We obtain equilibrium solutions for rotating compact stars including the special relativistic effects. The gravity is assumed to be Newtonian, but we used the active mass density, which takes into account all the energies such as motions of the fluids, internal energy, pressure energy in addition to the rest mass energy, in computing the gravitational potential using Poisson's equation. Such a treatment could be applicable to the neutron stars with relativistic motions or relativistic equation of state. We applied the Hachisu's self-consistent field (SCF) method to find spheroidal as well as toroidal sequences of equilibrium solutions. Our solutions show better agreement than Newtonian relativistic hydrodynamic approach that does not take into account the active mass, with general relativistic solutions. The physical quantities such as the peak density, equatorial radii of our solutions agree with general relativistic ones within 5%.Therefore our approach can be a simple alternative to the fully relativistic one when large number of model calculations are necessary as it requires much less computational resources.
We write down and apply the linearized fluid and gravitational equations consistent with pseudo-Newtonian simulations, whereby Newtonian hydrodynamics is used with a pseudo-Newtonian monopole and standard Newtonian gravity for higher multipoles. We thereby eliminate the need to use mode function matching to identify the active non-radial modes in pseudo-Newtonian core-collapse supernova simulations, in favor of the less complex and less costly mode frequency matching method. In doing so, we are able to measure appropriate boundary conditions for a mode calculation.
We perform resistive and viscous MHD simulations of axial jet launching from a magnetized thin accretion disk around a supermassive black hole. We compare the forces in our pseudo-Newtonian simulations for the Paczyński-Wiita and Kluźniak-Lee potentials. The results will help to find magnetic field configurations and physical parameters conducive to jet launching.
We have modeled hydrodynamical tori in the Klu{ź}niak-Lee pseudo-Newtonian potential. The tori in equilibrium were perturbed with uniform sub-sonic velocity fields: vertical, radial and diagonal respectively, and allowed to evolve in time. We identify the eigenmodes corresponding to those of slender tori. The results of our simulations are relevant to the investigation of high-frequency quasi-periodic oscillations observed in stellar-mass black hole binaries.
Pseudo-Newtonian potentials are a tool often used in theoretical astrophysics to capture some key features of a black-hole space-time in a Newtonian framework. As a result, one can use Newtonian numerical codes, and Newtonian formalism in general, in an effective description of important astrophysical processes such as accretion onto black holes. In this paper we develop a general pseudo-Newtonian formalism which pertains to the motion of particles, light, and fluids in stationary space-times. In return, we are able to assess the applicability of the pseudo-Newtonian scheme. The simplest and m…
The gravitational stability of a two-dimensional self-gravitating and differentially rotating gaseous disk in the context of post-Newtonian (hereafter PN) theory is studied. Using the perturbative method and applying the second iterated equations of PN approximation, the relativistic version of the dispersion relation for the propagation of small perturbations is found. We obtain the PN version of Toomre's local stability criterion by utilizing this PN dispersion relation. In other words, we find relativistic corrections to Toomre's criterion in the first PN approximation. Two stability parame…
We propose an approximate approach for studying the relativistic regime of stellar tidal disruptions by rotating massive black holes. It combines an exact relativistic description of the hydrodynamical evolution of a test fluid in a fixed curved spacetime with a Newtonian treatment of the fluid's self-gravity. Explicit expressions for the equations of motion are derived for Kerr spacetime using two different coordinate systems. We implement the new methodology within an existing Newtonian Smoothed Particle Hydrodynamics code and show that including the additional physics involves very little e…
The Johannsen-Psaltis spacetime describes a rotating black hole with parametric deviations from the Kerr metric. By construction this spacetime explicitly violates the no-hair theorems. Rotating black hole solutions in any modified theory of gravity could be written in terms of the Johannsen-Psaltis metric. We examined the accretion of gas onto a black hole described by the static limit of this spacetime. We employed a potential that generalises the Paczynski-Wiita potential to the static Johannsen-Psaltis metric. Our analysis utilised a recent pseudo-Newtonian formulation of the dynamics arou…
Static and uniformly rotating, cold and hot white dwarfs are investigated both in Newtonian gravity and general theory of relativity, employing the well-known Chandrasekhar equation of state. The mass-radius, mass-central density, radius-central density etc relations of stable white dwarfs with $μ=A/Z=2$ and $μ=56/26$ (where $A$ is the average atomic weight and $Z$ is the atomic charge) are constructed for different temperatures. It is shown that near the maximum mass the mass of hot rotating white dwarfs is slightly less than for cold rotating white dwarfs, though for static white dwarfs the …
We calculate the spectrum of inertial oscillation modes in a slowly rotating superfluid neutron star, including, for the first time, both the effects of finite temperatures and entrainment between superfluid neutrons and protons. We work in the Newtonian limit and assume minimal core composition (neutrons, protons and electrons). We also developed an approximate method that allows one to calculate the superfluid r-mode analytically. Finally, we derive and analyze dispersion relations for inertial modes in the superfluid NS matter in the short wavelength limit.
