How can Einstein's special and general relativity be explained? Can the future of the universe be predicted according to Einstein's theories? Is the universe one-dimensional or multi-dimensional? Where are we in this universe?

„Singularity Theorems in General Relativity‟ is to describe elaborately some basic results and applications of global aspects in gravitation and cosmology and the singularities therein. This thesis deals with homogeneous, inhomogeneous, isotropic and anisotropic cosmologies and singularities therein. The discussion is based on the use of general relativity and the differential space-time manifold. The space-time singularity theorems and the related theoretical advances towards understanding the structure of space-time was first established by Hawking, Penrose and Geroch. We have tried to give discussion on the basis of their theorems. General relativity models the physical universe as a four dimensional space-time manifold (M, g) which is differentiable, space-time orientable, connected, paracompact, Hausdorff and without boundary. It was realized that though locally the laws of physics are those of special relativity and space-time is very nearly flat rise to a non-flat, curved continuum which would also admit a suitable differential structure. The universe is not simply a random collection of irregular distributed matter, but it is a single entity, all parts of which are connected. When considering the large scale structure of the universe, the basic constituents are galaxies, which are congregation of more than 1010 stars bound together by their mutual gravitational attraction. The universe is the totality of galaxies which are causally connected. Soon after the Einstein‟s field equations were discovered, Friedmann showed that the universe must have originated a finite time ago from an epoch of infinite density and curvatures where all the known physical laws break down which we call „big bang‟. So we cannot predict what was happened in the period of big bang and before big bang. Therefore, we can say that it is a singularity in space-time topology. The Schwarzschild exterior solution of Einstein‟s field equations describes the gravitational fields outside a spherically symmetric star where there is no matter present and space-time is empty. The space-time distance ds for gravitating mass m in coordinates between two infinitesimally separated events is given by the metric;. (1) The above space-time has an apparent singularity at r = 2m as seen by the divergence of metric components of equation (1). It was thought initially that the above represents a singularity in the space-time itself and that physics goes seriously wrong at r = 2m. After some efforts it is realized that this is not a genuine space-time singularity but merely a coordinate defect, and what was really needed was an extension of the Schwarzschild manifold. Such an extension of the spacetime was obtained by Kruskal (1960) and Szekeres (1960) and this may be regarded as an important insight involving a global approach (Chapter–III). However at r = 0 there is a genuine curvature singularity where the Kretschman scalar ., space-time curvature components tend to infinity.A rigorous analysis of global properties of a general space-time was done by Hawking, Penrose and Geroch, who showed that under certain very general and physically reasonable conditions such as the positivity of energy, occurrence of trapped surface and suitable causality condition the space-time singularities must occur as an inevitable feature, as far as a wide range of gravitation theories describing the gravitational forces are concerned (Hawking and Ellis 1973). The existence of space-time singularities follows in the form of future or past incomplete nonspacelike geodesics in the space-time. Such a singularity would arise either in the cosmological scenarios, where it provides the origin of the universe or as the end state of the gravitational collapse of a massive star which has exhausted its nuclear fuel providing the pressure gradient against the inwards pull of gravity. Several global features for space-times were understood during this phase work, which resulted in the development of singularity theorems, which have been applied to further work on the Einstein‟s equations, asymptotic structure of space-time and such other areas.While the above developments represent a notable advance towards understanding the global structure of space-time, most of the problems remain unsolved. Apart from the existence of space-time singularities we presently know very little about the global structure of Einstein‟s equations. The theorems establish the existence of singularities in the form of either future or past incomplete non-spacelike geodesics for a very wide class of space-times. The theorems provide particularly no information on the nature or the physical significance of the singularities predicted. It is not known if the densities and curvatures will necessarily tend towards infinity along the non-spacelike trajectories falling into such singularities predicted by the singularity theorems. Thus, the possibility cannot be ruled out that in many cases the singularity theorems would predict physically genuine singularities; though it is not clear at all under what conditions the theorems must give rise to such curvature singularities. In the case of naked singularities it may be possible to communicate with outside observers far away to affect the dynamics of the outside universe. Hence, no causal effects from the singularity can reach any outside observer for whom the singularity is totally hidden within a black hole which is invisible apart from its possible gravitational effects.In the approximation of the star composed of homogeneous dust without any pressure, the curvature singularity forming as the end state of collapse will be completely covered by the event horizon and would be invisible to any external observer. The hypothesis that the above phenomenon is gravitationally true, that is the singularities forming in general gravitational collapse should always be covered by the event horizon of the gravity, and remains invisible to any external observer is called the cosmic censorship hypothesis. This hypothesis, originally proposed by Penrose, remain unproved as yet in the general case; despite many attempts towards a proof, and has been recognized as one of the most important open problems in general relativity and gravitational physics. However, this throws the black hole dynamics into serious doubt. Our aim is to discuss the global aspects of gravity, and also to discuss some applications of the results which are already available on the global structure of space-time.

