Gravitational Collapse of a Spherical Star with Heat Flow as a Possible Energy Mechanism of Gamma-Ray Bursts

We investigate the gravitational collapse of a spherically symmetric, inhomogeneous star, which is described by a perfect fluid with heat flow and satisfies the equation of state p=ρ/3 at its center. In the process of the gravitational collapse, the energy of the whole star is emitted into space. And the remaining spacetime is a Minkowski one without a remnant at the end of the process. For a star with a solar mass and solar radius, the total energy emitted is at the order of 10⁵⁴ erg, and the time-scale of the process is about 8 s. These are in the typical values for a gamma-ray burst. Thus, we suggest the gravitational collapse of a spherical star with heat flow as a possible energy mechanism of gamma-ray bursts.     

Spherically symmetric free fall collapse

The general dynamical equations for spherical gravitational collapse are derived by introducing the eigenvalue of the conformal Weyl tensor in the 2-2 component of the Einstein tensor and assuming the material content of the models to be a perfect fluid. Since this eigenvalue is coupled always with the material energy density, it has been interpreted as theenergy density of the free gravitational field whose presence is related with anisotropy and inhomogeneity. As a particular case, the collapse of a spherically symmetric dust (zero pressure) with vanishing radial acceleration (free fall collapse) is discussed. It is shown that the model is inhomogeneous with non-vanishing shear of the congruence of world lines of the dust particles. The model contains gravitational radiation by Szekere’s criterion since both shear invariant and the spatial gradient of density are non-vanishing. This is in contrast to the Oppenheimer-Synder model for which both the above mentioned characteristics are absent. A particular solution which is anisotropic and inhomogeneous has been given to prove the emission of gravitational radiation by the freely falling dust and in this case the energy density of the free gravitational field contains a typeN term superposed on the coulombian field.     

Relativistic effects in the calibration of electrostatic electron analyzers. I. Toroidal analyzers

Relativistic correction terms up to the second order are derived for the kinetic energy of an electron travelling along the circular central trajectory of a toroidal analyzer. Furthermore, a practical energy calibration equation of the spherical sector plate analyzer is written for the variable-plate-voltage recording mode. Accurate measurements with a spherical analyzer performed using kinetic energies from 600 to 2100 eV are in good agreement with this theory showing our approximation (neglect of fringing fields, and source and detector geometry) is realistic enough for actual calibration purposes.     

On the genericity of spacetime singularities

We consider here the genericity aspects of spacetime singularities that occur in cosmology and in gravitational collapse. The singularity theorems (that predict the occurrence of singularities in general relativity) allow the singularities of gravitational collapse to be either visible to external observers or covered by an event horizon of gravity. It is shown that the visible singularities that develop as final states of spherical collapse are generic. Some consequences of this fact are discussed.      

Nonsymmetric dynamical thin-shell wormhole in Robinson–Trautman class

The thin-shell wormhole created using the Darmois–Israel formalism applied to Robinson–Trautman family of spacetimes is presented. The stress energy tensor created on the throat is interpreted in terms of two dust streams and it is shown that asymptotically this wormhole settles to the Schwarzschild wormhole with a throat located at the position of the horizon. This behavior shows a nonlinear stability (within the Robinson–Trautman class) of this spherically symmetric wormhole. The gravitational radiation emitted by the Robinson–Trautman wormhole during the transition to spherical symmetry is indistinguishable from that of the corresponding black hole Robinson–Trautman spacetime. Subsequently, we show that the higher-dimensional generalization of Robinson–Trautman geometry offers a possibility of constructing wormholes without the need to violate the energy conditions for matter induced on the throat.     

Spherical Gravitational Collapse in f(R) Gravity with Linear Equation of State

In a paper[Gen. Relativ. Gravit. 48 (2016) 57] Chakrabarti and Banerjee investigated perfect fluid collapse in f(R) gravity model and claimed that such a collapse is possible. In this paper we show that without the assumption of dark energy it is not possible that perfect fluid spherical gravitational collapse will occur. We have solved the field equations by assuming linear equation of state (p=ωμ) in metric f(R) gravity with ω=-1. It is shown that Chakrabarti and Banerjee reached to false conclusion as they derived wrong field equations. We have also discussed formation of apparent horizon and singularity.     

Role of Modified Chaplygin Gas as an Unified Dark Matter-Dark Energy Model in Collapsing Spherically Symmetric Dust Cloud

In this work gravitational collapse of a spherical dust cloud in the background of unified dark matter-dark energy model in the form of modified Chaplygin gas is studied. It is found that invisible matter (dark matter-dark energy) alone in the form of modified Chaplygin gas forms black hole. Also when both components of the fluid are present then the collapse favours the formation of black hole in cases the invisible matter dominates over ordinary dust. The conclusion is totally opposite to the usually known results.     

