1.
General relativity
–
General relativity is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. General relativity generalizes special relativity and Newtons law of gravitation, providing a unified description of gravity as a geometric property of space and time. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter, the relation is specified by the Einstein field equations, a system of partial differential equations. Examples of such differences include gravitational time dilation, gravitational lensing, the redshift of light. The predictions of relativity have been confirmed in all observations. Although general relativity is not the only theory of gravity. Einsteins theory has important astrophysical implications, for example, it implies the existence of black holes—regions of space in which space and time are distorted in such a way that nothing, not even light, can escape—as an end-state for massive stars. The bending of light by gravity can lead to the phenomenon of gravitational lensing, General relativity also predicts the existence of gravitational waves, which have since been observed directly by physics collaboration LIGO. In addition, general relativity is the basis of current cosmological models of an expanding universe. Soon after publishing the special theory of relativity in 1905, Einstein started thinking about how to incorporate gravity into his new relativistic framework. In 1907, beginning with a thought experiment involving an observer in free fall. After numerous detours and false starts, his work culminated in the presentation to the Prussian Academy of Science in November 1915 of what are now known as the Einstein field equations. These equations specify how the geometry of space and time is influenced by whatever matter and radiation are present, the Einstein field equations are nonlinear and very difficult to solve. Einstein used approximation methods in working out initial predictions of the theory, but as early as 1916, the astrophysicist Karl Schwarzschild found the first non-trivial exact solution to the Einstein field equations, the Schwarzschild metric. This solution laid the groundwork for the description of the stages of gravitational collapse. In 1917, Einstein applied his theory to the universe as a whole, in line with contemporary thinking, he assumed a static universe, adding a new parameter to his original field equations—the cosmological constant—to match that observational presumption. By 1929, however, the work of Hubble and others had shown that our universe is expanding and this is readily 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 earliest version of the Big Bang models, in which our universe has evolved from an extremely hot, Einstein later declared the cosmological constant the biggest blunder of his life

2.
Black hole
–
A black hole is a region of spacetime exhibiting such strong gravitational effects that nothing—not even particles and electromagnetic radiation such as light—can escape from inside it. The theory of relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of the region from which no escape is possible is called the event horizon, although the event horizon has an enormous effect on the fate and circumstances of an object crossing it, no locally detectable features appear to be observed. In many ways a black hole acts like a black body. Moreover, quantum theory in curved spacetime predicts that event horizons emit Hawking radiation. This temperature is on the order of billionths of a kelvin for black holes of stellar mass, objects whose gravitational fields are too strong for light to escape were first considered in the 18th century by John Michell and Pierre-Simon Laplace. Black holes were considered a mathematical curiosity, it was during the 1960s that theoretical work showed they were a generic prediction of general relativity. The discovery of neutron stars sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality, black holes of stellar mass are expected to form when very massive stars collapse at the end of their life cycle. After a black hole has formed, it can continue to grow by absorbing mass from its surroundings, by absorbing other stars and merging with other black holes, supermassive black holes of millions of solar masses may form. There is general consensus that supermassive black holes exist in the centers of most galaxies, despite its invisible interior, the presence of a black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as visible light. Matter that falls onto a black hole can form an accretion disk heated by friction. If there are other stars orbiting a black hole, their orbits can be used to determine the black holes mass, such observations can be used to exclude possible alternatives such as neutron stars.3 million solar masses. On 15 June 2016, a detection of a gravitational wave event from colliding black holes was announced. The idea of a body so massive that light could not escape was briefly proposed by astronomical pioneer John Michell in a letter published in 1783-4. Michell correctly noted that such supermassive but non-radiating bodies might be detectable through their effects on nearby visible bodies. In 1915, Albert Einstein developed his theory of general relativity, only a few months later, Karl Schwarzschild found a solution to the Einstein field equations, which describes the gravitational field of a point mass and a spherical mass. A few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the solution for the point mass. This solution had a peculiar behaviour at what is now called the Schwarzschild radius, the nature of this surface was not quite understood at the time

