Spherically symmetric anisotropic charged solution under complete geometric deformation approach

We present a new systematic approach to find the exact gravitationally decoupled anisotropic spherical solution in the presence of electric charge by using the complete geometric deformation (CGD) methodology. To do this, we apply the transformations over both gravitational potentials by introducing two unknown deformation functions. This new systematic approach allows us to obtain the exact solution of the field equations without imposing any particular ansatz for the deformation functions. Specifically, a well-known mimic approach and equation of state (EOS) have been applied together for solving the system of equations, which determine the radial and temporal deformation functions, respectively. The matching conditions at the boundary of the stellar objects with the exterior Reissner–Nordström metric are discussed in detail. In order to see the physical validity of the solution, we used well-behaved interior seed spacetime geometry and solved the system of equations using the above approaches. Next, we presented several physical properties of the solution through their graphical representations. The stability and dynamical equilibrium of the solution have been also discussed. Finally, we predicted the radii and mass-radius ratio for several compact objects for different decoupling parameters together with the impact of the decoupling parameters on the thermodynamical observables.

Charged compact star in f(R, T) gravity in Tolman–Kuchowicz spacetime

In this current study, our main focus is on modeling the specific charged compact star SAX J 1808.4-3658 (M = 0.88 $$M_{\odot }$$ M ⊙ , R = 8.9 km) within the framework of $$f(R,\,T)$$ f ( R , T ) modified gravity theory using the metric potentials proposed by Tolman–Kuchowicz (Tolman in Phys Rev 55:364, 1939; Kuchowicz in Acta Phys Pol 33:541, 1968) and the interior spacetime is matched to the exterior Reissner–Nordström line element at the surface of the star. Tolman–Kuchowicz metric potentials provide a singularity-free solution which satisfies the stability criteria. Here we have used the simplified phenomenological MIT bag model equation of state (EoS) to solve the Einstein–Maxwell field equations where the density profile ($$\rho $$ ρ ) is related to the radial pressure ($$p_{\mathrm{r}}$$ p r ) as $$p_{\mathrm{r}}(r) = (\rho - 4B_{\mathrm{g}})/3$$ p r ( r ) = ( ρ - 4 B g ) / 3 . Furthermore, to derive the values of the unknown constants $$a,\, b,\, B,\, C$$ a , b , B , C and the bag constant $$B_{\mathrm{g}}$$ B g , we match our interior spacetime to the exterior Reissner–Nordström line element at the surface of stellar system. In addition, to check the physical validity and stability of our suggested model we evaluate some important properties, such as effective energy density, effective pressures, radial and transverse sound velocities, relativistic adiabatic index, all energy conditions, compactness factor and surface redshift. It is depicted from our current study that all our derived results lie within the physically accepted regime which shows the viability of our present model in the context of $$f(R,\,T)$$ f ( R , T ) modified gravity.

Gravitational Collapse and Singularity Removal in Rastall Theory

In the present work, we study spherically symmetric gravitational collapse of a homogeneous fluid in the framework of Rastall gravity. Considering a nonlinear equation of state (EoS) for the fluid profiles, we search for a class of nonsingular collapse solutions and the possibility of singularity removal. We find that depending on the model parameters, the collapse scenario halts at a minimum value of the scale factor at which a bounce occurs. The collapse process then enters an expanding phase in the postbounce regime, and consequently the formation of a spacetime singularity is prevented. We also find that, in comparison to the singular case where the apparent horizon forms to cover the singularity, the formation of apparent horizon can be delayed allowing thus the bounce to be causally connected to the external universe. The nonsingular solutions we obtain satisfy the weak energy condition (WEC) which is crucial for physical validity of the model.

Folded Cymba Concha: Is It Large and Stable Enough for Caudal Septal Extension Graft in Asian Rhinoplasty?

Background Septal extension grafting (SEG) is used for nasal tip projection and positioning. Often, insufficient quadrangular cartilage is available for grafting in Asians and in most secondary cases, the septum is already harvested. We utilized the folded cymba concha as an alternative for caudal SEG (CSEG) by modifying a tongue-in-groove technique. Objectives To evaluate the physical validity of the cymba concha for CSEG and compare its outcomes with those of septal quadrangular cartilage. Methods The mean length and width of 311 harvested consecutive folded cymba conchae were measured from intraoperative photographs. Data from 220 patients with >12 months of follow-up were retrospectively reviewed for clinical outcomes. Clinical demography was determined based on the need for additional spreader grafts. For clinical reliability, anthropometric photographs of patients in whom folded cymba conchae were used were compared with those in whom quadrangular cartilage was used. Results Mean lengths and widths of the folded cymba conchae in men and women were 24.2 ± 3.9 and 22.4 ± 3.7 mm, and 7.8 ± 1.9 and 7.2 ± 1.9 mm, respectively. Using the folded cymba concha graft significantly increased nasal tip projection by 28.9% and columellar-labial angle by 9.7%, improving both aspects postoperatively. Anthropometric comparison revealed no significant differences between folded cymba conchae and septal cartilage in terms of nasal tip projection (p = 0.264) and postoperative columellar-labial angle (p = 0.182). Conclusions Folded cymba conchal cartilage can be a primary option for CSEG in Asian septorhinoplasty cases or for individuals with insufficient septal cartilage remnants.

Nonsingular solution with anisotropic fluid in mini bang cosmology

In this work, we study cosmological evolution in the mini creation event with anisotropic fluid under the Bianchi-I spacetime. After providing the basic mathematical formalism of the model, we find out the exact solutions in its particular form to the field equations. In order to get physical validity, we have presented elaborate discussions on the graphical results, especially nonsingular behaviour of the model. It is shown that the model under mini bang can successfully exhibit several interesting cosmological features which have specific signatures to tally with the observational evidences.

Shadow cast of noncommutative black holes in Rastall gravity

We study the shadow and energy emission rate of a spherically symmetric noncommutative black hole in Rastall gravity. Depending on the model parameters, the noncommutative black hole can reduce to the Schwarzschild black hole. Since the nonvanishing noncommutative parameter affects the formation of event horizon, the visibility of the resulting shadow depends on the noncommutative parameter in Rastall gravity. The obtained sectional shadows respect the unstable circular orbit condition, which is crucial for physical validity of the black hole image model.

Calculation of the compressibility factor of gas-saturated oils

The article deals with a hypothetical model of the molecular structure of degassed and gas-saturated oils developed on the basis of the J. I. Frankel’s hole theory of liquid. Based on this model, the author of the article obtained semiempirical dependences for calculating compressibility factors of degassed and gassaturated oils. The fact that the obtained dependences are based on the noted model gives the necessary physical validity to them and the specific physical content to the empirical parameters contained in them. As a result, semi-empirical dependences become theoretical. Corresponding calculations confirm that their scope broadens as the types of oils and conditions for their finding.

Equations for beam waist measurement of high peak power lasers

We have derived a set of equations for beam waist at lens focus as a function of variable spot size and demonstrated their physical validity. The derived equations are useful for the estimation of the beam waist size of high peak power lasers focused with high numerical aperture lenses and for spot size measurement of long-range collimated Gaussian beams for several meters. We have described an indirect method to estimate the high peak power focused laser beam waist. The same treatment is extended to the Gaussian vortex beam for estimating its parameters at the beam waist. These results can be useful in the focused Gaussian beam and Gaussian vortex beam applications.