Kähler forms with associated metrics and cohomology classes are shown taking Kähler–Einstein metric.

Here I will show the L-currents formulated for the necessary charge required in string vibrations for the particle generator scheme taken as ∇_(p,q).

This paper attempts to delve into the hierarchy problem of particle physics taking into consideration the Calabi-Yau manifolds and D(p)-Branes.

The existence of the “Naked Singularity” has been shown taking the advantage of the Ring Singularity of the Kerr Black Hole and thereby making the way to manipulate the mathematics by taking the larger root of Δ as zero and thereby vanishing the ergosphere and event horizon making the way for the naked ring singularity which can be easily connected via a cylindrical wormhole and as ‘a wormhole is a black hole without an event horizon’ therefore, this cylindrical connection paved the way for the Einstein-Rosen Bridge allowing particles or null rays to travel from one universe to another ending up in a future directed Cauchy horizon while changing constantly from spatial to temporal and again spatial paving the entrance to another Kerr Black hole (which would act as a white hole) in the other universes.

Based on the hypothesis of the evolving machine intelligence that in essence gives birth to super-intelligent machines, this can be said that as proposed in the previous theories there will be an intelligence evolution hitting a singularity. In this paper we have hypothesized that machines may split into two categories based on the ‘type’ of intelligence explosion resulting one ‘type’ hitting hard singularity while one ‘type’ hitting soft singularity for a specific blow-up case called errored singularity marking the end point is discussed.

Relative time emerges from relative frequencies. It is the phase shift in relative frequencies due to infinitesimal loss in wave energy and corresponding enlargement in the wavelengths of oscillations; which occur in any clock between relative locations due to the relativistic effects or difference in gravitational potential; result error in the reading of clock time; which is wrongly presented as time dilation.

Representing the β bundles as an infinite fibre that when acts on the geometries been presented as -1 for hyperbolic or saddle curvature and +1 for elliptic or positive curvature with ±1 for both types of curvatures with the exception of 0 curvature Euclidean geometry can cause deformation or suspension η in the complex topological space T^* thereby creating genus g≥1 or with the  R_∩ formalism making the entire manifold M in the form of a suspended disc ∑D_Λ  to collapse as a ring M_R for non–intersection of infinite loops ∮_∞γ as the trivial assumptions for the extreme degrees of freedom.

Rocket science has always been fairly complex. Its not because, it deals only the properties of rocket dynamics, attitude control, propulsion systems but the complexity arises mostly as a result of its payload, whether its manned or unmanned, how to make that payload reaches to orbit? How to assemble them in orbit to make giant structures like space stations? And most importantly, the mechanisms and aerodynamics of the shuttle associated with the lifting of the rocket. This paper, not only helps to make ease out the complex terminology, rigorous mathematics, pain stroking equations into a simplified norms, like a non-fiction for the general readers but also, no pre-requisite knowledge in the field is needed to study this paper. However, every possible attempt have been make to simplify the dynamics of rocket sciences and control mechanisms to the most easier way that one can imagine, still, there are some complex terminologies but pictures are provided deliberately with facts and histories to boost up the way of understanding the subject much more better than before. It has been deliberately proved in this paper that rockets along with orbital mechanics, Kessler's syndrome, Lunar and Martial landing of the Apollo and the Curiosity rovers, is not the future of the humanity to reach out to the stars. Therefore, to eliminate time completely, to warp the space in a new way, to make the gravity constant at 1g Earth gravity, physics of Electrohydrodynamics -- Or, the physics beyond the rocket propulsion by harnessing the Anti-Gravity is discussed in details with various types of engines and experiments carried out throughout the globe. Just as a rocket become incapable of taking humans to some exoplanets millions of light years apart, Electrohydrodynamics have shown humanity hopes that, this can be achieved by applying clever physics by eliminating the hindrances of time, gravity, acceleration and fuels. Thus arrives the need to consider a totally different form of propulsion technology unknowingly discovered by Tesla and later put forward by Thomas Townsend Brown. The technology of the super-intelligent humans that the Earthmen have gathered by reverse engineering the crashed Unidentified Flying Objects which involves the perpetual motion mechanism of Anti-Gravity governed by Semi-Quantum Kinetics.

