Related papers: Conceptual Foundations of Special and General Rela…
The Principle of Relativity has so far been understood as the {\it covariance} of laws of Physics with respect to a general class of reference frame transformations. That relativity, however, has only been expressed with the help of {\it…
Einstein's theory of general relativity (GR) provides the best available description of gravity. The recent detection of gravitational waves and the first picture of a black hole have provided spectacular confirmations of GR, as well as…
Einstein's special theory of relativity starts with assumptions about how observations conducted in relatively moving inertial frames must compare. From these assumptions, conclusions can be drawn regarding the laws of physics in any one…
We consider two distinct limits of General Relativity that in contrast to the standard non-relativistic limit can be taken at the level of the Einstein-Hilbert action instead of the equations of motion. One is a non-relativistic limit and…
We introduce a designer approach for extended Brans-Dicke gravity that allows us to obtain the evolution of the scalar field by fixing the Hubble parameter to that of a $w$CDM model. We obtain analytical approximations for $\phi$ as a…
The empirical formula proposed by J. D. Anderson et al. [1] to reproduce the data on the Earth flyby anomalies is derived from special relativity (SR). The transverse Doppler shift together with the addition of velocities account for the…
Modifications of Special Relativity by the introduction of an invariant energy and/or momentum level (so-called Doubly Special Relativity theories, DSR) or by an energy-momentum dependence of the Planck constant (Generalized Uncertainty…
An exact solution of Einstein's field equations for a static spherically symmetric medium with a radially boost invariant energy-momentum tensor is presented. In the limit of an equation of state corresponding to a distribution of radially…
This review presents an overview of various kinds of models -- physical, abstract, mathematical, visual -- that can be used to present the concepts and applications of Einstein's general theory of relativity at the level of undergraduate…
This paper aims to provide teachers with a tool to teach the essential features of special relativity, considering the students' difficulties highlighted by numerous studies. Our proposal presents special relativity as the solution to the…
Equivalence principles are a major part of modern relativity theory. Gravitational shifts can already be calculated within the time domain as motion shifts, and we examine the consequences of reversing this argument and describing motion…
Newtonian gravity can be regarded as a hypothetic-deductive system where the inverse square law is the starting point from which gravitational phenomena are deduced. This operational form of presenting gravity endorses problem solving and…
We note that Einstein's relativistic Doppler formula presents a strange aspect. For incident light received under a fixed non zero angle, the Doppler shift will change from blueshift to redshift (or vice-versa) for some critical relative…
Among the so-called classical tests of general relativity (GR), light bending has been confirmed with an accuracy that increases as times goes by. Here we study the gravitational deflection of photons within the framework of classical and…
The Wheeler-DeWitt Equation represents a tool to study Quantum Gravity and Quantum Cosmology. Its solution in a very general context is, of course, impossible. To this purpose we consider some distortions of General Relativity like…
In the past, Kepler painstakingly derived laws of planetary motion using difficult to understand and hard to follow techniques. In 1843 William Hamilton created and described the quaternions, which extend the complex numbers and can easily…
This is an English translation of the Italian version of an encyclopedia chapter that appeared in the Italian Encyclopedia of the Physical Sciences, edited by Bruno Bertotti (1994). Following requests from colleagues we have decided to make…
We present the special theory of relativity taking the Doppler effect as the starting point, and derive several of its main effects, such as time dilation, length contraction, addition of velocities, and the mass-energy relation, and…
We consider the special and general relativistic extensions of the action principle behind the Schr\"odinger equation distinguishing classical and quantum contributions. Postulating a particular quantum correction to the source term in the…
Using dimensional analysis techniques we present an extension of Newton's gravitational theory built under the assumption that Milgrom's acceleration constant is a fundamental quantity of nature. The gravitational force converges to…