Quantum Non-Gravity and Stellar Collapse

Observational indications combined with analyses of analogue and emergent gravity in condensed matter systems support the possibility that there might be two distinct energy scales related to quantum gravity: the scale that sets the onset of quantum gravitational effects E_BE_{\rm B} (related to the Planck scale) and the much higher scale E_LE_{\rm L} signalling the breaking of Lorentz symmetry. We suggest a natural interpretation for these two scales: E_LE_{\rm L} is the energy scale below which a special relativistic spacetime emerges, E_BE_{\rm B} is the scale below which this spacetime geometry becomes curved. This implies that the first ‘quantum’ gravitational effect around E_BE_{\rm B} could simply be that gravity is progressively switched off, leaving an effective Minkowski quantum field theory up to much higher energies of the order of E_LE_{\rm L}. This scenario may have important consequences for gravitational collapse, inasmuch as it opens up new possibilities for the final state of stellar collapse other than an evaporating black hole.     

Charged shells in general relativity and their gravitational collapse

The boundary conditions for the gravitational and electromagnetic fields on charged shells are formulated. The shells are characterized in geometrical terms and the boundary conditions are manifestly covariant. The formalism is applied to the study of the gravitational collapse of homogeneous charged spherical shells. The law of conservation of energy, obtained by integrating the equations of motion of the shell and interpreted in full analogy with the special theory of relativity, is the starting point in analyzing the equilibrium states and the motion of the shells. It is concluded that no charge, however high it may be, can stop the gravitational collapse of the shell below the upper Nordström radius.     

Negative space charge and electric field intensity in polymeric insulators at low temperatures

The effect of negative space charge accumulation due to injection of electrons from cathode microprotrusions on the steady-state and transient electric field distributions in polymer dielectrics is discussed. An isolated microprotrusion is modeled by a spherical capacitor in which an electrode of smaller radius is the cathode. The calculations include the fact that the distribution of negative space charge depends on the rate of capture and liberation of electrons by traps, while the activation energy of this process depends on the electric field intensity. An exponential energy distribution is proposed for the traps. It is shown that significant electrical overvoltages can only appear near the cathode microtips immediately after switching on the voltage. In the course of 10⁻⁶–10⁻⁵ s, the coefficient of electrical overvoltage drops to a few units and approaches its steady-state value. The region of significant electrical overvoltage is localized, and is the same order as the dimensions of the microtip. Fiz. Tverd. Tela (St. Petersburg) 40, 1167–1172 (June 1998)     

被吸入电容器的金属片振动过程的功能关系

电中性的金属片被电容器所带电荷吸入其中而发生振动.这里讨论的问题:有或无阻尼时金属片的振动规律;电场力使金属片加速或减速运动过程中的功能转换;金属片振动过程中保持电容器的电量或电压不变,储能的变化;金属片的每一振动周期电源供给电容器的能量;电容器的电压、电量等参数的周期性变化.     

Self–similar and charged spheres in the free–streaming approximation

We evolve nonadiabatic charged spherical distributions of matter. Dissipation is described by the free–streaming approximation. We match a self–similar interior solution with the Reissner–Nordstr?m–Vaidya exterior solution. The transport mechanism is decisive to the fate of the gravitational collapse. Almost a half of the total initial mass is radiated away. The transport mechanism determines the way in which the electric charge is redistributed.     

Effects of electric field and hydrostatic pressure on donor binding energies in a spherical quantum dot

The binding energies of a hydrogenic donor in a GaAs spherical quantum dot in the Ga_1−xAl_xAs matrix are presented assuming parabolic confinement. Effects of hydrostatic pressure and electric field are discussed on the results obtained using a variational method. Effects of the spatial variation of the dielectric screening and the effective mass mismatch are also investigated. Our results show that (i) the ionization energy decreases with dot size, with the screening function giving uniformly larger values for dots which are less than about 25 nm, (ii) the hydrostatic pressure increases the donor ionization energy such that the variation is larger for a smaller dot, and (iii) the ionization energy decreases in an electric field. All the calculations have been carried out with finite barriers and good agreement is obtained with the results available in the literature in limiting cases.     

The structure of the integral of motion for a charged body in the relativistic theory of gravitation

The energy-momentum tensor in the relativistic theory of gravitation (RTG) is calculated for the Reissner-Nordström metric. The external gravitational energy of a collapsing body is found. Based on an analysis of its behavior near a gravitational radius, it is concluded that gravitational collapse is impossible.     

