Presence Of Weak Gravitational Field Research Articles

The plane piston problem with weak gravitational field in a dusty gas

In the present paper, the nature of a plane piston moving with constant velocity in a gas with dust particles in the presence of weak gravitational field is analyzed by using a combination of two methods, viz., perturbation method and similarity transformation. In perturbation method the physical variables are expanded as a series of small parameter. The zeroth order result represents the uniform flow which is affected by dust particles of the mixture without gravity. The first order result shows the consequence of applied gravity in a dusty gas. The effect of dust particles present in the gas and applied gravity on the distribution of flow variables has been discussed for the case of weak and strong shock wave. The structure of the shock wave front is also discussed.

Relativistic gas in a Schwarzschild metric

A relativistic gas in a Schwarzschild metric is studied within the framework of a relativistic Boltzmann equation in the presence of gravitational fields, where Marle’s model for the collision operator of the Boltzmann equation is employed. The transport coefficients of the bulk and shear viscosities and thermal conductivity are determined from the Chapman–Enskog method. It is shown that the transport coefficients depend on the gravitational potential. Expressions for the transport coefficients in the presence of weak gravitational fields in the non-relativistic (low temperature) and ultra-relativistic (high temperature) limiting cases are given. Apart from the temperature gradient the heat flux has two relativistic terms. The first one, proposed by Eckart, is due to the inertia of energy and represents an isothermal heat flux when matter is accelerated. The other, suggested by Tolman, is proportional to the gravitational potential gradient and indicates that—in the absence of an acceleration field—a state of equilibrium of a relativistic gas in a gravitational field can be attained only if the temperature gradient is counterbalanced by a gravitational potential gradient.

Particle motion in weak relativistic gravitational fields

We derive the geodesic equation of motion in the presence of weak gravitational fields produced by relativistic sources such as cosmic strings, decomposed into scalar, vector and tensor parts. To test the result, we perform the first N-body simulations with relativistic weak gravitational external fields. Our test case is a moving straight string, for which we recover the well-known result for the impulse on nonrelativistic particles. We find that the vector (gravito-magnetic) force is an essential contributor. Our results mean that it is now possible to incorporate straightforwardly into N-body simulations all weak relativistic sources, including networks of cosmic defects.

The Redshifts in Relativity

The progress of modern cosmology took off in 1917 when A. Einstein published his paper on general theory of relativity extending his work of special theory of relativity (1905). In 1922 Alexander Friedmann constructed a mathematical model for expanding Universe that had a big bang in remote past. The experimental evidences could come in 1929 by the pioneering work on nebular red shifts by Edwin Hubble and Milton Humason. Doppler’s red shift for light also comes as a deduction of special theory of relativity which provides a fundamental formalism for observational astronomy. It can also be deduced from cosmological red shift arising from the curvature of space time warp of the Universe depending on the evolution model opted for the Universe. The gravitational red shift comes as a consequence of the principle of equivalence in presence of weak gravitational field which expresses the identity of the gravitational and inertial mass. The gravitation itself is a manifestation of curvature in space time. Massive objects show noticeable bending of light near it which explains well the apparent images formation when added with the gravitational fall of the photons towards the object. Special and general theory of relativity can be realized as the best mathematical narrations of the cosmic dance. This paper highlights the experimental evidences in favor of relativity and their applications in cosmology which could be possible with the invention of ultra high precision instruments in last century.

Atomic clocks and inertial sensors

We show that the language of atom interferometry provides a unified picture for microwave and opticalatomic clocks as well as for gravito-inertial sensors. The sensitivity and accuracy of these devices is now such that a new theoretical framework common to all these interferometers is required that includes: (a) a fully quantum mechanical treatment of the atomic motion in free space and in the presence of a gravitational field (most cold-atom interferometric devices use atoms in ``free fall'' in a fountain geometry); (b) an account of simultaneous actions of gravitational and electromagnetic fields in the interaction zones; (c) a second quantization of the matter fields to take into account their fermionic or bosonic character in order to discuss the role of coherent sources and their noise properties; (d) a covariant treatment including spin to evaluate general relativistic effects. A theoretical description of atomic clocks revisited along these lines is presented, using both an exact propagator of atom waves in gravito-inertial fields and a covariant Dirac equation in the presence of weak gravitational fields. Using this framework, recoil effects, spin-related effects, beam curvature effects, the sensitivity to gravito-inertial fields and the influence of the coherence of the atom source are discussed in the context of present and future atomic clocks and gravito-inertial sensors.