# Salah A. MabkhoutThamar university · Department of Mathematics

Salah A. Mabkhout

I do researches in Cosmology, General Relativity, Mathematical physics, Hyperbolic universe, Dark Matter and Dark Energ.

## About

82

Publications

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78

Citations

Citations since 2017

Introduction

I solved the dynamical equations of cosmology. I have found that the shape of the Universe is Hyperbolic.The solution predicts the equation of state w = -1, the hyperbolic structure of the spacetime causes the observed accelerated expansion of the Universe without need for dark energy. I had modified the equation of motion in the hyperbolic spacetime that explained the flat rotation curve without need for dark matter. I have taught pure and applied mathematics for more than 25 years. I have published 12 books in mathematics (Arabic language) , 4 books in cosmology (English language) and 12 papers in cosmology in International peer reviewed journals.

Additional affiliations

January 2010 - April 2017

July 1994 - present

## Publications

Publications (82)

Abstract: The galactic dynamics, the CMB anisotropies and the gravitational lensing do not agree with the observations. Either an additional component of mysterious unseen nonbaryonic matter (Dark Matter) is needed -to bridge the gap between theory and observations- or, the theory of gravity should be modified. We prove the spacetime is hyperbolic....

We show that our hyperbolic equation of motion predicts the kinematics of the UDGs and traces their speed rotation curves.

The universe is currently expanding too fast — faster than theorists predict when they extrapolate from the early universe to the present day. “If the late and early universe don’t agree, we have to be open to the possibility of new physics,”. A mathematical discrepancy in the expansion rate of the Universe is now "pretty serious", and could point...

Here we display –in details- the tensor mathematics in deriving Schwarz schild metric and Friedmann equations.

In General Relativity, the unique spherically symmetric vacuum solution is the Schwarzschild metric, assuming asymptotically flat spacetime. Schwarzschild metric possesses singularity at the center (r=0) where curvature became infinite. Oppenheimer and others argued that when sufficient mass becomes concentrated it will collapse into its Schwarzsch...

There is an approximately linear relationship between redshift and distance at small scales for all the FLRW models, and departures from linearity at larger scales can be used to measure spatial curvature. Hubble's law describes a uniformly expanding flat universe. Hubble's law says: the furthest object recedes faster than the nearest one. Hubble's...

First we explain the CMB spectrum, its origin and how to extract the information. Assume a flat universe; Dark Matter, Dark Energy and inflation were assumed to exist in the early universe in order to predict the current anisotropies and the acoustic sound peaks observed in the CMB. Dark Matter and Dark Energy have never been detected while inflati...

A pressure-less flat-dust universe model is an oversimplification solution to the Einstein's Field equations. This led to a drastic failure in predicting the missing mass and the accelerating expansion of the universe. Geometry is the study of the local structures of the manifold, by means of measurement and observations. Topology is the study of t...

كتاب مبادئ الإحصاء والإحتمالات يحتوي محاضراتي التي قمت بتدريسها

Although perspective for nearby objects in hyperbolic space is very nearly identical to Euclidean space (i.e. the Universe locally is approximately flat consistent with local observations), the apparent angular size of distant objects falls off much more rapidly, in fact exponentially. The Universe is globally hyperbolic. The current observed densi...

The galactic dynamics, the CMB anisotropies and the gravitational lensing do not agree with the observations. Either an additional component of mysterious unseen nonbaryonic matter (Dark Matter) is needed -to bridge the gap between theory and observations- or, the theory of gravity should be modified. We prove the spacetime is hyperbolic. The probl...

We prove that the geometry of the universe is globally hyperbolic. We modify the laws of gravity. We develop the laws of gravity in the hyperbolic spacetime. Such laws fit the current observed data and ruling out both dark matter and dark energy.The hyperbolic time-density evolution equation, the scale factor, of the universe governs the evolution...

