Abstract:
According to general relativity the geometry of space depends on the distribution of matter or energy fields. The relation between the local geometrical parameters and the volume enclosed in given limits varies with the distribution of matter. Thus properties like particle number, mass or energy density, defined in the Euclidean tangent space, cannot be integrated to give conserved integral data like total number, mass or energy. To obtain integral conservation, a correction term must be added to account for the curvature of space. For energy this correction term is the equivalent of potential energy in Newtonian gravitation. With this correction the formation of black holes in the sense of singularities by gravitational collapse does no longer occur and the so called dark energy finds its natural explanation as potential energy of matter itself.

Abstract:
Gravitational-wave emission from stellar collapse has been studied for nearly four decades. Current state-of-the-art numerical investigations of collapse include those that use progenitors with more realistic angular momentum profiles, properly treat microphysics issues, account for general relativity, and examine non-axisymmetric effects in three dimensions. Such simulations predict that gravitational waves from various phenomena associated with gravitational collapse could be detectable with ground-based and space-based interferometric observatories. This review covers the entire range of stellar collapse sources of gravitational waves: from the accretion-induced collapse of a white dwarf through the collapse down to neutron stars or black holes of massive stars to the collapse of supermassive stars.

Abstract:
We present a number of parametric class of exact solutions of a radiating
star and the matching conditions required for the description of physically
meaningful fluid. A number of previously known class of solutions have been
rediscovered which describe well behaved nature of fluid distributions. The
interior matter fluid is shear-free spherically symmetric isotropic and
undergoing radial heat flow. The interior metric obeyed all the relevant
physical and thermodynamic conditions and matched with Vaidya exterior metric
over the boundary. Initially the interior solutions represent a static
configuration of perfect fluid which then gradually starts evolving into
radiating collapse. The apparent luminosity as observed by the distant observer
at rest at infinity and the effective surface temperature are zero in remote
past at the instant when collapse begins and at the stage when collapsing
configuration reaches the horizon of the black hole.

Abstract:
We here present a
relativistic model for a spherically symmetric anisotropic fluid to study the
various factors of physical and thermal phenomenon during the evolution of a
collapsing star dissipating energy in the form of radial heat flow. We also
proposed a table of some new parametric class of solutions which will be useful
for constructing the new compact star models. The constructed algorithm obeys
all the relevant requirements of a realistic model and matched with Vaidya
exterior metric over the boundary. At the initial stage the interior solutions
represent a static configuration of perfect fluid which then gradually starts
evolving into radiating collapse. The apparent luminosity as observed by the
distant observer at rest at infinity and the effective surface temperature are
zero in remote past at the instant when collapse begins and at the stage when
collapsing configuration reaches the horizon of the black hole.

Abstract:
In this work, the gravitational collapse of a spherically symmetric null shell with the flat interior and a charged Vaidya exterior spacetimes is studied. There is no gravitational impulsive wave present on the null hypersurface which is shear-free and contracting. It follows that there is a critical radius at which the shell bounces and starts expanding.

Abstract:
A point-mass concept has been elaborated from the equations of the gravitational field. One application of these deductions results in a black hole configuration of the Schwarzschild type, having no electric charge and no angular momentum. The critical mass of a gravitational collapse with respect to the nuclear binding energy is found to be in the range of 0.4 to 90 solar masses. A second application is connected with the speculation about an extended symmetric law of gravitation, based on the options of positive and negative mass for a particle at given positive energy. This would make masses of equal polarity attract each other, while masses of opposite polarity repel each other. Matter and antimatter are further proposed to be associated with the states of positive and negative mass. Under fully symmetric conditions this could provide a mechanism for the separation of antimatter from matter at an early stage of the universe.

Abstract:
Previous works have proposed gravitational collapse as the driving mechanism of extensional deformation of thickened continental crust. In this work we investigate the physical plausibility of this interpretation for the most important orogenic belts of the world by computing the spreading force induced by lateral variations of crustal thickness and the possible resisting forces. Two collapse mechanisms, one involving the upper crust only and the other the whole crust, have been considered. Particular attention has been devoted to constrain the uncertainty affecting such computations, mostly due to the large variability of the thermal and mechanical properties of rocks. The results obtained show that gravitational collapse is not a plausible mechanism in the four Mediterranean orogens here considered (Northern Apennines, Calabrian Arc, Hellenic Arc and Carpathians). For the other orogenic zones we have taken into account (Western U.S. Cordillera, Central Andes, Himalayas and Central Alps), the large uncertainty that affects the estimate of spreading and resisting forces does not allow to firmly assess the feasibility of gravitational collapse.

Abstract:
In this paper, the one-dimensional gravitational gas is evolved numerically using an eventdriven code. Two initial conditions are considered: (1) an initially uniform isolated system withno velocity dispersion and where the initial velocities are sine functions of the position, and (2)two “clusters” with initially constant phase-space densities in elliptical regions of phase space.

Abstract:
We introduce a novel model for the origin of the observable universe in which a flat universe with a positive vacuum energy is proceeded by a flat universe with a negative vacuum energy. A negative vacuum energy is consistent with a supersymmetric ground state similar to that predicted by superstring theories. A positive vacuum energy could emerge as a result of the gravitational collapse of the negative vacuum energy universe when the matter temperature reaches a characteristic value where supersymmetry is strongly broken. In principle this allows one to derive all the features of our expanding universe from a single parameter: the magnitude of the pre-big bang negative vacuum energy density. In this paper, a simple model for the big bang is introduced which allows us to use the present day entropy density, and temperature fluctuations of the CMB, together with the present day density of dark matter, to predict the magnitude of the negative vacuum energy. This model for the big bang also makes a dramatic prediction: dark matter consists of compact objects with masses on the order of 10^{4} solar masses. Remarkably this is consistent with numerical simulations for how the primordial fluctuations in the density of dark matter give rise to the observed inhomogeneous distribution of matter in our universe. Our model for the big bang also allows for the production of some compact objects with masses greater than 10^{4} solar masses which are consistent with observations of massive compact objects at the center of the earliest galaxies.

Abstract:
As first discovered by Choptuik, the black hole threshold in the space of initial data for general relativity shows both surprising structure and surprising simplicity. Universality, power-law scaling of the black hole mass, and scale echoing have given rise to the term “critical phenomena”. They are explained by the existence of exact solutions which are attractors within the black hole threshold, that is, attractors of codimension one in phase space, and which are typically self-similar. Critical phenomena give a natural route from smooth initial data to arbitrarily large curvatures visible from infinity, and are therefore likely to be relevant for cosmic censorship, quantum gravity, astrophysics, and our general understanding of the dynamics of general relativity.