Einstein published his first paper on relativistic cosmology in 1917, in which he added this cosmological constant to his field equations in order to force them to model a static universe.

In 1917, Einstein applied his theory to the universe as a whole, initiating the field of relativistic cosmology.

Ever more precise solar system tests confirmed the theory's predictive power, and relativistic cosmology, too, became amenable to direct observational tests.

* 1966 — Stephen Hawking and George Ellis show that any plausible general relativistic cosmology is singular

There he met the theoretical cosmologist R. C. Tolman, and studied relativistic cosmology.

A modification of Newton's theory would also imply a modification of general relativistic cosmology in as much as Newtonian cosmology is the limit of Friedman cosmology.

In the later years of his career, Tolman became increasingly interested in the application of thermodynamics to relativistic systems, and cosmology, work that culminated in an important 1934 monograph.

Indeed a critical analysis of the scientific content of Eureka reveals a non-causal correspondence with modern cosmology due to the assumption of an evolving Universe, but excludes the anachronistic anticipation of relativistic concepts such as black holes.

However, Einstein believed that the universe was apparently static, and since a static cosmology was not supported by the general relativistic field equations, he added a cosmological constant Λ to the field equations, which became

* John Wainwright ( dynamical systems techniques in relativistic cosmology, exact solutions )

Amal Kumar Raychaudhuri () ( 14 September 1923 – 18 June 2005 ) was a leading physicist well known for his contributions to relativistic cosmology, particularly Raychaudhuri's equation, which is a key ingredient in proving the Penrose-Hawking singularity theorems of general relativity.

The Navier – Stokes equations assume that the fluid being studied is a continuum ( it is infinitely divisible and not composed of particles such as atoms or molecules ), and is not moving at relativistic velocities.

In fluid mechanics and astrophysics, the relativistic Euler equations are a generalization of the Euler equations that account for the effects of special relativity.

Here is the relativistic rest energy density of the fluid, is the fluid pressure, is the four-velocity of the fluid, and is the Minkowski metric tensor with signature.

The relativistic Euler equations may be applied to calculate the speed of sound in a fluid with a relativistic equation of state ( that is, one in which the pressure is comparable with the internal energy density, including the rest energy ; where is the classical internal energy per unit mass ).

The speed of light in a colinear moving fluid is predicted accurately by the colinear case of the relativistic formula.

In relativistic physics, Supplee's paradox ( also called the submarine paradox ) arises when considering the buoyant force exerted on a relativistic bullet immersed in a fluid subject to an ambient gravitational field.

If a bullet with neutral buoyancy passes through a fluid at a relativistic speed, will its increased mass in the fluid's frame of reference cause it to sink, or will the fluid's increased mass in the bullet's frame of reference cause it to rise?

In this context, gravity wave refers to a classical fluid wave, and is completely unrelated to the relativistic gravitational wave.

The stress-energy tensor of a relativistic fluid can be written in the form

Special relativistic, gravitational, and cosmological redshifts can be understood under the umbrella of frame transformation laws.

Before the present general relativistic cosmological model was developed, Albert Einstein proposed a way to dynamically stabilize a cosmological scenario that would necessarily collapse in on itself due to the gravitational attraction of the matter constituents in the universe.

Wilhelm Anderson applied a relativistic correction to this model, giving rise to a maximum possible mass of approximately 1. 37 kg.

The twin paradox illustrates a feature of the special relativistic spacetime model, the Minkowski space.

Some alternative models replace the black hole with a newly formed magnetar, although most other aspects of the model ( the collapse of the core of a massive star and the formation of relativistic jets ) are the same.

In this model, pre-existing low-energy photons are scattered by relativistic electrons within the explosion, augmenting their energy by a large factor and transforming them into gamma-rays.

Arnold Sommerfeld introduced the fine-structure constant in 1916, as part of his theory of the relativistic deviations of atomic spectral lines from the predictions of the Bohr model.

* 1915 Arnold Sommerfeld develops a modified Bohr atomic model with elliptic orbits to explain relativistic fine structure

The theory of relativistic heat conduction is a model that is compatible with the theory of special relativity.

Alterations to the Fourier model provided for a relativistic model of heat conduction, avoiding this problem.

Paul Dirac, for example, used algebraic constructions to produce a relativistic model for the electron, predicting its magnetic moment and the existence of its antiparticle, the positron.

According to the modern, quantum-mechanical understanding of the hydrogen atom, the average distance between electron and proton is ≈ 1. 5a < sub > 0 </ sub >,< ref > Modern physics, by Serway, Moses, Moyer, Example 8. 9, p284 The value 1. 5a < sub > 0 </ sub > is approximate, not exact, because it neglects reduced mass, fine structure effects ( such as relativistic corrections ), and other such small effects .</ ref > somewhat different than the value in the Bohr model (≈ a < sub > 0 </ sub >), but certainly the same order of magnitude.

A simple model of beaming however, illustrates the basic relativistic effects connecting the luminosity emitted in the rest frame of the jet, S < sub > e </ sub > and the luminosity observed on Earth, S < sub > o </ sub >.

He wrote an expression for a parametrized unit hyperbola, which other authors later used as a model for relativistic velocity.

In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative scalar field theory.

* Arnold Sommerfeld develops a modified Bohr atomic model with elliptic orbits to explain relativistic fine structure.

His research on quasars has included development of the relativistic blast wave model for variability, introduction of reverberation mapping to analyze variable emission line profiles, the two-phase model for quasar emission line regions, and the development of the theory of coronae and winds from accretion disks.

For a hydrogenic atom, the gross structure energy levels only depend on the principal quantum number n. However, a more accurate model takes into account relativistic and spin effects, which break the degeneracy of the energy levels and split the spectral lines.

The relativistic model was developed in 1964 by three independent groups: Robert Brout and Francois Englert ; Peter Higgs ; and Gerald Guralnik, C. R. Hagen, and Tom Kibble.

As long as we stay below relativistic speeds ( see Relativistic dynamics ), this model will accurately simulate all relevant behavior.

The sine-Gordon equation is a relativistic wave equation in 1 + 1 dimensions that also exhibits the soliton phenomenon and which became an important model of solvable relativistic field theory.