Gravitational singularity in the context of Geodesics in general relativity

General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1916 and is the accepted description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy, momentum and stress of whatever is present, including matter and radiation. The relation is specified by the Einstein field equations, a system of second-order partial differential equations.

Newton's law of universal gravitation, which describes gravity in classical mechanics, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity, however, are beyond Newton's law of universal gravitation in classical physics. These predictions concern the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light, and include gravitational time dilation, gravitational lensing, the gravitational redshift of light, the Shapiro time delay and singularities/black holes. So far, all tests of general relativity have been in agreement with the theory. The time-dependent solutions of general relativity enable us to extrapolate the history of the universe into the past and future, and have provided the modern framework for cosmology, thus leading to the discovery of the Big Bang and cosmic microwave background radiation. Despite the introduction of a number of alternative theories, general relativity continues to be the simplest theory consistent with experimental data.

An accretion disk is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a massive central body. The central body is most frequently a star. Friction, uneven irradiance, magnetohydrodynamic effects, and other forces induce instabilities causing orbiting material in the disk to spiral inward toward the central body. Gravitational and frictional forces compress and raise the temperature of the material, causing the emission of electromagnetic radiation. The frequency range of that radiation depends on the central object's mass. Accretion disks of young stars and protostars radiate in the infrared; those around neutron stars and black holes in the X-ray part of the spectrum. The study of oscillation modes in accretion disks is referred to as diskoseismology.

Physics beyond the Standard Model (BSM) refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the inability to explain the fundamental parameters of the Standard Model, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy. Another problem lies within the mathematical framework of the Standard Model itself: the Standard Model is inconsistent with that of general relativity, and one or both theories break down under certain conditions, such as spacetime singularities like the Big Bang and black hole event horizons.

Theories that lie beyond the Standard Model include various extensions of the standard model through supersymmetry, such as the Minimal Supersymmetric Standard Model (MSSM) and Next-to-Minimal Supersymmetric Standard Model (NMSSM), and entirely novel explanations, such as string theory, M-theory, and extra dimensions. As these theories tend to reproduce the entirety of current phenomena, the question of which theory is the right one, or at least the "best step" towards a Theory of Everything, can only be settled via experiments, and is one of the most active areas of research in both theoretical and experimental physics.

Quantum gravity (QG) is a field of theoretical physics that seeks unification of the theory of gravity with the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, as well as in the early stages of the universe moments after the Big Bang.

Three of the four fundamental forces of nature are described within the framework of quantum mechanics and quantum field theory: the electromagnetic interaction, the strong force, and the weak force; this leaves gravity as the only interaction that has not been fully accommodated. The current understanding of gravity is based on Albert Einstein's general theory of relativity, which incorporates his theory of special relativity and deeply modifies the understanding of concepts like time and space. Although general relativity is highly regarded for its elegance and accuracy, it has limitations: the gravitational singularities inside black holes, the ad hoc postulation of dark matter, as well as dark energy and its relation to the cosmological constant are among the current unsolved mysteries regarding gravity, all of which signal the collapse of the general theory of relativity at different scales and highlight the need for a gravitational theory that goes into the quantum realm. At distances close to the Planck length, like those near the center of a black hole, quantum fluctuations of spacetime are expected to play an important role. Finally, the discrepancies between the predicted value for the vacuum energy and the observed values (which, depending on considerations, can be of 60 or 120 orders of magnitude) highlight the necessity for a quantum theory of gravity.

A black hole is an astronomical body so compact that its gravity prevents anything, including light, from escaping. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. The boundary of no escape is called the event horizon. In general relativity, a black hole's event horizon seals an object's fate but produces no locally detectable change when crossed. General relativity also predicts that every black hole should have a central singularity, where the curvature of spacetime is infinite.

In many ways, a black hole acts like an ideal black body, as it reflects no light. Quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is of the order of billionths of a kelvin for stellar black holes, making it essentially impossible to observe directly.

A Belinski–Khalatnikov–Lifshitz (BKL) singularity is a model of the dynamic evolution of the universe near the initial gravitational singularity, described by an anisotropic, chaotic solution of the Einstein field equation of gravitation. According to this model, the universe is chaotically oscillating around a gravitational singularity in which time and space become equal to zero or, equivalently, the spacetime curvature becomes infinitely big. This singularity is physically real in the sense that it is a necessary property of the solution, and will appear also in the exact solution of those equations. The singularity is not artificially created by the assumptions and simplifications made by the other special solutions such as the Friedmann–Lemaître–Robertson–Walker, quasi-isotropic, and Kasner solutions.

The model is named after its authors Vladimir Belinski, Isaak Khalatnikov, and Evgeny Lifshitz, then working at the Landau Institute for Theoretical Physics.

Fuzzballs are hypothetical objects in superstring theory, intended to provide a fully quantum description of the black holes predicted by general relativity.

The fuzzball hypothesis dispenses with the singularity at the heart of a black hole by positing that the entire region within the black hole's event horizon is actually an extended object: a ball of strings, which are advanced as the ultimate building blocks of matter and light. Under string theory, strings are bundles of energy vibrating in complex ways in both the three familiar dimensions of space as well as in extra dimensions. Fuzzballs provide resolutions to two major open problems in black hole physics. First, they avoid the gravitational singularity that exists within the event horizon of a black hole. General relativity predicts that at the singularity, the curvature of spacetime becomes infinite, and it cannot determine the fate of matter and energy that falls into it. Physicists generally believe that the singularity is not a real phenomenon, and proposed theories of quantum gravity, such as superstring theory, are expected to explain its true nature. Second, they resolve the black hole information paradox: the quantum information of matter falling into a black hole is trapped behind the event horizon, and seems to disappear from the universe entirely when the black hole evaporates due to Hawking radiation. This would violate a fundamental law of quantum mechanics requiring that quantum information be conserved.

A de Sitter universe is a cosmological solution to the Einstein field equations of general relativity, named after Willem de Sitter. It models the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are dominated by the cosmological constant, thought to correspond to dark energy in our universe or the inflaton field in the early universe. According to the models of inflation and current observations of the accelerating universe, the concordance models of physical cosmology are converging on a consistent model where our universe was best described as a de Sitter universe at about a time ${\displaystyle t}$ = 10 s after the fiducial Big Bang singularity, and far into the future.