3.
Loop quantum gravity
–
Loop quantum gravity is a theory that attempts to describe the quantum properties of the universe and gravity. It is also a theory of quantum spacetime because, according to relativity, gravity is a manifestation of the geometry of spacetime. LQG is an attempt to merge quantum mechanics and general relativity, from the point of view of Einsteins theory, it comes as no surprise that all attempts to treat gravity simply like one more quantum force have failed. According to Einstein, gravity is not a force – it is a property of space-time itself, Loop quantum gravity is an attempt to develop a quantum theory of gravity based directly on Einsteins geometrical formulation. The main output of the theory is a picture of space where space is granular. The granularity is a consequence of the quantization. It has the nature as the granularity of the photons in the quantum theory of electromagnetism. Here, it is itself that is discrete. In other words, there is a minimum distance possible to travel through it, more precisely, space can be viewed as an extremely fine fabric or network woven of finite loops. These networks of loops are called spin networks, the evolution of a spin network over time is called a spin foam. The predicted size of this structure is the Planck length, which is approximately 10−35 meters, According to the theory, there is no meaning to distance at scales smaller than the Planck scale. Therefore, LQG predicts that not just matter, but space itself, has an atomic structure, today LQG is a vast area of research, developing in several directions, which involves about 30 research groups worldwide. They all share the physical assumptions and the mathematical description of quantum space. Research into the consequences of the theory is proceeding in several directions. Among these, the most well-developed is the application of LQG to cosmology, LQC applies LQG ideas to the study of the early universe and the physics of the Big Bang. Its most spectacular consequence is that the evolution of the universe can be continued beyond the Big Bang, the Big Bang appears thus to be replaced by a sort of cosmic Big Bounce. In 1986, Abhay Ashtekar reformulated Einsteins general relativity in a closer to that of the rest of fundamental physics. Carlo Rovelli and Lee Smolin defined a nonperturbative and background-independent quantum theory of gravity in terms of these loop solutions, in 1994, Rovelli and Smolin showed that the quantum operators of the theory associated to area and volume have a discrete spectrum

4.
AdS/CFT correspondence
–
On one side are anti-de Sitter spaces which are used in theories of quantum gravity, formulated in terms of string theory or M-theory. On the other side of the correspondence are conformal field theories which are quantum field theories, the duality represents a major advance in our understanding of string theory and quantum gravity. It also provides a toolkit for studying strongly coupled quantum field theories. This fact has been used to study aspects of nuclear. The AdS/CFT correspondence was first proposed by Juan Maldacena in late 1997, important aspects of the correspondence were elaborated in articles by Steven Gubser, Igor Klebanov, and Alexander Markovich Polyakov, and by Edward Witten. By 2015, Maldacenas article had over 10,000 citations and our current understanding of gravity is based on Albert Einsteins general theory of relativity. Formulated in 1915, general relativity explains gravity in terms of the geometry of space and time and it is formulated in the language of classical physics developed by physicists such as Isaac Newton and James Clerk Maxwell. The other nongravitational forces are explained in the framework of quantum mechanics, developed in the first half of the twentieth century by a number of different physicists, quantum mechanics provides a radically different way of describing physical phenomena based on probability. Quantum gravity is the branch of physics that seeks to describe gravity using the principles of quantum mechanics, currently, the most popular approach to quantum gravity is string theory, which models elementary particles not as zero-dimensional points but as one-dimensional objects called strings. In the AdS/CFT correspondence, one typically considers theories of quantum gravity derived from string theory or its modern extension, in everyday life, there are three familiar dimensions of space, and there is one dimension of time. Thus, in the language of physics, one says that spacetime is four-dimensional. The quantum gravity theories appearing in the AdS/CFT correspondence are typically obtained from string and this produces a theory in which spacetime has effectively a lower number of dimensions and the extra dimensions are curled up into circles. A standard analogy for compactification is to consider an object such as a garden hose. Thus, an ant crawling inside it would move in two dimensions, the application of quantum mechanics to physical objects such as the electromagnetic field, which are extended in space and time, is known as quantum field theory. In particle physics, quantum field theories form the basis for our understanding of elementary particles, quantum field theories are also used throughout condensed matter physics to model particle-like objects called quasiparticles. In the AdS/CFT correspondence, one considers, in addition to a theory of quantum gravity and this is a particularly symmetric and mathematically well behaved type of quantum field theory. In the AdS/CFT correspondence, one considers string theory or M-theory on an anti-de Sitter background and this means that the geometry of spacetime is described in terms of a certain vacuum solution of Einsteins equation called anti-de Sitter space. It is closely related to space, which can be viewed as a disk as illustrated on the right

