar PSR 1913+16 is not due to the insufficiency of the quadrupole formula and can be attributed to a mass-energy loss due to the contraction of the binary's members. Assuming that the pair's primary is a typical, noncontracting pulsar, is in favour of a slowly contracting, neutron-star companion, thus limiting the member's radii to at most 25 km and 28 km, respectively. The primary's computed total absolute luminosity is in excellent agreement with the observed upper limit of its X-ray and optical luminosities. Moreover, the companion's slow contraction rate implies that its present total absolute luminosity presents a maximum at wavelengths characteristic of X-rays. Finally, it suggests that if the energy-loss remains constant, the duration of the contraction phase will be of the order of 108 y and the final radius about 25 km.

To the gods alone belongs it never to be old or die. But all things else melt with all-powerful time….
Sophocles

With the advent of grand unified theories (GUTs) has come the concept (among others) that baryons (protons, etc.) can decay by changing into leptons (“Diamonds are not forever.”) and vice versa, baryonic matter can be created from the thermal blackbody radiation in the early universe (provided, of course, that the hot big-bang model is basically correct). Using this concept, models have been suggested to generate a universal baryon asymmetry, with the consequence that no important amount of antimatter would be left in the universe at the present time (see, e.g. Langacker 1981 and references therein). These models have been motivated by observational constraints on antimatter, at least in our little corner of the universe (Steigman 1976). However, some of these constraints have been shown to be overrestrlctive (Stecker 1978, Allen 1981) and an alternative model, also based on GUTs, has been suggested which maintains matter-antimatter (I.e., baryon) symmetry on a universal scale, but results in separate “fossil domains” of clusters of matter galaxies and clusters of antimatter galaxies.

The present universe has small vacuum energy density (cosmological constant) and small spatial curvature. Therefore, before symmetry breaking, it had to have huge positive vacuum energy density, significant curvature, and low entropy. Because the energy positivity condition was not then satisfied, there need not have been an initial singularity (Hot Big Bang). If the universe is spatially open or the initial entropy high enough, then before the elementary particle phase transition, it was indeed an inflecting universe with an initial singularity. But if the universe is spatially closed and of low initial entropy, it needed to be a curvature-dominated bouncing universe, with a minimum size and maximum temperature (Tepid Little Bang). The closure of the present universe will therefore determine whether or not there was an initial singularity.

If the universe is spatially closed, and the simplest cosmological models are valid approximations, then in ∼ 1011 years the universe will recollapse into an antibang. (A “bang” is explosive, whereas an “antibag” may be considered implosive.) In this note I shall add one or two details to the seminal work of Rees (1969).

At present cosmology experiences a qualitatively new state of its development. Up to now cosmological theory successfully extrapolated to the past the Universe we observe now. This extrapolation was reliable up to the temperatures T ∼1010K. The endeavors to advance nearer to the singularity imply that even cardinally new hypotheses in the elementary particle physics (e.g. Hagerdorn's hypothesis) brought about the relatively insignificant variations in cosmology—the Universe expansion rate obeyed the power law as before, the main features of the cosmological model (homogeneity, singularity, the existence of horizone, etc.) remained unchanged.

We propose to discuss here the possibility of the origin and existence of primordial black holes and their expected parameters in the scenarios of the early Universe in which vacuum phase transitions play a decisive role.

Grand Unified strings may provide us with the primordial density fluctuations needed for galaxy formation. The properties and the cosmological evolution of such strings are discussed. A Grand Unified Theory with strings is constructed.

Using already tested physics of matter-antimatter interaction, an attempt is made of a check of the bi-partition model of the Universe of Fliche, Souriau and Triay (1982b). No inconsistency is found.

The standard big bang model has always had a couple of fundamental problems: the universe's matter excess and the isotropy of the cosmic microwave background radiation. Recent developments in particle physics now point to answers to these problems and lead to new models for the causal structure of the early universe. One interesting possibility is the formation of multiple bubble universes. In such models there exist event horizons and the thermal background radiation can be produced by the Hawking mechanism.

The “standard” hot big bang model accounts for the expansion of the Universe, the existence of the microwave background radiation, and the mass fraction of the light elements up to 4He. It does not account for the high degree of isotropy and homogeneity of the Universe in the large, nor of the existence of structure (galaxies, clusters) on smaller scales. Other problems, such as the lepton to baryon ratio, the preponderance of matter over antimatter, and the “coincidences” of dimensionless ratios of several fundamental physical and cosmological “constants” also lie outside of the “standard” model at present.

In this paper, we discuss theoretical and observational aspects of an SEP violation. We present a two-times theory as a possible framework to handle an SEP violation and summarize the tests performed to check the compatibility of such violation with a host of data ranging from nucleosynthesis to geophysics. We also discuss the dynamical equations needed to analyze radar ranging data to reveal an SEP violation and in particular the method employed by Shapiro and Reasenberg.

A non-technical introduction is given to (a) the inflationary universe, (b) the production of baryon asymmetry by GUTs, (c) the possible role of massive neutrinos and (d) the possible role of the massive photinos and goldstinos of broken supersymmetric theories.