In special relativity, energy is closely related to momentum. Just as space and time in this theory are different aspects of a larger entity called space-time, energy and momentum are simply different aspects of a uniform, four-dimensional quantity that physicists call four moments. Therefore, if energy is a source of gravity, momentum must also be a source. The same applies to quantities directly related to energy and momentum, namely internal pressure and tension. Taken together, in general relativity, it is mass, energy, momentum, pressure and tension that serve as gravitational sources: they are, as matter tells space-time how it should bend. In the mathematical formulation of the theory, all these quantities are only aspects of a more general physical quantity called the energy-momentum tensor. [21] Einstein`s field equations are nonlinear and are considered difficult to solve. Einstein used approximation methods to develop the first predictions of the theory. But in 1916, astrophysicist Karl Schwarzschild found the first non-trivial exact solution of Einstein`s field equations, the Schwarzschild metric. This solution laid the groundwork for describing the final stages of gravitational collapse and the objects now known as black holes.
In the same year, the first steps were taken to generalize the Schwarzschild solution to electrically charged objects, eventually leading to the Reissner–Nordström solution, which is now associated with electrically charged black holes. [7] In 1917, Einstein applied his theory to the universe as a whole, establishing the field of relativistic cosmology. In accordance with contemporary thought, he assumed a static universe and added a new parameter – the cosmological constant – to his original field equations to fit this observational assumption. [8] By 1929, however, the work of Hubble and others had shown that our universe was expanding. This can easily be described by the expanding cosmological solutions found by Friedmann in 1922, which do not require a cosmological constant. Lemaître used these solutions to formulate the first version of the Big Bang models, in which our universe evolved from an extremely hot and dense previous state. [9] Einstein later declared that the cosmological constant was the greatest mistake of his life. [10] Unlike all other modern theories of fundamental interactions, general relativity is a classical theory: it does not include the effects of quantum physics. The search for a quantum version of general relativity answers one of the most fundamental open questions in physics. Although there are promising candidates for such a theory of quantum gravity, especially string theory and loop quantum gravity, there is currently no coherent and complete theory. It has long been hoped that a theory of quantum gravity would also eliminate another problematic feature of general relativity: the presence of spatiotemporal singularities. These singularities are limits (“sharp edges”) of space-time, where geometry is poorly defined, so that general relativity itself loses its predictive power.
In addition, there are so-called singularity theorems that predict that such singularities must exist in the universe if the laws of general relativity were valid without quantum modifications. The best known examples are the singularities associated with model universes that describe black holes and the beginning of the universe. [44] Franco Selleri and Antony Valentini are examples of prominent physicists who support neo-Lorentz explanations of general relativity. [108] Some exact solutions in general relativity, such as the Alcubierre drive, are examples of distortion drive, but these solutions require an exotic distribution of matter and generally suffer from semiclassical instability. [150] Over the past century, numerous experiments have confirmed the validity of special and general relativity. In the first major test of general relativity in 1919, astronomers measured the deflection of light from distant stars as starlight passed near our sun, proving that gravity actually distorts or bends space. Einstein`s equations are at the heart of general relativity. They provide a precise formulation of the relationship between the geometry of space-time and the properties of matter in the language of mathematics. Specifically, they are formulated using the concepts of Riemannian geometry, in which the geometric properties of a space (or spacetime) are described by a quantity called metric.
The metric encodes the information needed to calculate basic geometric concepts of distance and angle in curved space (or spacetime). Several physicists, including Einstein, were looking for a theory that would reconcile Newton`s law of gravity and special relativity. Only Einstein`s theory proved consistent with experiments and observations. To understand the basic ideas of the theory, it is instructive to follow Einstein`s thought between 1907 and 1915, from his simple thought experiment with a free-falling observer to his entirely geometric theory of gravity. [1] 1962 Hermann Bondi, M.
