arXiv subjects

Mohsen Fathi

Publications and source records attributed to Mohsen Fathi.

At least 55 records · Page 3Linked to original sources

arXiv2023

Carathéodory's thermodynamics of the Schwarzschild black hole surrounded by quintessence

In this paper, we apply the Carathéodory's method of geometrothermodynamics to investigate the behavior of the main thermodynamic parameters associated with a Schwarzschild black hole surrounded by quintessence. The corresponding Pfaffian form is constructed by means of the Schwarzschild radius $r_s$, and the quintessential radius $r_γ$ as independent variables. This form is then used to characterize the thermodynamic manifold. The homogeneity of the system allows for the recognition of the empirical temperature and entropy, and thus, connects with the usual laws of thermodynamics. In particular, we show that the Helmholtz and Gibbs free energies lead to the same value for the Schwarzschild black hole, in the case of the vanishing cosmological term.

gr-qc↗

arXiv2023

Spherical photon orbits around a rotating black hole with quintessence and cloud of strings

In this paper, we calculate the analytical solutions for the radii of planar and polar spherical photon orbits around a rotating black hole that is associated with quintessential field and cloud of strings. This includes a full analytical treatment of a quintic that describes orbits on the equatorial plane. Furthermore, The radial profile of the impact parameters is studied and the radii corresponding to the extreme cases are derived. For the more general cases, we also discuss the photon regions that form around this black hole. To simulate the orbits that appear in different inclinations, we analytically solve the latitudinal and azimuth equations of motion in terms of the Weierstrassian elliptic functions, by considering the radii of spherical orbits, in their general form, as the initial conditions. The period and the stability conditions of the orbits are also obtained analytically.

gr-qc↗

arXiv2022

Study of null and time-like geodesics in the exterior of a Schwarzschild black hole with quintessence and cloud of strings

Recently, an analytical study of radial and circular orbits for null and time-like geodesics that propagate in the spacetime produced by a Schwarzschild black hole associated with cloud of strings, in a universe filled by quintessence, has been done in Ref. \cite{Mustafa:2021}. In this paper, we complete the aforementioned study by investigating possible analytical solutions to the equations of motion for other types of bound orbits, besides taking into account the cases of unbound orbits. This requires an extensive study of the corresponding effective potentials that categorize the test particle motion. We follow the standard Lagrangian dynamics to parametrize the radial and angular geodesics and the resultant (hyper-)elliptic integrals of motion are treated accordingly. We also simulate the orbits which correspond to different levels of energy in the effective potentials.

gr-qc↗

arXiv2021

Analytical study of light ray trajectories in Kerr spacetime in the presence of an inhomogeneous anisotropic plasma

We calculate the exact solutions to the equations of motion that govern the light ray trajectories as they travel in a Kerr black hole's exterior that is considered to be filled with an inhomogeneous and anisotropic plasmic medium. This is approached by characterizing the plasma through conceiving a radial and an angular structure function, which are let to be constant. The description of the motion is carried out by using the Hamilton-Jacobi method, that allows defining two effective potentials, characterizing the evolution of the polar coordinates. The elliptic integrals of motion are then solved analytically, and the evolution of coordinates is expressed in terms of the Mino time. This way, the three-dimensional demonstrations of the light ray trajectories are given respectively.

gr-qc↗

arXiv2021

The role of elliptic integrals in calculating the gravitational lensing of a charged Weyl black hole surrounded by plasma

In this paper, we mainly aim at highlighting the importance of (hyper-)elliptic integrals in the study of gravitational effects caused by strongly gravitating systems. For this, we study the application of elliptic integrals in calculating the light deflection as it passes a plasmic medium, surrounding a charged Weyl black hole. To proceed with this, we consider two specific algebraic ansatzes for the plasmic refractive index, and we characterize the photon sphere for each of the cases. This will be used further to calculate the angular diameter of the corresponding black hole shadow. We show that the complexity of the refractive index expressions, can result in substantially different types of dependencies of the light behavior on the spacetime parameters.