We prove that the geometry of the universe is globally hyperbolic. We modify the laws of gravity. We develop the laws of gravity in the hyperbolic spacetime. Such laws fit the current observed data and ruling out both dark matter and dark energy.The hyperbolic time-density evolution equation, the scale factor, of the universe governs the evolution...

Abstract
If the expression i=√(-1) has a solution that is not a real number, what might be that? So the question is a philosophical and foundational one, simply to wonder about what we are dealing with. Concern about the foundations of mathematics therefore means that the problem of imaginary numbers is in fact a problem and cannot be dismissed as...

According to Occam’s razor the model should be aesthetically pleasing, that is ”If you have two theories that both explain the observed facts, then you should use the simplest with the fewest assumptions. We compare between the Flat Universe paradigm and the Hyperbolic Universe paradigm via the table below. The Hyperbolic Universe is aesthetically...

The main pillar of the Big Bang paradigm is the expansion of the Universe predicted by the cosmological redshift. Singularity is inevitable in the Big Bang model. The Universe is hyperbolic as we did prove mathematically; where the cosmological redshift is no longer a distance indicator. After all, in the hyperbolic spacetime a group of objects wou...

The main pillar of the Big Bang paradigm is the expansion of the Universe predicted by the cosmological redshift. Singularity is inevitable in the Big Bang model. The Universe is hyperbolic as we did prove mathematically; where the cosmological redshift is no longer a distance indicator. We show the manifold of the hyperbolic Universe is complete w...

Penrose –Hawking singularity theorems pre-assume asymptote flat spacetime. This false flat spacetime paradigm produces such singularities at the Big Bang and the center of the Black Holes. The Universe is globally hyperbolic as we did prove mathematically [S. A. Mabkhout, Phys. Essays 25, 112 (2012)]. We prove that the hyperbolic time evolution equ...

Hubble’s law describes a uniformly expanding flat universe. Hubble’s law doesn`t explain why distant objects were receding fastest. There is an approximately linear relationship between redshift and distance at small scales for all the FLRW models, and departures from linearity at larger scales can be used to measure spatial curvature. Locally the...

The Universe is globally hyperbolic as we did prove mathematically [S. A. Mabkhout, Phys. Essays 25, 112 (2012)]. The solution predicts the equation of state of cosmology ( P = -𝝆 ). Penrose said if the curvature is not equal to zero, then inflation is out. The hyperbolic universe inflates exponentially produces an accelerated expansion of the univ...

If the expression squrt( -1) has a solution that is not a real number, what might be that? So the question is a philosophical and foundational one, simply to wonder about what we are dealing with. Concern about the foundations of mathematics therefore means that the problem of imaginary numbers is in fact a problem and cannot be dismissed as superf...

Hubble's law describes a uniformly expanding flat universe. Hubble's law doesn`t explain why distant objects were receding fastest. There is an approximately linear relationship between redshift and distance at small scales for all the FLRW models, and departures from linearity at larger scales can be used to measure spatial curvature. Locally the...

Submitted article in recent progress in spacevtechnology journal

The universe is globally hyperbolic as we did prove mathematically. The false flat universe paradigm needs mysterious ingredients: dark energy , dark matter and inflation to pridge the gap between theory and observations. In testing the validity of any scientific paradigm, the key creterion is whether measurements agree with what is expected given...

This book addresses the latest advances in general relativity research, including the classical world and spinor formalisms; keys to understanding gravity; the continuum mechanics of space-time; new evidences on matter without energy-stress tensor; a new approach to study gravitational stability of the solutions to the Einstein equations; Mond theo...

The Universe is globally hyperbolic as we did prove mathematically [S. A. Mabkhout, Phys. Essays 25, 112 (2012)]. We show that the equation of the hyperbolic time evolution of the universe characteristics the hyperbolic universe and traces its manifold dynamical geometry shouldn't break down even at the initial Big Bang moment. Hence, singularity d...