Neutronization and Protonization of Nuclei: Two Possible Ways of the Evolution of Astrophysical Objects and the Laboratory Electron-Nucleus Collapse

We consider the peculiarities of the fundamental nuclear transformations running both in the shell of a heavy star compressed by the strong gravitational field and during the laboratory electron-nucleus collapse where the compression occurs at the expense of the electron-nucleus interaction in a volume occupied by a degenerate electron gas, define their analogs, and analyze the differences. It is shown that the account of relativistic and nonlinear corrections to the Coulomb electron-nucleus interaction gives the possibility to realize two alternative ways for the evolution of the star matter which depend on both the rate of compression upon the gravitational collapse and the initial isotope composition of a star on the stage preceding the collapse. Upon the relatively slow compression of a heavy star in the process of gravitational collapse after the attainment of the threshold electron density, there occur the stage-by-stage neutronization of nuclei and the formation of a neutron star with a great concentration of neutrons and a low concentration of protons and electrons. This process is characterized by the presence of a bounded interval of the density of a relativistic degenerate gas of electrons (“the neutronization corridor”), in the scope of which the neutronization runs with a decrease in the Fermi energy and the release of energy in the form of fast neutrinos. At a higher electron density, the process of protonization becomes energy-gained. In this case, an increase in both the charge of nuclei and the concentration of degenerate electrons causes the continuous increase in the binding energy of electrons and nuclei which turns out to be more significant than the increase in the Fermi energy of electrons. The transition of nuclei through “the neutronization corridor” into “the protonization zone”, which ranges up to the nuclear density of a substance, is possible only in the case of a very fast compression of a heavy star. Such a process leads to the possibility of the formation of proton stars with a very small residual concentration of neutrons and a great (nuclear) concentration of protons and electrons. It is shown that analogous effects can be realized during the laboratory electron-nucleus collapse. Due to a microscopic size of the collapse zone, a great velocity of its formation, and a relatively low rate of neutronization, the passage of the electron-nucleus substance through “the neutronization corridor” weakly affects its state. In this case, the main mechanism of transformations is the process of protonization with a simultaneous increase in the concentration of degenerate electrons.     

Model of internal gravitational collapse

The concept of internal gravitational collapse is introduced, and the metrics associated with an initially collapsing sphere and the collapse of a spherical layer are found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 47–50, August, 1974.     

Spherical and non-spherical bubbles in cosmological phase transitions

The cosmological remnants of a first-order phase transition generally depend on the perturbations that the walls of expanding bubbles originate in the plasma. Several of the formation mechanisms occur when bubbles collide and lose their spherical symmetry. However, spherical bubbles are often considered in the literature, in particular for the calculation of gravitational waves. We study the steady state motion of bubble walls for different bubble symmetries. Using the bag equation of state, we discuss the propagation of phase transition fronts as detonations and subsonic or supersonic deflagrations. We consider the cases of spherical, cylindrical and planar walls, and compare the energy transferred to bulk motions of the relativistic fluid. We find that the different wall geometries give similar perturbations of the plasma. For the case of planar walls, we obtain analytical expressions for the kinetic energy in the bulk motions. As an application, we discuss the generation of gravitational waves.     

Non-static spherically symmetric clusters of particles in general relativity: I

In an ingenious way rotation (but no angular momentum) has been introduced in the case of spherical symmetry by Einstein, who has considered a stationary cluster of particles moving freely under the influence of the gravitational field produced by all of them together. The aim of the present work is to extend his idea to the non-static case, and it seems that under some circumstances instead of an indefinite gravitational collapse there is a minimum of the volume and a bouncing back.     

Thomas-Fermi theory for atomic nuclei revisited

The recently developed semiclassical variational Wigner-Kirkwood (VWK) approach is applied to finite nuclei using external potentials and self-consistent mean fields derived from Skyrme interactions and from relativistic mean field theory. VWK consists of the Thomas-Fermi part plus a pure, perturbative ?² correction. In external potentials, VWK passes through the average of the quantal values of the accumulated level density and total energy as a function of the Fermi energy. However, there is a problem of overbinding when the energy per particle is displayed as a function of the particle number. The situation is analyzed comparing spherical and deformed harmonic oscillator potentials. In the self-consistent case, we show for Skyrme forces that VWK binding energies are very close to those obtained from extended Thomas-Fermi functionals of ?⁴ order, pointing to the rapid convergence of the VWK theory. This satisfying result, however, does not cure the overbinding problem, i.e., the semiclassical energies show more binding than they should. This feature is more pronounced in the case of Skyrme forces than with the relativistic mean field approach. However, even in the latter case the shell correction energy for e.g., ²⁰⁸Pb turns out to be only ∼−6 MeV what is about a factor two or three off the generally accepted value. As an ad hoc remedy, increasing the kinetic energy by 2.5%, leads to shell correction energies well acceptable throughout the periodic table. The general importance of the present studies for other finite Fermi systems, self-bound or in external potentials, is pointed out.