Tamal Sarkar

Newtonian analogue of Schwarzschild de-Sitter spacetime: Influence on the local kinematics in galaxies

The late time accelerated expansion of the Universe demands that even in local galactic-scales it is desirable to study astrophysical phenomena, particularly relativistic accretion related phenomena in massive galaxies or in galaxy mergers and the dynamics of the kiloparsecs-scale structure and beyond, in the local-galaxies in Schwarzschild-de Sitter (SDS) background, rather than in Schwarzschild or Newtonian paradigm. Owing to the complex and nonlinear character of the underlying magnetohydrodynamical equations in general relativistic (GR) regime, it is quite useful to have an Newtonian analogous potential containing all the important GR features that allows to treat the problem in Newtonian framework for study of accretion and its related processes. From the principle of conserved Hamiltonian of the test particle motion, here, a three dimensional Newtonian analogous potential has been obtained in spherical geometry corresponding to SDS/Schwarzschild anti-de Sitter (SADS) spacetime, that reproduces almost all of the GR features in its entirety with remarkable accuracy. The derived potential contains an explicit velocity dependent term of the test particle that renders an approximate relativistic modification of Newtonian like potential. The complete orbital dynamics around SDS geometry and the epicyclic frequency corresponding to SDS metric have been extensively studied in the Newtonian framework using the derived potential. Applying the derived analogous potential it is found that the current accepted value of

EXACT RELATIVISTIC NEWTONIAN REPRESENTATION OF GRAVITATIONAL STATIC SPACETIME GEOMETRIES

\Lambda \sim 10^{-56} \rm cm^{-2}

Logical Design of Quaternary Signed Digit Conversion Circuit and its Effectuation using Operational Amplifier

moderately influences both sonic radius as well as Bondi accretion rate, especially for spherical accretion with smaller values of adiabatic constant and temperature, which might have interesting consequences on the stability of accretion disk in AGNs/radio galaxies.

Orbital Dynamics Using Pseudo-Newtonian Potential

We construct a self-consistent relativistic Newtonian analogue corresponding to gravitational static spherical symmetric spacetime geometries, staring directly from a generalized scalar relativistic gravitational action in Newtonian framework, which gives geodesic equations of motion identical to those of the parent metric. Consequently, the derived velocity-dependent relativistic scalar potential, which is a relativistic generalization of Newtonian gravitational potential, exactly reproduces the relativistic gravitational features corresponding to any static spherical symmetric spacetime geometry in its entirety, including all the experimentally tested gravitational effects in the weak field up to the present. This relativistic analogous potential is expected to be quite useful in studying wide range of astrophysical phenomena, especially in strong field gravity.

Spectral lags of flaring events in LS I+61°303 from RXTE Observations

In binary number system carry is a major problem in arithmetical operation. We have to suffer O(n) carry propagation delay in n-bit binary operation. To overcome this problem signed digit is required for carry free arithmetical operation. Further, literature reviews suggest that multi-valued logic (MVL) would be a better choice to address the problem of developing faster chips for performing faster computational operation. Quaternary Signed Digit (QSD) have a major contribution in higher radix (=4) carry free arithmetical operation. For digital implementation, the signed digit quaternary numbers are represented using 3-bit 2s compliment notation. In this paper, a simple and new technique of binary (2s compliment) to QSD conversion is proposed and described. Well-known operational amplifier (OPAMP) based digital to analog converter circuit is also given to verify the above technique.

Effects of the dark energy and flat rotation curve on the gravitational time delay of particle with non-zero mass

Particle trajectories in different Spherically Symmetric static space-time metrics are studied employing Pseudo Newtonian potential (PNP).

Newtonian analogue of corresponding space–time dynamics of rotating black holes: implication for black hole accretion

This work reports the first discovery of(negative) spectral lags in X-ray emission below 10 ke V from the gamma ray binary LS I+61?303 during large flaring episodes using Rossi X-ray Timing Explorer(RXTE) observations. It is found from the RXTE data that during the flares, low energy(3–5 ke V) variations lead the higher energy(8–10 ke V) variations by a few tens of seconds whereas no significant time lag is observed during the non-flaring states. The observed spectral lag features for flaring events suggest that inverse Compton scattering may be operating, at least in some part of the system. Another possibility is that the sites of particle acceleration may be different for flaring and non-flaring events such as in the microquasar model, in which the flaring radiation may come from hot spots sitting above the black hole while steady state emissions are due to the jets.

All-optical switching by Kerr nonlinear prism and its application to of binary-to-gray-to-binary code conversion

The effects of several dark energy models on gravitational time delay of particles with non-zero mass are investigated and analytical expressions for the same are obtained at the first order accuracy. Also the expression for gravitational time delay under the influence of conformal gravity potential that well describes the flat rotation curve of spiral galaxies is derived. The findings suggest that (i) the conformal gravity description of dark matter reduces the net time delay in contrast to the effect of normal dark matter, and therefore in principle the models can be discriminated using gravitational time delay observations, and (ii) the effect of dark energy/flat rotation curve may be revealed from high-precision measurements of gravitational time delay of particles involving the megaparsec and beyond distance scale.