Abstract: Black holes owe their existence to the presence of singularity. Singularity appears theoretically as a result to the Schwarzschild solution in asymptotically flat spacetime. Such an approximated Schwarzschild solution creates singularity (when r = 0). This false paradigm constitutes our observation. The observer is operating within a "par...

Although the perspective for nearby objects in hyperbolic space is very nearly identical to Euclidean space (i.e., the universe locally is approximately flat consistent with local observations), the apparent angular size of distant objects falls off much more rapidly, in fact exponentially.
The universe is globally hyperbolic as we did prove mathem...

The equation of the radius of the universe, which I found as a solution to the first dynamical equation of cosmology (time-time component), reveals that the curvature of the universe must be negative, yielding a hyperbolic and open universe. Moreover, when I applied this equation to the Planck scale, it predicted the Planck length, which verifies m...

كتاب (المعادلات التفاضلية): الكتاب من تسعةأبواب يقع في 200 صفحة لطلاب الهندسة والعلوم والتربية (رياضيات-فيزياء) ويشمل المقررات الآتية
المعادلات التفاضلية العادية (معادلات الرتبة الأولى والثانية الخطية ومعادلة بيرنوللي اللاخطية والمعادلات المتجانسة واللامتجانسة وأنظمة المعادلات التفاضلية الأولية بطرائق الحذف والمحددات والمصفوفات)
الدوال الخاصة (الن...

هذا الكتاب يسلط الضوء على تاريخ الرياضيات المصرية,البابلية, العربية, الأوروبية إضافة إلى فلسفة الرياضيات والميتافيزيقا.وهو عبارة عن محاضراتي في مقرر تاريخ الرياضيات

This book contain : operation research- Transportation model- Nonlinear program. Game theory
in Arabic where symbole snd equations in English.

إن العالم على المستوى المجهري يعمل بطرق غاية في الغرابة وغير مألوفة لدرجة أن العقل البشري , الذي تأطر على مر العصور ليدرك ظواهر الحياة اليومية و يألفها , عاجز عن اللحاق بمعطيات نظرية الكم والإمساك بتلابيبها , سلوك الطبيعة على المستوى المجهري منافٍ للعقل كما يقول فينمان . من المؤكد أن نظرية الكم أربكت فهم العقل للطبيعة و الواقع . إن التعرف على روح م...

هذا الكتاب يحتوي محاضراتي في مقرري التحليل المركب والتحليل العددي

we derived four formulae for the bounded integrals for the powers of sinx.cosx

## Questions

Questions (17)

There are billions of Black Holes. Any Black Hole consists of a singular points each with an infinitely density and curvature. How could our finite Cosmos contains as such many infinities? If those singular points are just mere artificial mathematics there w`t be any problem. Otherwise, if they are physically exist, our Cosmos would have an enormous infinities as their singular points exist in their parent Black Holes! If we did sum up those infinities the Universe would have infinite density!

Assume a flat universe, Dark Matter, Dark Energy and inflation were assumed to exist in the early universe in order to predict the current anisotropies and the acoustic sound peaks observed in the CMB. Dark Matter and Dark Energy have never been detected while inflation is not even a scientific theory. Dwarf galaxies don't fit standard model and challenges cold dark matter cosmology. Large scale structure formation assumes the presence of dark matter in the early universe. However, most early massive galaxies are strongly dominated by normal matter. The CMB predictions for H0 assume that the contents of the universe are well described by atomic matter, cold dark matter, and dark energy. If this description is incomplete, the predictions could be wrong.

## Projects

Project (1)

Newton`s laws of gravity do no longer hold in non-Euclidean geometry. In General Relativity Theory gravity is a geometry. In order to modify the laws of gravity, first you should modify the geometry itself. Hence, establish the modified laws of gravity from the updated non-Euclidean geometry. We prove that the geometry of the universe is globally hyperbolic.We develop the laws of gravity in the hyperbolic spacetime. Such laws fit the current observed data and solve the dark matter and dark energy mysterious.