The most conventional approaches to find axion-like particles (ALP) or notably axions typically lies on their coupling with photons. However, if the coupling is extremely weak then there is a chance that they decouple themselves from the standard model physics and becomes invisible which are a source of stochastic gravitational waves at the epoch of the early universe formation, solving the riddle of the axion origin mystery and the origin of weak gravitational waves. Having the axion decay constant rates as 𝑓≥1016−1+1GeV, the axion signals which can be detected by either ground/space based observatories or pulsar timing arrays shows a broad space parameter of axion mass thus helping to probe the exis-tents of invisible axions originating in the early universe. The ALP or axions generally couple to a dark gauge bosons which at the onset of oscillations produces tachyonic instabilities that increases the visible parameter for the ALP or axion dark matters. The quantum fluctuations that arises and getting amplified by the strong coupling of axion/ALP to dark boson modes sources chiral gravitational waves (GWs). The accurate spectrum of these GWs have been calculated from the U(1) gauge fields pro-duced by axion dark matters. The explosive outbursts of gauge fields indicates the advantage of non-linear data analysis over linear modes to calculate the exact GWs spectrums. The ground/space based interferometers and pulsar timing arrays have the ability to probe the bottom up approach of the axions, in the weakly coupled regime which otherwise remains unconstrained. Further, it has been discussed the kinetic mixing mechanism and the dark gauge photon mass over the insensitivity of the couplings to standard model fields. The ALP scenarios or realistic axions may provide us useful infor-mations about the signal templates of the early universe, as well as useful datas for GW experiments. Throughout the paper we will assume the axion field being homogeneous the equations of motions for the gauge boson modes depend on the parametric valued scales 𝑘 =𝑘.

Equivalence, duality, and invariance are the pin-points of unification in modern theoretical physics that got the twist of topologies when going beyond the notions of differential and conformal domains to geometries to the symplectic norm of topologies with the pillars being the algebraic geometry taking the counting of specified states through the Enumerative ones.

Type-II emphasizing Type-II(B) in Ramond–Ramond Sector has been analyzed and computed from the Atiyah–Hirzebruch spectral sequence taking E_i sheets for the concerned values of i = 4=∞ and for E_n^(p,q) for n=1,2,3; several varieties of K–Theories where a transitive approach has been shown from the KK–Theory to K–Theory to String Theory concerning Fredholm modules of Atiyah–Singer Index Theorem and the Baum–Connes conjecture with respect to the Hilbert–A, Hilbert–B module and c*-algebras also in the reduced form taking Morita equivalence and the Kasparov composition product where extended relations has been provided between the equivalence of noncommutative geometry and noncommutative topology channelized through Poincaré Duality, Thom Isomorphism and Todd class.

This paper contributes an extensive analysis of Dark Matter (DM) along with associated materials regarding the interpretation of its evidence from ‘cosmic microwave background radiation’, ‘gravitational lensing’, ‘galactic mergers and collisions’, ‘evolution and formation of galaxies’, ‘galactic clusters’, ‘Lambda-CDM models of the observable universe. Massive Astrophysical Compact Halo Objects (MACHOs), Weakly Interacting Massive Particles (WIMP’s), Strongly Interacting Massive Particles (SIMPs), along with hot, warm, and cold DM, shedding an extensive overview of the γ_elastic of the cold DM after the chemical equilibrium is reached and kinetic decoupling happens earlier for γ_(in-elastic) accounting for 85% of the dominated matter in the universe. Scaler-Vector-Tensor (SVT) Gravity, MOdified Newtonian Dynamics (MONDs), and Gravity of Entropy (GoE) have emerged as a supplement of the modified General Relativity (GR) as a source of non-baryonic DM scenarios in the universe. Observable evidence has been taken into account for the ‘dispersion of velocity’, ‘galactic rotation curves’, ‘Lyman-α forest simulations’, ’21 cm red-shift spectra’, ‘satellite sky surveys’, ‘formation of structures’, and ‘supernova measurements of Type Ia’. Direct evidence in the underground chamber for ‘nuclear giggles’ either ‘Cryogenic experiments CRESST, CDMS’ or ‘noble liquid gases XENON’ as a result of DM scattering via VECTOR-PORTALS and Indirect evidence as a result of sky-surveys like satellite telescopes ANTARES, AMANDA or through the ‘collider experiments’ in LHC, CERN, Geneva, Switzerland.