5.
String theory
–
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. It describes how strings propagate through space and interact with each other. On distance scales larger than the scale, a string looks just like an ordinary particle, with its mass, charge. In string theory, one of the vibrational states of the string corresponds to the graviton. Thus string theory is a theory of quantum gravity, String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. Despite much work on problems, it is not known to what extent string theory describes the real world or how much freedom the theory allows to choose the details. String theory was first studied in the late 1960s as a theory of the nuclear force. Subsequently, it was realized that the properties that made string theory unsuitable as a theory of nuclear physics made it a promising candidate for a quantum theory of gravity. The earliest version of string theory, bosonic string theory, incorporated only the class of known as bosons. It later developed into superstring theory, which posits a connection called supersymmetry between bosons and the class of particles called fermions. In late 1997, theorists discovered an important relationship called the AdS/CFT correspondence, one of the challenges of string theory is that the full theory does not have a satisfactory definition in all circumstances. Another issue is that the theory is thought to describe an enormous landscape of possible universes, and these issues have led some in the community to criticize these approaches to physics and question the value of continued research on string theory unification. In the twentieth century, two theoretical frameworks emerged for formulating the laws of physics, one of these frameworks was Albert Einsteins general theory of relativity, a theory that explains the force of gravity and the structure of space and time. The other was quantum mechanics, a different formalism for describing physical phenomena using probability. In spite of successes, there are still many problems that remain to be solved. One of the deepest problems in physics is the problem of quantum gravity. The general theory of relativity is formulated within the framework of classical physics, in addition to the problem of developing a consistent theory of quantum gravity, there are many other fundamental problems in the physics of atomic nuclei, black holes, and the early universe. String theory is a framework that attempts to address these questions

6.
Edward Witten
–
Edward Witten is an American theoretical physicist and professor of mathematical physics at the Institute for Advanced Study in Princeton, New Jersey. Witten is a researcher in string theory, quantum gravity, supersymmetric quantum field theories, in addition to his contributions to physics, Wittens work has significantly impacted pure mathematics. In 1990 he became the first and so far the only physicist to be awarded a Fields Medal by the International Mathematical Union, in 2004, Time magazine stated that Witten is widely thought to be the worlds smartest living theoretical physicist. Witten was born in Baltimore, Maryland, to a Jewish family and he is the son of Lorraine Witten and Louis Witten, a theoretical physicist specializing in gravitation and general relativity. Witten attended the Park School of Baltimore, and received his Bachelor of Arts with a major in history and he published articles in The New Republic and The Nation. In 1968, Witten published an article in The Nation arguing that the New Left had no strategy and he worked briefly for George McGoverns presidential campaign. Witten attended the University of Wisconsin–Madison for one semester as a graduate student before dropping out. He held a fellowship at Harvard University, visited Oxford University, was a fellow in the Harvard Society of Fellows. Witten was awarded the Fields Medal by the International Mathematical Union in 1990, Time and again he has surprised the mathematical community by a brilliant application of physical insight leading to new and deep mathematical theorems. E has made an impact on contemporary mathematics. In his hands physics is once again providing a source of inspiration. As an example of Wittens work in mathematics, Atiyah cites his application of techniques from quantum field theory to the mathematical subject of low-dimensional topology. In particular, Witten realized that a theory now called Chern–Simons theory could provide a framework for understanding the mathematical theory of knots. Another result for which Witten was awarded the Fields Medal was his proof in 1981 of the energy theorem in general relativity. This theorem asserts that the energy of a gravitating system is always positive. It establishes Minkowski space as a ground state of the gravitational field. While the original proof of this due to Richard Schoen and Shing-Tung Yau used variational methods. Wittens work gave a proof of a classical result, the Morse inequalities