the Physics community, to all those interested in ER = EPR, GR = QM and the AdS/CFT correspondence conjecture, you should consider how the multi-fold theory and the E/G conjecture explain and realize them in a multi-fold universe. In a multi-fold universe, gravity emerges from Entanglement through the multi-fold mechanisms. As a result, gravity-like effects appear in between entangled particles, that they be real or virtual. Long range, massless gravity results from entanglement of massless virtual particles. Entanglement of massive virtual particles leads to massive gravity contributions at very smalls scales. Multi-folds mechanisms also result into a spacetime that is discrete, with a random walk fractal structure and non-commutative geometry that is Lorentz invariant and where spacetime nodes and particles can be modeled with microscopic black holes. All these recover General Relativity (GR) at large scales and semi-classical models remain valid till smaller scale than usually expected. Gravity can therefore be added to the Standard Model resulting into what we defined as SMG. This can contribute to resolving several open issues with the Standard Model without New Physics other than gravity, i.e. no new particles or forces. These considerations hints at an even stronger relationship between gravity and the Standard Model. This paper provides references to how AdS(5), the AdS/CFT correspondences, ER=EPR and GR=QM conjectures are encountered in a multi-fold universe and explained microscopically. It leads to the E/G conjecture, that gravity and entanglement explain one another even in our real universe. Outside multi-fold theories, the main additions that we provide and lead to the new interpretation, e.g. the E/G conjecture, come from i) multi-fold mechanisms that allow path integrals to include traversing of the multi-fold, something typically not considered with the wormholes models prevalent with these other conjecture because of transferability challenges in the real universe ii) a SMG model where in-flight right-handed neutrinos suddenly allow for wormhole to be traversed and look like multi-fold even in our real universe.The multi-fold paper [1] proposes contributions to several open problems in physics, like the reconciliation of General Relativity (GR) with Quantum Physics, explaining the origin of gravity proposed as emerging from quantum (EPR- Einstein Podolsky Rosen) entanglement between particles, detailing contributions to dark matter and dark energy, and explaining other Standard Model mysteries without requiring New Physics beyond the Standard Model other than the addition of gravity to the Standard Model Lagrangian. All this is achieved in a multi-fold universe that may well model our real universe, which remains to be validated. With the proposed model of [1], spacetime and Physics are modeled from Planck scales to quantum and macroscopic scales and semi-classical approaches appear valid till very small scales. In [1], it is argued that spacetime is discrete, with a random walk-based fractal structure, fractional and noncommutative at, and above Planck scales (with a 2-D behavior and Lorentz invariance preserved by random walks till the early moments of the universe). Spacetime results from past random walks of particles. Spacetime locations and particles can be modeled as microscopic black holes (Schwarzschild for photons and concretized spacetime coordinates, and metrics between Reisner Nordstrom [2] and Kerr Newman [3] for massive and possibly charged particles – the latter being possibly extremal). Although possibly surprising, [1] recovers results consistent with others (see [4] and its references), while also being able to justify the initial assumptions of black holes from the gravity or entanglement model in a multi-fold universe. The resulting gravity model recovers General Relativity at larger scale, as a 4D process, with massless gravity, but also with massive gravity components at very small scale that make gravity non-negligible at these scales. Semi-classical models also turn out to work well till way smaller scales that usually expected. In this paper, we make a call to the Physics community to pay attention at how like the AdS/CFT correspondence, the ER = EPR and the GR = QM conjectures are encountered and modeled in the multi-fold theory [1,9]: it should, if nothing else, inspire some progress with these conjectures. The paper is intentionally short to maintain the focus on the call to the Physics community, instead of the details that can be found in the references.The results of [1] lead to the E/G conjecture: in a multi-fold universe, entanglement is gravity and gravity is entanglement. In other words, entanglement creates gravity effects and gravity results from entanglement effects. The conjecture is that this statement applies also to our real universe . This result is really essential and the holy grail in our view of work like the AdS/CFT correspondence conjecture, the ER = EPR conjecture and the GR = QM conjecture. From a multi-fold point of view, all these works have so far blocked on challenges with the traversability of wormholes, something that multi-fold mechanisms avoid, while the multi-fold theory also seems to resolve wormhole traversability with the right role played in SMG 2 by in-flight right-handed neutrinos3 . We suggest focusing on [1,5,6,8,10] for more details. The proposed references answer much of these issues in surprising ways. Outside multi-fold theories, the main additions that we provide and lead to the new interpretation, e.g. the E/G conjecture, come from i) multi-fold mechanisms [1] that allow path integrals to include traversing of the multi-fold, something typically not considered with the wormholes models prevalent with these other conjecture because of transferability challenges in the real universe ii) a SMG model where in-flight right-handed neutrinos suddenly allow for wormhole to be traversed and look like multi-fold even in our real universe [8]. More details on the multifold theory and latest developments can be tracked at [7,9].

Conclusion: The detailed exploration of Einstein’s publications leads to the conclusion that his modeling of the double-gravity of photons and the modeling of bending of their paths by the Sun are unrelated. The definition of gravity as the result of bending of space by mass is an unsubstantiated model, which is not causatively based because Gravity was one of the starting axioms that Einstein used to derive gravity. This, according to the Goedeltheorem, is a classic case of circular argumentation, and thus the gravity-property is invalid. Newton’s equations are based on the properties of gravity without a fundamental consideration of the gravity-origin. Comment: Leubner’s discovery of Gravity is independent of Einstein’s and Newton’s models, and did not presume the origin or presence of gravity. The properties of gravity as anti-energy are fully compatible with many observations and properties in the Universe.The absence of Einstein’s space-bending and the discovery that gravity is anti-energy allow explanations and modeling of many observations in the Universe that have not been modeled before. One is the calculation of solar orbit-changes of planetary and other objects since their formation. It also predicts orbit changes until they leave their solar orbits. 6 It also answers to the question of why and when Mars’ surface transitioned from wet to its present ice-age. Without the definition of gravity as space-bending, problems of the mass and bending of the Universe can be ignored. The anti-energy model and the movement of galaxies and stars are well below the speed of light. Thus, the Newton equations for closed systems, e.g. the Sun, can be applied to the Universe.8 The model relates the Hubble-correlation to the average universal mass-loss rate. A condensed derivation of the Hubble-constant with the Leubner-Newton approach is presented in Appendix 2. Detailed information of this model is available in Reference . Hubble-measurements from Earth are dependent on the relative distance and position of the emitting galaxy. This may allow estimating the center of the Universe and its diameter. The modeling of movement and components of the Universe is most successfully achieved by following fundamental rules.