gr-qc↗

arXiv2021

Probing the parameters of a Schwarzschild black hole surrounded by quintessence and cloud of strings through four standard astrophysical tests

In this paper, we concern about applying general relativistic tests on the spacetime produced by a static black hole associated with cloud of strings, in a universe filled with quintessence. The four tests we apply are precession of the perihelion in the planetary orbits, gravitational redshift, deflection of light, and the Shapiro time delay. Through this process, we constrain the spacetime's parameters in the context of the observational data, which results in about $\sim 10^{-9}$ for the cloud of strings parameter, and $\sim 10^{-20}$ m$^{-1}$ for that of quintessence. The response of the black hole to the gravitational perturbations is also discussed.

gr-qc↗

arXiv2021

Adiabatic evolution of Hayward black hole

In this letter we use the Carathéodory's approach to thermodynamics, to construct the thermodynamic manifold of the Hayward black hole. The Pfaffian form representing the infinitesimal heat exchange reversibly is considered to be $δQ_{\mathrm{rev}}\equiv {\rm d}r_s-\mathcal{F}_H {\rm d}l$, previously obtained by Molina \& Villanueva \cite{fmv20}, where $r_s$ is the Schwarzschild radius, $l$ is the Hayward's parameter responsible for the possible regularization of the Schwarzschild black hole, and $\mathcal{F}_H$ is the intensive variable called the Hayward's force. By solving the associated Cauchy problem, the adiabatic paths are confined to the non-extremal manifold, and therefore, the status of the second and third laws are preserved. Consequently, the extremal sub-manifold corresponds to the {adiabatically disconnected} boundary of the manifold. In addition, the merger of two extremal Hayward black holes is analyzed.

gr-qc↗

arXiv2021

Adiabatic analysis of the rotating BTZ black hole

In this paper we analyze some interesting features of the thermodynamics of the rotating BTZ black hole from the Carathéodory axiomatic postulate, for which, we exploit the appropriate Pfaffian form. The allowed adiabatic transformations are then obtained by solving the corresponding Cauchy problem, and are studied accordingly. Furthermore, we discuss the implications of our approach, regarding the the second and third laws of black hole thermodynamics. In particular, the merging of two extremal black holes is studied in detail.

gr-qc↗

arXiv2021

Ergosphere, photon region structure, and the shadow of a rotating charged Weyl black hole

In this paper, we explore the photon region and the shadow of the rotating counterpart of a static charged Weyl black hole, which has been previously discussed according to null and time-like geodesics. The rotating black hole shows strong sensitivity to the electric charge and the spin parameter, and its shadow changes from being oblate to being sharp by increasing in the spin parameter. Comparing the calculated vertical angular diameter of the shadow with that of M87*, we found that the latter may possess about $10^36$ protons as its source of electric charge, if it is a rotating charged Weyl black hole. A complete derivation of the ergosphere and the static limit is also presented.

gr-qc↗

arXiv2021

Gravitational Rutherford scattering of electrically charged particles from a charged Weyl black hole

Considering electrically charged test particles, we continue our study of the exterior dynamics of a charged Weyl black hole which has been previously investigated regarding the motion of mass-less and (neutral) massive particles. In this paper, the deflecting trajectories of charged particles are designated as being gravitationally Rutherford-scattered and detailed discussions of angular and radial particle motions are presented.

gr-qc↗

arXiv2020

Motion of massive particles around a charged Weyl black hole and the geodetic precession of orbiting gyroscopes

The advanced state of cosmological observations constantly tests the alternative theories of gravity that originate from Einstein's theory. However, this is not restricted to modifications to general relativity. In this sense, we work in the context of Weyl's theory, more specifically, on a particular black hole solution for a charged massive source, which is confronted with the classical test of the geodetic precession, to obtain information about the parameters associated with this theory. To fully assess this spacetime, the complete geodesic structure for massive test particles is presented.