7.
Cosmological constant
–
In cosmology, the cosmological constant is the value of the energy density of the vacuum of space. It was originally introduced by Albert Einstein in 1917 as an addition to his theory of relativity to hold back gravity and achieve a static universe. Einstein abandoned the concept after Hubbles 1929 discovery that all galaxies outside the Local Group are moving away from each other, from 1929 until the early 1990s, most cosmology researchers assumed the cosmological constant to be zero. When Λ is zero, this reduces to the field equation of general relativity. When T is zero, the equation describes empty space. The cosmological constant has the effect as an intrinsic energy density of the vacuum. In this context, it is moved onto the right-hand side of the equation, and defined with a proportionality factor of 8π, Λ = 8πρvac. It is common to quote values of energy density directly, though using the name cosmological constant. A positive vacuum energy density resulting from a cosmological constant implies a negative pressure, if the energy density is positive, the associated negative pressure will drive an accelerated expansion of the universe, as observed. This ratio is usually denoted ΩΛ, and is estimated to be 0. 6911±0.0062, according to results published by the Planck Collaboration in 2015. In a flat universe ΩΛ is the fraction of the energy of the due to the cosmological constant. Another ratio that is used by scientists is the equation of state, usually denoted w and this ratio is w = −1 for a true cosmological constant, and is generally different for alternative time-varying forms of vacuum energy such as quintessence. To counteract this possibility, Einstein added the cosmological constant, likewise, a universe that contracts slightly will continue contracting. However, the cosmological constant remained a subject of theoretical and empirical interest, empirically, the onslaught of cosmological data in the past decades strongly suggests that our universe has a positive cosmological constant. The explanation of this small but positive value is a theoretical challenge. Observations announced in 1998 of distance–redshift relation for Type Ia supernovae indicated that the expansion of the universe is accelerating. When combined with measurements of the microwave background radiation these implied a value of ΩΛ ≈0.7. There are other causes of an accelerating universe, such as quintessence

8.
Quantum gravity
–
Quantum gravity is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics, and where quantum effects cannot be ignored. The current understanding of gravity is based on Albert Einsteins general theory of relativity, the necessity of a quantum mechanical description of gravity is sometimes said to follow from the fact that one cannot consistently couple a classical system to a quantum one. This is false as is shown, for example, by Walds explicit construction of a consistent semiclassical theory, the problem is that the theory one gets in this way is not renormalizable and therefore cannot be used to make meaningful physical predictions. As a result, theorists have taken up more radical approaches to the problem of quantum gravity, a theory of quantum gravity that is also a grand unification of all known interactions is sometimes referred to as The Theory of Everything. As a result, quantum gravity is a mainly theoretical enterprise, much of the difficulty in meshing these theories at all energy scales comes from the different assumptions that these theories make on how the universe works. Quantum field theory, if conceived of as a theory of particles, General relativity models gravity as a curvature within space-time that changes as a gravitational mass moves. Historically, the most obvious way of combining the two ran quickly into what is known as the renormalization problem, another possibility is to focus on fields rather than on particles, which are just one way of characterizing certain fields in very special spacetimes. This solves worries about consistency, but does not appear to lead to a version of full general theory of relativity. Quantum gravity can be treated as a field theory. Effective quantum field theories come with some high-energy cutoff, beyond which we do not expect that the theory provides a description of nature. The infinities then become large but finite quantities depending on this finite cutoff scale and this same logic works just as well for the highly successful theory of low-energy pions as for quantum gravity. Indeed, the first quantum-mechanical corrections to graviton-scattering and Newtons law of gravitation have been explicitly computed. In fact, gravity is in ways a much better quantum field theory than the Standard Model. Specifically, the problem of combining quantum mechanics and gravity becomes an issue only at high energies. This problem must be put in the context, however. While there is no proof of the existence of gravitons. The predicted find would result in the classification of the graviton as a force similar to the photon of the electromagnetic field. Many of the notions of a unified theory of physics since the 1970s assume, and to some degree depend upon

