Narrow Results

Accurate to the first order in the uniform angular velocity, the general relativistic frame dragging effect of the moments of inertia and the radii of gyration of two kinds of neutron stars are calculated in a relativistic σ – ω model. The calculation shows that the dragging effect will diminish the moments of inertia and radii of gyration.

The $\gamma$-bands are analyzed through the variation of the energy of the $2_{\gamma }^{+}$ excitation and the energies of excited level sequence of $\gamma$-bands with respect to various parameters. The shape phase transition observed at N = 88–90 is reviewed through its influence on the energies of $\gamma$-band. The correlation of the $2_{\gamma }^{+}$ excitation energies with the collective shape signature observable $R_{4/2}$ indicates a connection with the nuclear equilibrium structure. The study of excited level sequence in the $\gamma$-band with respect to the ground band signifies that the two bands differ in deformation.

Recently, Harko et al. [Phys. Rev. D88, 044032 (2013)] have derived an exact solution of the spherically symmetric field equations in EiBI gravity, describing a compact star with decreasing pressure but increasing energy density. We have explored some features of this solution by restricting the range of the parameter $\kappa$ which satisfies four energy conditions for 10 equation of states (EOSs). Viability and deviations of these features in the light of updated observed properties of neutron stars (NS) have been explored completely. A comparison of those features with recent observations may uncover the future implication of this paper. Analysis of our results indicates that this solution may be used as an alternative EOS.

A new paradigm for black holes is introduced. It is known as the External Energy Paradigm. The paradigm asserts that all energies of a black hole are external quantities; they are absent inside the horizon. These energies include constituent mass, gravitational energy, electrostatic energy, rotational energy, heat energy, etc. As a result, quantum particles with charges and spins cannot exist inside the black hole. To validate the conclusion, we derive the moment of inertia of a Schwarzschild black hole and find that it is exactly equal to mass $\times$ (Schwarzschild radius)², indicating that all mass of the black hole is located at the horizon. This remarkable result can resolve several long-standing paradoxes in black hole theory; such as why entropy is proportional to area and not to volume, the singularity problem, the information loss problem and the perplexing firewall controversy.

We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous medium model, where all characteristics and fields are defined everywhere in the volume but they follow some generalized equations which are derived by using fractional integrals of fractional order. The order of fractional integral can be equal to the fractal mass dimension of the solid. Fractional integrals are considered as an approximation of integrals on fractals. We suggest the approach to compute the moments of inertia for fractal solids. The dynamics of fractal solids are described by the usual Euler's equations. The possible experimental test of continuous medium model for fractal solids is considered.

We reveal three new discoveries in black hole physics previously unexplored in the Hawking era. These results are based on the remarkable 1971 discovery of the irreducible mass of the black hole by Christodoulou and Ruffini, and subsequently confirmed by Hawking.

• (1)The Horizon Mass Theorem states that the mass at the event horizon of any black hole — neutral, charged, or rotating — is always twice its irreducible mass observed at infinity.
• (2)The External Energy Theorem asserts that the rotational energy of a Kerr black hole exists completely outside the horizon. This is due to the fact that the irreducible mass does not contain rotational energy.
• (3)The Moment of Inertia Theorem shows that every black hole has a moment of inertia. When the rotation stops, the irreducible mass of a Kerr black hole becomes the moment of inertia of a Schwarzschild black hole. This is recognized as the rotational equivalent of the rest mass of a moving body in relativity.

Thus after 50 years, the irreducible mass has gained a new and profound significance. No longer is it a limiting value in rotation, it determines black hole dynamics and structure. What is believed to be a black hole is a mechanical body with an extended structure. Astrophysical black holes are likely to be massive compact objects from which light cannot escape.

The neutron-proton (n-p) isovector pairing effect on the nuclear moment of inertia has been studied within the framework of the BCS approximation. An analytical expression of the moment of inertia, that explicitly depends upon the n-p pairing, has been established using the Inglis cranking model. The model was first tested numerically for nuclei such as N = Z and whose experimental values of the moment of inertia are known (i.e. such as 16 ≤ Z ≤ 40). It has been shown that the n-p pairing effect is non-negligible and clearly improves the theoretical predictions when compared to those of the pairing between like particles. Secondly, predictions have been established for even-even proton-rich rare-earth nuclei. It has been shown that the n-p pairing effect is non-negligible when N = Z and rapidly decreases with increasing values of (N-Z).

The deformation structure of the even–even ytterbium, hafnium and tungsten nuclei is investigated in framework of the collective model, the single-particle Schrödinger fluid model and the cranked Nilsson model. Accordingly, we have calculated the rotational and vibrational energies, the nuclear moments of inertia, the total ground-state energy, the quadrupole moment, the liquid drop (LD) energy, the Strutinsky inertia, the LD inertia, the volume conservation factor , the smoothed energy, the Bardeen, Cooper and Schrieffer (BCS) energy and the G-value of the ytterbium: ¹⁷⁰Yb, ¹⁷²Yb and ¹⁷⁴Yb, hafnium: ¹⁷⁶Hf, ¹⁷⁸Hf and ¹⁸⁰Hf and tungsten: ¹⁸²W, ¹⁸⁴W and ¹⁸⁶W nuclei as functions of the deformation parameters β, γ, which are assumed to vary in the ranges (-0.50 ≤ β ≤ 0.50) and (0° ≤ γ ≤ 60°). Also, two polynomials in β are obtained to produce results in good agreement with the corresponding results for the total ground-state energy and the quadrupole moment of the mentioned nine nuclei.

