Saha Equation for Partially Ionized Relativistic Hydrogen Plasma in Rindler Space

Abstract

It is well-known that the conventional Lorentz transformations are the spacetime coordinate transformations between two inertial frames of references [1]. However, following the principle of equivalence, it is trivial to obtain the space-time transformations between a uniformly accelerated frame and an inertial frame and vice-versa in the same manner as it is done in special theory of relativity [2, 3, 4, 5, 6]. In the present scenario the flat spacetime geometry is called the Rindler space. For the sake of illustration of principle of equivalence, one may state, that a reference frame undergoing an accelerated motion in absence of gravitational field is equivalent to a frame at rest in presence of a gravitational field. Therefore, in the present picture, the magnitude of the uniform acceleration is exactly equal to the strength of gravitational field. We may assume that the gravitational field is produced by a strong gravitating object. We further approximate that the gravitational field is constant within a small domain of special region. Since it is exactly equal to the uniform acceleration of the moving frame, this is also called the local acceleration of the frame.