When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star's mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected. The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.

On Continued Gravitational Contraction

In order to shed some light on the current discussion about f(R)-gravity theories we derive and discuss the bounds imposed by the energy conditions on a general f(R) functional form The null and strong energy conditions in this framework are derived from Raychaudhuri's equation along with the requirement that gravity is attractive, whereas the weak and dominant energy conditions are stated from a comparison with the energy conditions that can be obtained in a direct approach via an effective energy-momentum tensor for f(R) gravity As a concrete application of the energy conditions to locally homogeneous and isotropic f(R) cosmology, the recent estimated values of the deceleration and jerk parameters are used to examine the bounds from the weak energy condition on the parameters of two families of f(R)-gravity theories

Energy conditions in f(R) gravity

The treatment of first-order phase transitions for standard grand unified theories is shown to break down for models with radiatively induced spontaneous symmetry breaking. It is argued that proper analysis of these transitions which would take place in the early history of the universe can lead to an explanation of the cosmological homogeneity, flatness, and monopole puzzles.

Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking

We explore the recently introduced modified Gauss–Bonnet gravity (Sharif and Ikram in Eur Phys J C 76:640, 2016), $$f(\mathcal {G},T)$$
 pragmatic with $$\mathcal {G}$$
 , the Gauss–Bonnet term, and T, the trace of the energy-momentum tensor. Noether symmetry approach has been used to develop some cosmologically viable $$f(\mathcal {G},T)$$
 gravity models. The Noether equations of modified gravity are reported for flat FRW universe. Two specific models have been studied to determine the conserved quantities and exact solutions. In particular, the well known deSitter solution is reconstructed for some specific choice of $$f(\mathcal {G},T)$$
 gravity model.

/pdf/noether-symmetry-approach-in-f-mathcal-g-t-f-g-t-gravity-12r5okchqu.pdf

Noether symmetry approach in $$f(\mathcal {G},T)$$ f ( G , T ) gravity

The aim of this paper is to explore some physically viable aspects for the possible emergence of compact stars in f(G,T) theory of gravity with some particular models, where G and T are Gauss–Bonnet invariant and trace of stress–energy tensor, respectively. We present basic formalism of this modified theory in the presence of anisotropic source. We explore some realistic aspects using the energy conditions with physical parameters. Three distinct known star models namely, SAXJ1808.4−3658, Her X−1 and 4U1820−30, are used for this systematic investigation. The physical behavior of anisotropic stresses, energy density, energy conditions, measure of anisotropy and stability of compact stars are discussed through plots. We conclude that compactness at the core of a star model increases and energy conditions hold.

Role of f(G,T) gravity on the evolution of relativistic stars

The aim of this paper is to introduce a new modified gravity theory named $$f(\mathcal {G},T)$$
 gravity (
 $$\mathcal {G}$$
 and T are the Gauss–Bonnet invariant and trace of the energy-momentum tensor, respectively) and investigate energy conditions for two reconstructed models in the context of FRW universe. We formulate general field equations, divergence of energy-momentum tensor, equation of motion for test particles as well as corresponding energy conditions. The massive test particles follow non-geodesic lines of geometry due to the presence of an extra force. We express the energy conditions in terms of cosmological parameters like the deceleration, jerk, and snap parameters. The reconstruction technique is applied to this theory using de Sitter and power-law cosmological solutions. We analyze the energy bounds and obtain feasible constraints on the free parameters.

/pdf/energy-conditions-in-f-mathcal-g-t-gravity-1cyklvgihd.pdf

Energy conditions in f(\mathcal {G},T) gravity

The aim of this paper is to introduce a new modified gravity theory named as $f(\mathcal{G},T)$ gravity ($\mathcal{G}$ and $T$ are the Gauss-Bonnet invariant and trace of the energy-momentum tensor, respectively) and investigate energy conditions for two reconstructed models in the context of FRW universe. We formulate general field equations, divergence of energy-momentum tensor, equation of motion for test particles as well as corresponding energy conditions. The massive test particles follow non-geodesic lines of geometry due to the presence of extra force. We express energy conditions in terms of cosmological parameters like deceleration, jerk and snap parameters. The reconstruction technique is applied to this theory using de Sitter and power-law cosmological solutions. We analyze energy bounds and obtain feasible constraints on free parameters.

/pdf/energy-conditions-in-f-mathcal-g-t-gravity-4co6atwxhe.pdf

Energy Conditions in $f(\mathcal{G},T)$ Gravity

Stability analysis of some reconstructed cosmological models in f(G , T) gravity

The aim of this paper is to explore warm inflation in the background of f(G) theory of gravity using scalar fields for the FRW universe model. We construct the field equations under slow-roll approximations and evaluate the slow-roll parameters, scalar and tensor power spectra and their corresponding spectral indices using viable power-law model. These parameters are evaluated for a constant as well as variable dissipation factor during intermediate and logamediate inflationary epochs. We also find the number of e-folds and tensor- scalar ratio for each case. The graphical behavior of these parameters proves that the isotropic model in f(G) gravity is compatible with observational Planck data.

Warm inflation in f(G) theory of gravity

This paper explores the stability of the Einstein universe against linear homogeneous perturbations in the background of f(&#x1d4a2;,T) gravity. We construct static as well as perturbed field equations and investigate stability regions for the specific forms of generic function f(&#x1d4a2;,T) corresponding to conserved as well as nonconserved energy-momentum tensor. We use the equation-of-state parameter to parameterize the stability regions. The graphical analysis shows that the suitable choice of parameters lead to stable regions of the Einstein universe.

Ayesha Ikram

Papers

Energy conditions in f(\mathcal {G},T) gravity

Energy Conditions in $f(\mathcal{G},T)$ Gravity

Stability analysis of some reconstructed cosmological models in f(G , T) gravity

Warm inflation in f(G) theory of gravity

Stability analysis of Einstein universe in f(,T) gravity