Thermodynamics under the extended uncertainty principle background: Q−ϕ criticality analysis

The study of thermodynamics in the background of the “extended uncertainty principle (EUP)” comes into interest in recent eras. In this article, we consider a charged black hole (BH) in higher dimensional space–time and present the thermodynamic parameters, based on a semiclassical framework, initially. Then we extend the same within the EUP background. We also analyze the $Q-\varphi$ criticality and find the critical points (${\varphi }_c,Q_c$ and $T_c$) when $Q-\varphi$ criticality appears. We study the effects of EUP on phase transition for higher dimensions ($d=5$) by plotting the $Q-\varphi$ diagrams. Further, we investigate the stability (thermal and global) of the BHs by employing the specific heat and the Gibbs free energy without and within EUP correction and compare the results with the Schwarzschild BHs in higher dimensions.     

Analysis of resonant curves and phase portrait in the earth–moon system by using its unperturbed solution and earth’s equatorial ellipticity

In this research article, we have investigated resonant curves due to the rate of change of earth’s equatorial ellipticity parameter $\left(\dot{\gamma }\right)$, steady-state value of the angular velocity of the moon $\left({\dot{\theta }}_{mo}\right)$, and angular velocity of barycenter $\left(\dot{{\alpha }_0}\right)$ in the Earth-Moon system. Equations of motion of the moon are determined in a spherical coordinate system with the help of the gravitational potential of the earth. By using the unperturbed solution, equations of motion of the moon reduced into the second-order differential equation. From the solution it is observed that resonance occurs due to the frequencies $\dot{\gamma }$, ${\dot{\theta }}_{m0}$, and $\dot{{\alpha }_0}$ at the resonant points ${\dot{\theta }}_{m0}=2\dot{\gamma }$, $3{\dot{\theta }}_{m0}=2\dot{\gamma }$, ${\dot{\theta }}_{m0}=\dot{\gamma }$, ${\dot{\theta }}_{m0}={\dot{\alpha }}_0$. Finally, we have analyzed the phase portrait and phase space by method of Poincaré section when the system is free from forces.     

On the Sun’s distance from the center and the shape of the inner halo in the Galaxy: Gaia EDR3, HST and literature globular clusters

A statistical method is used to derive both the Sun’s distance $r_0$ from the Galactic Center (GC) and the 3D geometry of the inner ($<$ 25 kpc) halo. The spatial distribution of the 138 Gaia EDR3 globular clusters (GCs) with distances established on a combination of HST and literature data of Baumgardt and Vasiliev (2021) is explored. An estimate by using these ancient objects of the pressure-supported subsystem of the Galaxy with newly derived distances leads to the mean $r_0=7.81\pm 0.14$ kpc. The distribution of GCs within 25 kpc is almost spherically symmetric, and has the shape of an ellipsoid with a major axis of its symmetry slightly elongated toward the Sun and two minor axes of almost the same length. The obtained scale-length ratio of the major axis to the minor axis in the plane and to the vertical axis of the ellipsoid is $\approx$ 1:0.8:0.7. Based on the papers of a series, for practical use we argue to employ the following Sun’s distances from the GC and the plane: $r_0=8.15\pm 0.15$ kpc and $z_0=15\pm 5$ pc.