A modified phenomenological model is used to calculate nuclear energy levels and describe successfully the backbending of the moment of inertia for the ground state bands in even–even isotopes of Hf and Dy nuclei. The model is a combination of the Myers and Swiatecki model with variable moment inertia (VMI) model. Since the Myers and Swiatecki model has a deviation from experimental energies in which it takes into account pairing effect with constant moment of inertia, in the rotation of nuclei, the Coriolis force acts to de-pair the nucleons pair and align their angular momentum with nuclei total angular momentum, thus Coriolis force increasing and decrease the rotational energy. So, the moment of inertia varies with the angular momentum. Therefore, we modified this model by adding a term to make the moment of inertia vary with angular momentum in the same manner of the VMI model which has a term added to the rotational energy equation. The modified model fits remarkably with the experimental observation and other models in many cases with the use of few parameters especially in rotational nuclei regions similar to Hf and Dy nuclei.

An expression of the particle-number projected nuclear moment of inertia (MOI) has been established in the neutron–proton (np) isovector pairing case within the cranking model. It generalizes the one obtained in the like-particles pairing case. The formalism has been, as a first step, applied to the picket-fence model. As a second step, it has been applied to deformed even–even nuclei such as $(N-Z)=0,2,4,$ and of which the experimentally deduced values of the pairing gap parameters ${\mathrm{\Delta }}_{t{t}^{\prime }}$, $t,t^{\prime }=n,p$, are known. The single-particle energies and eigenstates used are those of a deformed Woods–Saxon mean-field. It was shown, in both models, that the np pairing effect and the projection one are non-negligible. In realistic cases, it also appears that the np pairing effect strongly depends on $(N-Z)$, whereas the projection effect is practically independent from the same quantity.

This paper proposes a technique that can estimate the inertia parameters of a graspless unknown object, which is pushed by robot fingers. Using the fingertip different accelerations (or angular accelerations), velocities (or angular velocities) and forces information measured in pushing operations, the algorithms to estimate the object mass (or moment of inertia) are described. Then, a line called C.M. Line, is defined in this paper. The line contains the center of mass and is between two fingertips which are in point-contact with an object side. By using two or more orientation-different C.M. lines, an algorithm to estimate the center of mass of the object is given. Lastly, experimental verification on the proposed approach is performed and its results are outlined.

This paper explores how the analysis of differential elements and dimensional analysis can simplify the computation of the moment of inertia of certain rigid bodies by exploiting symmetries in these bodies. Integration is used scarcely, if at all, throughout this paper to emphasize the versatility of the method employed.

A very important property in the study of rigid body dynamics, moment of inertia describes the resistance of an object to any change in its angular velocity, given a certain amount of torque. Although many novel methods have been developed to simplify its calculation, this paper presents a remarkable theorem in moment of inertia that has never been widely used, the three-axis theorem. The theorem provides an alternative way for moment of inertia computation and better visualization in integrating each infinitesimal constituent mass element of a rigid body. The key idea is to focus on the distance from this infinitesimal mass to the intersection of the three axes, instead of its distance to a certain rotational axis.

If one rolls a vertically standing hula hoop forward with backspin applied, it moves once far away and then eventually back to hand. In this paper, we study such a motion of a rolling hula hoop from both theoretical and experimental aspects. The hula hoop is rolling with slipping immediately after it leaves the hand, and its motion will transit to that of without slipping due to the transition of the frictional force from kinetic friction to static friction. We show that the experimental results analyzed by Tracker software can be well described by equations of motion that take into account the deformation of the hula hoop. Theoretical and experimental studies in this paper are suitable for university students in physics courses. The video analyzed in this paper can be viewed at https://youtu.be/i4j1lDhCI2os.

We reveal three new discoveries in black hole physics previously unexplored in the Hawking era. These results are based on the remarkable 1971 discovery of the irreducible mass of the black hole by Christodoulou and Ruffini, and subsequently confirmed by Hawking.

1. The Horizon Mass Theorem shows that the mass at the event horizon of any black hole: neutral, charged, or rotating, depends only on twice its irreducible mass observed at infinity.

2. The External Energy Conjecture proposes that the electrostatic and rotational energy of a general black hole exist completely outside the horizon due to the nature of the irreducible mass.

3. The Moment of Inertia Property shows that every Kerr black hole has a moment of inertia. When the rotation stops, there is an irreducible moment of inertia as a result of the irreducible mass.

Thus after 50 years, the irreducible mass has gained a new and profound significance. No longer is it just a limiting value in energy extraction, it can also determine black hole dynamics and structure. What is believed to be a black hole is a physical body with an extended structure. Astrophysical black holes are likely to be massive compact objects from which light cannot escape.

Nuclear pairing gaps of normally deformed nuclei are investigated by using the particle-number conserving formalism for the cranked shell model, in which the blocking effects are treated exactly. Both rotational frequency ω-dependence and seniority ν-dependence of the pairing gap are investigated.