arXiv subjects

I. Husin

Publications and source records attributed to I. Husin.

3 recordsLinked to original sources

arXiv2018

Hermiticity of the Volume Operators in Loop Quantum Gravity

The aim of this article is to provide a rigorous-but-simple steps to prove the hermiticity of the volume operator of Rovelli-Smolin and Ashtekar-Lewandowski using the angular momentum approach, as well as pointing out some subleties which have not been given a lot of attention previously. Besides of being hermitian, we also prove that both volume operators are real, symmetric, and positive semi-definite, with respect to the inner product defined on the Hilbert space over SU(2). Other special properties follows from this fact, such as the possibility to obtain real orthonormal eigenvectors. Moreover, the matrix representation of the volume operators are degenerate, such that the real positive eigenvalues always come in pairs for even dimension, with an additional zero if the dimension is odd. As a consequence, one has a freedom in choosing the orthonormal eigenvectors for each 2-dimensional eigensubspaces. Furthermore, we provide a formal procedure to obtain the spectrum and matrix representation of the volume operators. In order to compare our procedure with the earlier ones existing in the literature, we give explicit computational examples for the case of monochromatic quantum tetrahedron, where the eigenvalues agrees with the standard earlier procedure.

gr-qc↗

arXiv2018

Compactness, masses and radii of compact stars within the Eddington-inspired Born-Infeld theory

We investigate the compactness, masses and radii of realistic neutron stars (NSs) and quark stars (QSs) within the Eddington-inspired Born-Infeld (EiBI) theory of gravity, and the energy conditions of their apparent equation of states (EOSs). We show that the maximum compactness and maximum masses constraints extracted from the recent pulsars masses and radii observations can provide the upper and lower limits of $κ$ value of EiBI theory. By using BSP parameter set of relativistic mean field (RMF) model to describe NS core EOS including hyperons, it can be estimated that $ (2.7 \le κ_g \le 7.9) \times$ $\rm 10^{-2} m^5 kg^{-1} s^{-2}$. If we use confined-isospin-density-dependent-mass (CIDDM) model with additional scalar Coulomb term with QSK046 parameter set to describe QS EOS, we can obtain lesser value i.e., $ (1.6 \le κ_g\le 2.2) \times$ $\rm 10^{-2} m^5 kg^{-1} s^{-2}$. We have also observed that for large $κ$ values, mass-radius relations of NSs and QSs do not exceed causality restrictions because the compactness of NS and QS are saturated after passing certain large critical value. This observation is in agreement with the results obtained in Ref.\cite{Delsate12} for the case of pressure-less stars. We have also found that if $κ$ larger than certain non-zero value, the CIDDM with vector Coulomb model prediction of QS can reach the maximum mass $\gtrsim$ 2 $M_\odot$. We have found also that if the NS or QS EOS becomes stiffer, the upper limit of $κ$ from compactness constraint becomes smaller and lower limit of $κ$ from maximum masses constraint becomes larger. We also observe that the uncertainty of the systematic in canonical mass compact stars radii measurements data can affect the $κ$ range. It is also shown that the non-physical apparent EOS of NSs and QSs can satisfy the energy conditions.

gr-qc↗

arXiv2017

Neutron stars in the braneworld within the Eddington-inspired Born-Infeld gravity

We propose the disappearance of "the hyperon puzzle" in neutron star (NS) by invoking two new-physics prescriptions: modified gravity theory and braneworld scenario. By assuming that NS lives on a $3$-brane within a $5d$ empty AdS bulk, gravitationally governed by Eddington-inspired Born-Infeld (EiBI) theory, the field equations can be effectively cast into the usual Einstein's with "apparent" anisotropic energy-momentum tensor. Solving the corresponding brane-TOV equations numerically, we study its mass-radius relation. It is known that the appearance of finite brane tension $λ$ reduces the compactness of the star. The compatibility of the braneworld results with observational constraints of NS mass and radius can be restored in our model by varying the EiBI's coupling constant, $κ$. We found that within the astrophysically-accepted range of parameters ($0<κ<6\times10^6\text{m}^2$ and $λ\gg1~ \text{MeV}^4$) the NS can have mass $\sim2.1~ \text{M}_\odot$ and radius $\sim10$ km.

astro-ph.CO↗