arXiv subjects

Banibrata Mukhopadhyay

Publications and source records attributed to Banibrata Mukhopadhyay.

At least 199 records · Page 11Linked to original sources

arXiv2002

Pseudo-Newtonian Potentials to Describe the Temporal Effects on Relativistic Accretion Disks around Rotating Black Holes and Neutron Stars

Two pseudo-Newtonian potentials, which approximate the angular and epicyclic frequencies of the relativistic accretion disk around rotating (and counter rotating) compact objects, are presented. One of them, the Logarithmically Modified Potential, is a better approximation for the frequencies while the other, the Second-order Expanded potential, also reproduces the specific energy for circular orbits in close agreement with the General Relativistic values. These potentials may be included in time dependent hydrodynamical simulations to study the temporal behavior of such accretion disks.

astro-ph↗

arXiv2002

Description of Pseudo-Newtonian Potential for the Relativistic Accretion Disk around Kerr Black Holes

We present a pseudo-Newtonian potential for accretion disk modeling around the rotating black holes. This potential can describe the general relativistic effects on accretion disk. As the inclusion of rotation in a proper way is very important at an inner edge of disk the potential is derived from the Kerr metric. This potential can reproduce all the essential properties of general relativity within 10% error even for rapidly rotating black holes.

astro-ph↗

arXiv2002

Fluid flow and inertial forces in black hole space times

We discuss the nature of the radial and azimuthal components of centrifugal force associated with fluid flows in the equatorial plane of black hole space times. The equations of motion are solved for the radial and azimuthal components of the 3-velocity V^i which are then used in evaluating the nature of the various components of inertial accelerations. It is shown that the reversal of centrifugal force is governed mainly by the dominance of the azimuthal velocity and the reversal occurs for r, mostly at 2m <~ r <~ 3m, depending upon the boundary condition.

gr-qc↗

arXiv2002

Effect of Coriolis force on Accretion Flows around Rotating Compact Object

Using the generalised set of fluid equations that include the `Coriolis force' along with the centrifugal and pressure gradient forces, we have reanalysed the class of self similar solutions, with the pseudo-Newtonian potential. We find that the class of solutions is well behaved for almost the entire parameter space except for a few selected combinations of $γ$ and $α$ for the co-rotating flow. The analysis of the Bernoulli number shows that whereas it remains positive for co-rotating flow for $f>1/3$, for the counter-rotating flow it does admit both positive and negative values, indicating the possibility of energy transfer in either direction.

astro-ph↗

arXiv2002

Hydrodynamical Study of Advective Accretion flow around Neutron Stars

Here we study the accretion process around a neutron star, especially for the cases where shock does form in the accretion disk. In case of accretion flows around a black hole, close to the horizon matter is supersonic. On the other hand for the case of neutron stars and white dwarfs, matter must be subsonic close to the inner boundary. So the nature of the inflowing matter around neutron stars and white dwarfs are strictly different from that around black holes in the inner region of the disk. Here we discuss a few phenomena and the corresponding solutions of hydrodynamic equations of matter in an accretion disk around a slowly rotating neutron star without magnetic field.

astro-ph↗

arXiv2002

Dynamics of electromagnetic waves in Kerr geometry

Here we are interested to study the spin-1 particle i.e., electro-magnetic wave in curved space-time, say around black hole. After separating the equations into radial and angular parts, writing them according to the black hole geometry, say, Kerr black hole we solve them analytically. Finally we produce complete solution of the spin-1 particles around a rotating black hole namely in Kerr geometry. Obviously there is coupling between spin of the electro-magnetic wave and that of black hole when particles propagate in that space-time. So the solution will be depending on that coupling strength. This solution may be useful to study different other problems where the analytical results are needed. Also the results may be useful in some astrophysical contexts.

