Gravitational collapse of a dust ball — The external observer's point of view

The problem of collapse of a dust ball has been studied in detail from the point of view of an external observer (O). It is seen that although there is no material pressure from the point of view of the comoving observer, there is a non-vanishing material pressure in the ball from the point of view of O. In the early stages of collapse (w.r.t. O), this pressure is positive everywhere inside the ball, while during the later stages, if one goes outwards from the centre towards the surface of the ball, this pressure is negative up to a certain value of the radial coordinate, and then changes its sign thereafter. On the basis of this pressure, one can understand the physics of the whole scenario of collapse w.r.t. O; in particular, the important feature is that in the ultimate stages an event horizon is formed asymptotically and there is no collapse to a point (as takes place from the point of view of the comoving observer).     

Extreme relativistic model for neutron stars and pulsars

Exact solutions have been obtained for a massive fluid sphere under the extreme causality condition (dP/dρ)=1. Radial pulsational stability of these structures has been discussed. It is found that for pulsationally stable configurations the surface to central density ratio is greater than 0.30, the maximum values for surface and central redshifts are 0.85 and 3.40 respectively in the extreme case, and the maximum mass and size are respectively 4.8M _⊙ and 20.1 km. It has also been shown that these structures are gravitationally bound, with a maximum binding energy per unit rest mass equal to 0.25 for a surface to central density ratio ?0.40. Slow rotation of these configurations has also been considered, and the relative drag and moment of inertia have been calculated. These results have been applied to the Crab pulsar and the mass of the pulsar has also been calculated based upon this model.     

Core-envelope models for massive fluid spheres

The solution of equation of state corresponding to equality =₃ gives non-terminating solutions for isothermal neutron star cores. Hence, for this equality, core-envelope models have been developed by taking another equation of state, corresponding to the condition ₃, in the envelope. Various static, pulsational, and rotational parameters pertaining to neutron star models are calculated. These models are gravitationally bound and stable for radial perturbations and slow rotations.     

Motion of test particles in parabolic density distributions

A detailed study of the motion of test-particles [either having a nonzero rest-mass or zero rest-mass] has been carried out for Tolman's type VII solution with vanishing surface density, which is one of the few physically relevant exact solutions of Einstein's field equations for static and spherically symmetric mass distributions.The trapping angles, 0, at which the test-particles escape these configurations are calculated and the trajectories of test-particles are studied in detail. The types of trajectories found for this spacetime geometry are: (1) arc-like trajectories, (2) spiral-like trajectories ending into a circle of constant radius, (3) trajectories with a cusp at the minimum distance, (4) double-bounded trajectories, and (5) double-bounded trajectories with a cusp at the minimum distance. The test-particles following the trajectories of type (1) and type (3) escape the configuration while others are trapped within the structure. Besides the advancement of periastron of the orbits the retrogradation of periastrons are also observed.The stability of the structures is considered by using the variational method (Chandrasekhar, 1964a,b), and its is seen that the structures remain stable at least for a central redshift,z0, as large as 5.09.These studies may distinguish relativistic cluster from a Newtonian one and may find application to the local models of quasi-stellar objects (QSOs).     

Massive configurations with constant densities

Two new classes of solutions with constant observed proper and rest mass densities are described. Unlike the well-known solution of constant coordinate mass density, these solutions pertain to realistic physical situations. For these solutions, the various relevant parameters, viz. the redshifts (dP/d)₀ and binding coefficients have been calculated.     

Evaluating the effects of catch-and-release angling on Cape stumpnose Rhabdosargus holubi in a South African estuary

Fisheries managers are increasingly promoting catch-and-release (C&R) to manage recreationally angled fish stocks. Despite this, there is a scarcity of information on the effects of C&R on estuarine-dependent species. Cape stumpnose Rhabdosargus holubi dominates the recreational fisheries catch and provides an important source of food for subsistence fishers in some temperate South African estuaries. The health and survival of R. holubi exposed to a C&R event was investigated by examining their physiological stress response (blood glucose and lactate), reflex impairment (reflex action mortality predictors [RAMP]) and short-term (12-hour) survival. Fish were captured and exposed to one of three air-exposure treatments: 0 s, 30 s or 90 s. Stress and health were measured either immediately (immediate) or one hour after (delayed) the C&R event. There was no significant difference in blood glucose between air-exposure treatments, but there was a significant difference between the mean immediate and delayed glucose levels within each treatment (F_(2,143) = 81.8, p < 0.01). In contrast, blood lactate level was significantly higher in the 90-s treatment (p < 0.05). Immediate blood lactate levels were significantly lower than the delayed samples for each treatment (F = 4.29, p = 0.02; n = 169). Although all fish exhibited at least one reflex impairment, the RAMP score was significantly higher in the 90-s air-exposure treatment (H_(2,86) = 9.73, p = 0.007). Also, RAMP scores were significantly lower in the delayed samples (p < 0.01). Although short-term mortality was relatively low (2.3%) for this species, it was highest in the 90-s treatment (7%). These results suggest that physiological stress is higher when R. holubi are exposed to longer periods of air exposure and that the physiological stress of fish subject to a C&R event is best measured after a delay.     

Stellar structures with constant local adiabatic index under extreme relativistic conditions

Stellar structures with a constant local adiabatic index Γ have been discussed under the extreme relativistic condition (dP/dρ=1, at the center of the configuration). The equation of state,Pαρ^Γ, where ρ _r is the rest-mass density leads to the relations, (i)ρ=AP ^1/Γ?P/(Γ?1) between energy density and pressure, and (ii)e=NP between internal energy density and pressure, where the constantN may be called local polytropic index. The local adiabatic index, Γ, is found to be related to the adiabatic index, γ, through a simple relation, Γ=γ(1+P/ρ). The maximum value of surface redshift comes out to be 0.614 when σ=(P/ρ)₀=0.6. The structure are bound for σ≤0.83 and the maximum value of the binding coefficient is 0.181 at σ=0.4. For bound structures the central redshift z₀≤8.24. The maximum mass of neutron star based upon such a model comes out to be 2.39M _⊙ (for σ=0.4) and the maximum size comes out to be 13.7 km (for σ=0.2).     

A two-density neutron star model with continuity of density

Tolman's V solution has found wide application to the redshift problems in astrophysics but it has a drawback that there is singularity at the centre. We have developed a two-density model with a parabolic density distribution in the core ande r ²ⁿ in the envelope. The most distinctive feature of the model is that there is a continuity of all four variables (E, P, , and ) at the boundary. In other analytic core-envelope models the continuity of only three varaibles is possible. This two-density structure has been used to model neutron stars and their mass, size, and red shifts have been obtained.     

Static massive configurations with constant local adiabatic exponents

In this work an exhaustive study of static massive configurations with a constant local adiabatic exponent (₁) has been made under various physical conditions at the centre. The static parameters of these structures have been calculated at the extreme causality condition. These structures have been used to model neutron stars and the various neutron star parameters have been calculated. The radial pulsation and rotation of these configurations have also been discussed.     

Internal temperature of isothermal neutron star core matter

Two new equations of state obtained for matter constituting isothermal neutron star core by using isentropic nature of matter for the equalities =₂ and =₃ (where 's are usual adiabatic exponents) have been utilised to discuss the internal temperature of core. The temperature of matter has been obtained asT=T _a(P+E)/. Variation ofT/T _a(t) with energy density has been discussed for these new equations of state and some standard equations of state for nuclear matter.