gr-qc↗

arXiv2020

Classical tests on a charged Weyl black hole: bending of light, Shapiro delay and Sagnac effect

In this paper, we apply the classical test of general relativity on a charged Weyl black hole, whose exterior geometry is defined by altering the spherically symmetric solutions of Weyl conformal theory of gravity. The tests are basically founded on scrutinizing the angular geodesics of light rays propagating in the gravitating system caused by the black hole. In this investigation, we bring detailed discussions about the bending of light, together with two other relativistic effects, known as the Shapiro and the Sagnac effects. We show that the results are in good conformity with the general relativistic effects, besides giving long-distance corrections caused by the cosmological nature of the background geometry under study.

gr-qc↗

arXiv2019

Photons trajectories on a first order scale-dependent static BTZ black hole

In this paper we study the motion of massless particles on a static BTZ black hole background in the context of scale-dependent gravity, which is characterized by the running parameter $ε$. Thus, by using standard methods we obtain the equation of motions and then analytic solutions are found. The relevant non-trivial differences appear when we compare our solution against the classical counterpart.

gr-qc↗

arXiv2018

Homothetic Congruences in General Relativity

The kinematical characteristics of distinct infalling homothetic fields are discussed by specifying the transverse subspace of their generated congruences to the energy-momentum deposit of the chosen gravitational system. This is pursued through the inclusion of the base manifold's cotangent bundle in a generalized Raychaudhuri equation and its kinematical expressions. Exploiting an electromagnetic energy-momentum tensor as the source of non-gravitational effects, I investigate the evolution of the mentioned homothetic congruences, as they fall onto a Reissner-Nordstrom black hole. The results show remarkable differences to the common expectations from infalling congruences of massive particles.

gr-qc↗

arXiv2018

Congruence Kinematics in Conformal Gravity

In this paper we calculate the kinematical quantities of the Raychaudhuri equations, to characterize a congruence of time-like integral curves, according to the vacuum radial solution of Weyl theory of gravity. Also the corresponding flows are plotted for definite values of constants.

physics.gen-ph↗

arXiv2018

Congruence Convergence in pp-wave Spacetime

We argue that the well-known geodesic completeness property of pp-waves, can be disregarded once the geodesics are extracted as being extended along sets of Brinkmann coordinates. This issue is investigated in the more general context of congruence convergence and we show that the problem leads to diverse issues for non-geodesic congruences. The discussion is mostly based on the null congruence expansion and a generalized Raychaudhuri equation is also provided.

gr-qc↗

arXiv2017

Covariant kinematics of light in media and a generalized Raychaudhuri equation

There is ongoing interest in adopting various tools and ideas from general relativity for optical applications and the study of light propagation through natural or engineered media. Here, the covariant kinematics of light propagating through arbitrary dielectric media in curved space-times are derived, allowing for analysis and tracing of congruences of light through media that may smoothly vary in character between vacuum, positively refracting, and negatively refracting; or null, timelike, and spacelike with respect to the background metric. The kinematics are then used to generalize the Raychaudhuri equation -- an important tool in general relativity that describes the focus of a congruence. These results will be useful for the analysis of optical devices, particularly those designed using transformation optics, and serve as theoretical tools to study generalized concepts in general relativity.

gr-qc↗

arXiv2016

Gravitational Collapse in Repulsive $R+μ^4/R$ Gravity

In this paper we work out collapsing conditions for a spherical star in the weak field limit of the $R+μ^4/R$ gravity and discuss the importance of the parameter $μ$ to generate different criteria in the theory. Such criteria are proved to be resulting in a variety of different fates for the evolution of the outer shells of stars. Furthermore, we investigate the special case of violating the first junction condition and point out corresponding contradictions to the normal cases. These results show that the consistency of the $R+μ^4/R$ theory of gravity with the common astrophysical predictions relies highly on the adoption of the parameter $μ$ and satisfaction/violation of the first junction condition. For those anomalous results, further observational attempts are mandatory.

gr-qc↗