gr-qc↗

arXiv2001

Stability of Accretion Disks in Presence of Nucleosynthesis

We study the effect of nuclear reaction on a thin, axisymmetric, differentially rotating, inviscid, steady accretion flow around a black hole from an analytical point of view. We find that for most of the reasonable disk parameters, when $p-p$-reaction, dissociation of deuterium and helium are taken into account, the transonic region of the disk continues to have the inner sonic point and if the temperature of the flow at the injection sonic point could be raised (by say, some heating processes) the flow would to pass through this inner sonic point. Otherwise, the flow may be unstable. We use the sonic point analysis to study the solution. In the rest of the disk parameters the inner sonic point is absent altogether and the flow will definitely be unstable.

astro-ph↗

arXiv2001

Behaviour of spin-half particles in curved space-time

We study the behaviour of spin-half particles in curved space-time. Since Dirac equation gives the dynamics of spin-half particles, we mainly study the Dirac equation in Schwarzschild, Kerr, Reissner-Nordström geometry. Due to the consideration of existence of black hole in space-time (the curved space-time), particles are influenced and equation will be modified. As a result the solution will be changed from that due to flat space.

gr-qc↗

arXiv2001

Nucleosynthesis in Advective Accretion Disk around Compact Object

We study the nucleosynthesis in accretion disk around compact object. When matter falls towards the compact object, due to interactions in nuclear species nuclear energy is released in the high temperature. In some region of parameter space nuclear energy becomes comparable or higher to the energy release due to the viscous effect of the disk. In those regions disk may become unstable. Also the changes of nuclear abundance in the disk are significant.

astro-ph↗

arXiv2000

Scattering of Dirac Waves off Kerr Black Holes

Chandrasekhar separated the Dirac equation for spinning and massive particles in Kerr geometry into radial and angular parts. Here we solve the complete wave equation and find out how the Dirac wave scatters off Kerr black holes. The eigenfunctions, eigenvalues and reflection and transmission co-efficients are computed. We compare the solutions with several parameters to show how a spinning black hole distinguishes mass and energy of incoming waves. Very close to the horizon the solutions become independent of the particle parameters indicating an universality of the behaviour.

astro-ph↗

arXiv2000

Dirac equation in Kerr geometry and its solution

Chandrasekhar separated the Dirac equation for spinning and massive particles in Kerr geometry into radial and angular parts. In the present review, we present solutions of the complete wave equation and discuss how the Dirac wave scatters off Kerr black holes. The eigenfunctions, eigenvalues and reflection and transmission co-efficients are computed for different Kerr parameters. We compare the solutions with several parameters to show how a spinning black hole distinguishes mass and energy of incoming waves. Very close to the horizon, the solutions become independent of the particle parameters indicating an universality of the behaviour.

astro-ph↗

arXiv2000

Solution of Dirac equation around a spinning Black Hole

Chandrasekhar separated the Dirac equation for spinning and massive particles in Kerr geometry in radial and angular parts. Chakrabarti solved the angular equation and found the corresponding eigenvalues for different Kerr parameters. The radial equations were solved asymptotically by Chandrasekhar. In the present paper, we use the WKB approximation to solve the spatially complete radial equation and calculate analytical expressions of radial wave functions for a set of Kerr and wave parameters. From these solutions we obtain local values of reflection and transmission coefficients.

gr-qc↗

arXiv2000

Behaviour of spin-1/2 particle around a charged black hole

Dirac equation is separable in curved space-time and its solution was found for both spherically and axially symmetric geometry. But most of the works were done without considering the charge of the black hole. Here we consider the spherically symmetric charged black hole background namely Reissner-Nordstrom black hole. Due to presence of the charge of black-hole charge-charge interaction will be important for the cases of incoming charged particle (e.g. electron, proton etc.). Therefore both gravitational and electromagnetic gauge fields should be introduced. Naturally behaviour of the particle will be changed from that in Schwarzschild geometry. We compare both the solutions. In the case of Reissner-Nordstrom black hole there is a possibility of super-radiance unlike Schwarzschild case. We also check this branch of the solution.