9.
Black hole information paradox
–
The black hole information paradox is a puzzle resulting from the combination of quantum mechanics and general relativity. Calculations suggest that information could permanently disappear in a black hole. A fundamental postulate of the Copenhagen interpretation of quantum mechanics is that information about a system is encoded in its wave function up to when the wave function collapses. The evolution of the function is determined by a unitary operator. There are two principles in play, Quantum determinism means that given a present wave function, its future changes are uniquely determined by the evolution operator. Reversibility refers to the fact that the operator has an inverse. The combination of the two means that information must always be preserved, specifically, Hawkings calculations indicated that black hole evaporation via Hawking radiation does not preserve information. Today, many believe that the holographic principle demonstrates that Hawkings conclusion was incorrect. In 2004 Hawking himself conceded a bet he had made, agreeing that black hole evaporation does in fact preserve information, in 1975, Stephen Hawking and Jacob Bekenstein showed that black holes should slowly radiate away energy, which poses a problem. From the no-hair theorem, one would expect the Hawking radiation to be independent of the material entering the black hole. This violates Liouvilles theorem and presents a physical paradox, but since everything within the interior of the black hole will hit the singularity within a finite time, the part which is traced over partially might disappear completely from the physical system. Hawking remained convinced that the equations of black-hole thermodynamics together with the no-hair theorem led to the conclusion that quantum information may be destroyed and this annoyed many physicists, notably John Preskill, who bet Hawking and Kip Thorne in 1997 that information was not lost in black holes. The solution to the problem that concluded the battle is the holographic principle, with this, Susskind quashes Hawking in quarrel over quantum quandary. There are various ideas about how the paradox is solved and his argument assumes the unitarity of the AdS/CFT correspondence which implies that an AdS black hole that is dual to a thermal conformal field theory. When announcing his result, Hawking also conceded the 1997 bet, according to Roger Penrose, loss of unitarity in quantum systems is not a problem, quantum measurements are by themselves already non-unitary. Penrose claims that quantum systems will in no longer evolve unitarily as soon as gravitation comes into play. The Conformal Cyclic Cosmology advocated by Penrose critically depends on the condition that information is in fact lost in black holes, the significance of the findings was subsequently debated by others. Information is irretrievably lostAdvantage, Seems to be a consequence of relatively non-controversial calculation based on semiclassical gravity

10.
Causal sets
–
The causal sets program is an approach to quantum gravity. Its founding principles are that spacetime is discrete and that spacetime events are related by a partial order. This partial order has the meaning of the causality relations between spacetime events. The conformal factor that is left undetermined is related to the volume of regions in the spacetime and this volume factor can be recovered by specifying a volume element for each space time point. The volume of a space time region could then be found by counting the number of points in that region, causal sets was initiated by Rafael Sorkin who continues to be the main proponent of the program. He has coined the slogan Order + Number = Geometry to characterize the above argument, the program provides a theory in which space time is fundamentally discrete while retaining local Lorentz invariance. Ruth Kastner developed the relativistic transactional interpretation which is argued that it can provide the dynamics for the causal sets program, a causal set is a set C with a partial order relation ⪯ that is Reflexive, For all x ∈ C, we have x ⪯ x. Antisymmetric, For all x, y ∈ C, we have x ⪯ y ⪯ x ⟹ x = y, transitive, For all x, y, z ∈ C, we have x ⪯ y ⪯ z implies x ⪯ z. Locally finite, For all x, z ∈ C, we have card < ∞, here card denotes the cardinality of a set A. Well write x ≺ y if x ⪯ y and x ≠ y, the set C represents the set of spacetime events and the order relation ⪯ represents the causal relationship between events. Although this definition uses the convention we could have chosen the irreflexive convention in which the order relation is irreflexive. The causal relation of a Lorentzian manifold satisfies the first three conditions and it is the local finiteness condition that introduces spacetime discreteness. Given a causal set we may ask whether it can be embedded into a Lorentzian manifold, an embedding would be a map taking elements of the causal set into points in the manifold such that the order relation of the causal set matches the causal ordering of the manifold. A further criterion is needed however before the embedding is suitable, if, on average, the number of causal set elements mapped into a region of the manifold is proportional to the volume of the region then the embedding is said to be faithful. This is called the Hauptvermutung, meaning fundamental conjecture and it is difficult to define this conjecture precisely because it is difficult to decide when two spacetimes are similar on large scales. Modelling spacetime as a set would require us to restrict attention to those causal sets that are manifold-like. Given a causal set this is a property to determine. The difficulty of determining whether a set can be embedded into a manifold can be approached from the other direction