118614591
Possible potentials responsible for stable circular relativistic orbits
Bertrand's theorem in classical mechanics of the central force fields attracts us because of its predictive power. It categorically proves that there can only be two types of forces which can produce stable, circular orbits. In this paper an attempt has been made to generalize Bertrand's theorem to the central force problem of relativistic systems. The stability criterion for potentials which can produce stable, circular orbits in the relativistic central force problem has been deduced and a general solution of it is presented. It is seen that the inverse square law passes the relativistic test but the kind of force required for simple harmonic motion does not. Special relativistic effects do not allow stable, circular orbits in the presence of a force which is proportional to the negative of the displacement of the particle from the potential centre.
118788230
GEODESIC FLOWS AND THEIR DEFORMATIONS IN BERTRAND SPACETIMES
In this article we will discuss some features of a particular spacetime called Bertrand space-time of Type II (BST-II). The talk discusses about the energy conditions and the ESR parameters in this spacetime.
37817960
Geodesics in information geometry: classical and quantum phase transitions.
We study geodesics on the parameter manifold for systems exhibiting second order classical and quantum phase transitions. The coupled nonlinear geodesic equations are solved numerically for a variety of models which show such phase transitions in the thermodynamic limit. It is established that both in the classical as well as in the quantum cases, geodesics are confined to a single phase and exhibit turning behavior near critical points. Our results are indicative of a geometric universality in widely different physical systems.
118728848
On Geodesic Flows and Their Deformations in Bertrand Space-times
We study the energy conditions and geodesic deformations in Bertrand space-times. We show that these can be thought of as interesting physical space-times in certain regions of the underlying parameter space, where the weak and strong energy conditions hold. We further compute the ESR parameters and analyze them numerically. The focusing of radial time-like and radial null geodesics is shown explicitly, which verifies the Raychaudhuri equation.
53636345
MAGNETIC FIELDS IN RELATIVISTIC COLLISIONLESS SHOCKS
We present a systematic study on magnetic fields in gamma-ray burst (GRB) external forward shocks (FSs). There are 60 (35) GRBs in our X-ray (optical) sample, mostly from Swift. We use two methods to study B (fraction of energy in magnetic field in the FS): (1) for the X-ray sample, we use the constraint that the observed flux at the end of the steep decline is ≥ X-ray FS flux; (2) for the optical sample, we use the condition that the observed flux arises from the FS (optical sample light curves decline as ~t –1, as expected for the FS). Making a reasonable assumption on E (jet isotropic equivalent kinetic energy), we converted these conditions into an upper limit (measurement) on B n 2/(p + 1) for our X-ray (optical) sample, where n is the circumburst density and p is the electron index. Taking n = 1 cm–3, the distribution of B measurements (upper limits) for our optical (X-ray) sample has a range of ~10–8-10–3 (~10–6-10–3) and median of ~few × 10–5 (~few × 10–5). To characterize how much amplification is needed, beyond shock compression of a seed magnetic field ~10 μG, we expressed our results in terms of an amplification factor, AF, which is very weakly dependent on n (AF∝n 0.21). The range of AF measurements (upper limits) for our optical (X-ray) sample is ~1-1000 (~10-300) with a median of ~50 (~50). These results suggest that some amplification, in addition to shock compression, is needed to explain the afterglow observations.
53358770
Evidence for mild deviation from power-law distribution of electrons in relativistic shocks: GRB 090902B
Many previous studies have determined that the long lasting emission at X-ray, optical and radio wavelengths from gamma-ray bursts (GRBs), called the afterglow, is likely produced by the external forward shock model. In this model, the GRB jet interacts with the circum-stellar medium and drives a shock that heats the medium, which radiates via synchrotron emission. In this work, we carried out a detailed analysis of the late time afterglow data of GRB 090902B using a very careful accounting of the Inverse Compton losses. We find that in the context of the external forward shock model, the only viable option to explain the X-ray and optical data of GRB 090920B is to have the electron energy distribution deviate from a power-law shape and exhibit some slight curvature immediately downstream of the shock front (we explored other models that rely on a single power-law assumption, but they all fail to explain the observations). We find the fraction of the energy of shocked plasma in magnetic field to be ∼10 −6 using late time afterglow data, which is consistent with the value obtained using early gamma-ray data. Studies like the present one might be able to provide a link between GRB afterglow modelling and numerical simulations of particle acceleration in collisionless shocks. We also provide detailed calculations for the early (10 3 s) high-energy (>100 MeV) emission and confirm that it is consistent with origin in the external forward shock. We investigated the possibility that the ∼10 keV excess observed in the spectrum during the prompt phase also has its origin in the external shock and found the answer to be negative.
18482227
Angular Momentum Redistribution by Waves in the Sun
We calculate the angular momentum transport by gravito-inertial-Alfven waves and show that, so long as prograde and retrograde gravity waves are excited to roughly the same amplitude, the sign of angular momentum deposit in the radiative interior of the Sun is such as to lead to an exponential growth of any existing small radial gradient of rotation velocity just below the convection zone. This leads to formation of a strong thin shear layer (of thickness about 0.3% R☉) near the top of the radiative zone of the Sun on a timescale of order 20 yr. When the magnitude of differential rotation across this layer reaches about 0.1 μHz, the layer becomes unstable to shear instability and undergoes mixing, and the excess angular momentum deposited in the layer is returned to the convection zone. The strong shear in this layer generates a toroidal magnetic field which is also deposited in the convection zone when the layer becomes unstable. This could possibly start a new magnetic activity cycle seen at the surface.
199635013
Connecting String/M Theory to the Electroweak Scale and to LHC Data
The Standard Model of particle physics explains (almost) all observed non-gravitational microscopic phenomena but has many open theoretical questions. We are on the threshold of unraveling the mysteries of the Standard Model and discovering its extension. This could be achieved in the near future with the help of many experiments in particle physics and cosmology, the LHC in particular. Assuming that data confirming the existence of new physics beyond the Standard Model is obtained, one is left with the very important and challenging task of solving the "Inverse Problem", \emph{viz.} "How can one deduce the nature of the underlying (perhaps microscopic) theory from data?" This thesis explores this question in detail, and also proposes an approach to address the problem in a meaningful way which could prove crucial to the possible solution to this problem in the future. The proposed approach has three aspects - a) To systematically study classes of microscopic (string/$M$ theory) constructions to the extent that they could be connected to low energy physics (electroweak scale), b) To find patterns of experimental observables which are sensitive to the properties of the underlying theoretical constructions thereby allowing us to distinguish among different constructions, and c) To try to get insights about the qualitative features of the theoretical model from data in a bottom-up approach which complements the top-down approach and strengthens it as well. This thesis studies all the above aspects in detail. The methods used and results obtained in this thesis will hopefully be of great importance in solving the Inverse Problem.
15932775
No universality for the electron power-law index ( p) in gamma-ray bursts and other relativistic sources
The gamma-ray burst (GRB) prompt emission is believed to be from highly relativistic electrons accelerated in relativistic shocks. From the GRB high-energy power-law spectral indices β observed by the Burst and Transient Source Experiment (BATSE) Large Area Detectors (LAD), we determine the spectral index, p, of the electrons' energy distribution. Both the theoretical calculations and numerical simulations of the particle acceleration in relativistic shocks show that p has a universal value ≈2.2-2.3. We show that the observed distribution of p during GRBs is not consistent with a δ-function distribution or a universal p value, with the width of the distribution ≥0.54. The distributions of p during X-ray afterglows are also investigated and found to be inconsistent with a δ-function distribution. The p distributions in blazars and pulsar wind nebulae are also broad, inconsistent with a δ-function distribution.