gr-qc↗

arXiv1999

Nucleosynthesis in accretion flows around Black Holes

Significant nucleosynthesis is possible in the centrifugal pressure-supported dense and hot region of the accretion flows which deviate from Keplerian disks around black holes. We compute composition changes and energy generations due to such nuclear processes. We use a network containing 255 species and follow the changes in composition. Highly viscous, high-accretion-rate flows deviate from a Keplerian disk very close to the black hole and the temperature of the flow is very small due to Compton cooling. No significant nucleosynthesis takes place in these cases. Low-viscosity and lower-accretion-rate hot flows deviate farther out and significant changes in composition are possible in these cases. We suggest that such changes in composition could be contributing to the metallicities of the galaxies. Moreover, the radial variation of the energy generation/absorption specifically due to proton capture and photo-dissociation reactions could cause instabilities in the inner regions of the accretion flows. For most of these cases sonic point oscillations may take place. We discuss the possibility of neutrino emissions.

astro-ph↗

arXiv1999

Dirac Equation in Kerr Geometry

We are familiar with Dirac equation in flat space by which we can investigate the behaviour of half-integral spin particle. With the introduction of general relativistic effects the form of the Dirac equation will be modified. For the cases of different background geometry like Kerr, Schwarzschild etc. the corresponding form of the Dirac equation as well as the solution will be different. In 1972, Teukolsky wrote the Dirac equation in Kerr geometry. Chandrasekhar separated it into radial and angular parts in 1976. Later Chakrabarti solved the angular equation in 1984. In 1999 Mukhopadhyay and Chakrabarti have solved the radial Dirac equation in Kerr geometry in a spatially complete manner. In this review we will discuss these developments systematically and present some solutions.

gr-qc↗

arXiv1999

Nucleosynthesis Around Black Holes

Study of nucleosynthesis in accretion disks around black holes was initiated by Chakrabarti et al. (1987). In the present work we do the similar analysis using the state-of-the-art disk model, namely, Advective Accretion Disks. During the infall, matter temperature and density are generally increased which are first computed. These quantities are used to obtain local changes in composition, amount of nuclear energy released or absorbed, etc. under various inflow conditions. In the cases where the magnetic viscosity is dominant neutron torus may be formed. We also talk about the fate of Li^7 and D during the accretion. The outflowing winds from the disk could carry the new isotopes produced by nucleosynthesis and contaminate the surroundings. From the degree of contamination, one could pinpoint the inflow parameters.

astro-ph↗

arXiv1999

Instantaneous Reflection and Transmission Coefficients and a Special Method to Solve Wave Equation

People are familiar with quantum mechanical reflection and transmission coefficient. In all those cases corresponding potentials are usually assumed as of constant height and depth. For the cases of varying potential, corresponding reflection and transmission coefficients can be found out using WKB approximation method. But due to change of barrier height, reflection and transmission coefficients should be changed from point to point. Here we show the analytical expressions of the instantaneous reflection and transmission coefficients. Here as if we apply the WKB approximation at each point, so we call it as Instantaneous WKB method or IWKB method. Once we know the forward and backward wave amplitudes we can find out corresponding wave function by calculating Eiconal. For the case of analytically complicated potential corresponding differential equation seems to be unsolvable analytically. If the potentials are well behaved then obviously these could be replaced by functions of simple expression of same behaviour which can be integrated analytically and the equation is now possible to solve analytically.

math-ph↗

arXiv1999

Semi-analytical Solution of Dirac equation in Schwarzschild Geometry

Separation of the Dirac equation in the spacetime around a Kerr black hole into radial and angular coordinates was done by Chandrasekhar in 1976. In the present paper, we solve the radial equations in a Schwarzschild geometry semi-analytically using Wentzel-Kramers-Brillouin approximation (in short WKB) method. Among other things, we present analytical expression of the instantaneous reflection and transmission coefficients and the radial wave functions of the Dirac particles. Complete physical parameter space was divided into two parts depending on the height of the potential well and energy of the incoming waves. We show the general solution for these two regions. We also solve the equations by a Quantum Mechanical approach, in which the potential is approximated by a series of steps and found that these two solutions agree. We compare solutions of different initial parameters and show how the properties of the scattered wave depend on these parameters.

gr-qc↗