[30] **viXra:1404.0478 [pdf]**
*replaced on 2014-05-01 10:13:40*

**Authors:** S.C. Gaudie

**Comments:** 15 pages; A4 paper; portrait orientation; mostly font 11; UK English; Freelance scientist.

This is the first “theory" in a sequence of three.
[by:- tetrahedron_1_3_6@aol.co.uk All should be available on http://vixra.org]
[1] General Theory of the 3D Cobweb Universe [http://vixra.org/all/1404]
[2] Spherical Topology - The Basis for Fundamental Forces of the Universe
[3] Sphere Geometry of Forces & Fundamental Particles of the Universe [viXra:1311.0196 ]
There was only minor connections of logic along the sequence (insufficient for a reference or a Wikipedia citation!). The flash of inspired intuition overwhelmed logic and the “verifiable facts” in the General Theory of the Cobweb Universe. Each theory was “believed to be better" than the previous one, (in the areas that it covers) without any verifiable proof!
This is called a General Theory because it covers many diverse aspects.
The consequences & conclusions:-
NOTE: As most of these concepts are of a "jigsaw puzzle type theory", be aware that if one concept is flawed the others can remain valid.
Overall, this puts forward a comprehensive, “collective theory" exploring new possibilities and to explain the diverse observations made, including:-
[1] A stringy universe.
[2] Small even-sized particles of energy & matter.
[3] the number of other universes limited in number by "quantum numbers".
[4] there is a family tree of universes.
[5] there is a family tree of forces.
[6] local expansion leading up to creation of the next multiverse level. No dark energy required, it is just the natural evolution of the multi-dimensional, multi-universe!
[7] multi-dimensional, multi-universe nature of matter.
[8] This theory ties up with string theories for 11, 16 and 26 dimensions.
A brief overview of the contents & the 11 novel concepts:-
The new concept / aspects of /consequences of the embryonic “3D cobweb structure of the universe":-
Everyday & scientific assumptions -Summary -Details -Scientific
[1] Cubically connected space
[2] Interconnectedness & intertwining
[3] "Surface splitting" of universes
[4] Space-time start
[5] The quantum numbers of the evolving family of universes
[6] The evolving family tree of universes
[7] Helices of space & double helices of time. Time is an UNSTABLE "substance"
[8] Entropy of Dimensional Expansion
[9] The Big Bang
[10] The matter and gravity
[11] The Holographic principle.
Testable aspects:- 5 verifiable testable observations.

**Category:** Relativity and Cosmology

[29] **viXra:1404.0464 [pdf]**
*submitted on 2014-04-26 07:13:38*

**Authors:** Ramzi Suleiman

**Comments:** 5 Pages.

A modified version of the Twin Paradox (TP), termed the Traveling Twins Paradox (TTP), is described. In the TTP, the twins move towards each other, via two identical fast vehicles, from two starting points, located along the x axis at coordinates +(l+ ∆l) and –(l+ ∆l), respectively. The twins first accelerate up to velocity v along identical runways of length ∆l each, then they shut down engines and travel towards each other with constant equal velocities (v). After passing each other they use the same runways to decelerate and stop. Unlike the standard TP, the scenario of the TTP is completely symmetric. Moreover, in the range (-l, +l) the TTP system is inertial. Thus, all solutions resorting to a preferred frame of reference (the "staying" twin in the standard TP), or to General Relativity (acceleration/deceleration effects) do not apply. This implies that the TTP poses an unsolvable paradox in Special Relativity.

**Category:** Relativity and Cosmology

[28] **viXra:1404.0463 [pdf]**
*replaced on 2014-11-18 11:05:21*

**Authors:** Dmitriy Skripachov

**Comments:** 7 Pages.

This article describes a new model of gravitation based on idea of interconnection of
the gravitational interaction with the curvature of space (but only 3-dimensional, without
the ”curvature” of time). It is proposed to consider the space consisting of unit cells with
dimensions comparable to the size of elementary particles. Curvature of space is interpreted
through the change in the relative volume of unit cells. In the gravitational field the curva-
ture of space is qualified as a decrease in the distension of space with increasing distance from
the center of the attracting body. As an important complement of the kinematic relativistic
effects of moving bodies is introduced a new kinematic effect of longitudinal distension of
comoving space. It is alleged that the gravitational interaction is manifested as a result of
following of changes of kinematic effects of moving bodies for change in the local distension
of curved space. It is shown that the extrapolation of the fall of matter on the center of the
attracting body leads to the conclusion about the existence of density limit, as which can
be accepted the matter density of the neutron star.

**Category:** Relativity and Cosmology

[27] **viXra:1404.0453 [pdf]**
*submitted on 2014-04-24 05:39:44*

**Authors:** Leonardo Rubino

**Comments:** 12 Pages.

Let’s ask the atom if what I called Other Relativity stands with numbers.
(…and also when Taylor no longer applies)

**Category:** Relativity and Cosmology

[26] **viXra:1404.0445 [pdf]**
*submitted on 2014-04-23 06:58:09*

**Authors:** Mustafa Salti, Irfan Acikgoz

**Comments:** 10 Pages. Rom. J. Phys. Vol.59, Nos:3-4 (2014) 214-223.

The spin precession of a Dirac particle in monotonically increasingly boosted coordinates is calculated using torsion gravity (teleparallel theory of gravity). Also, we find the vector and the axial-vector parts of the torsion tensor.

**Category:** Relativity and Cosmology

[25] **viXra:1404.0439 [pdf]**
*submitted on 2014-04-21 13:35:48*

**Authors:** Fernando Loup

**Comments:** 63 Pages.

Warp Drives are solutions of the Einstein Field Equations that
allows superluminal travel within the framework of General
Relativity. There are at the present moment two known solutions:
The Alcubierre warp drive discovered in $1994$ and the Natario
warp drive discovered in $2001$. The major drawback concerning
warp drives is the huge amount of negative energy able to sustain
the warp bubble.In order to perform an interstellar space travel
to a "nearby" star at $20$ light-years away in a reasonable amount
of time a ship must attain a speed of about $200$ times faster
than light.However the negative energy density at such a speed is
directly proportional to the factor $10^{48}$ which is
$1.000.000.000.000.000.000.000.000$ times bigger in magnitude than
the mass of the planet Earth!! Although the energy conditions of
General Relativity forbids the existence of negative energy the
Casimir Effect first predicted by Casimir in $1948$ and verified
experimentally by Lamoreaux in $1997$ allows sub-microscopical
amounts of it. Lamoreaux obtained experimentally negative energy
densities of $10^{-4} \frac{Joules}{Meter^{3}}$.This is an
extremely small value $10^{20}$ times lighter than the ones of a
body of $1$ kilogram in a cubic meter of space or
better:$100.000.000.000.000.000.000$ times lighter than the ones
of a body of $1$ kilogram in a cubic meter of space. We introduce
in this work a shape function that will low the negative energy
density requirements in the Natario warp drive from $10^{48}
\frac{Joules}{Meter^{3}}$ to
$10^{-7} \frac{Joules}{Meter^{3}}$
a result $1000$ times lighter than the ones obtained by Lamoreaux
proving that the Casimir Effect can generate and sustain a Natario
warp drive spacetime.We also discuss other warp drive
drawbacks:collisions with hazardous interstellar matter(asteroids
or comets) that may happen in a real interstellar travel and
Horizons(causally disconnected portions of spacetime).

**Category:** Relativity and Cosmology

[24] **viXra:1404.0435 [pdf]**
*replaced on 2014-05-29 21:32:47*

**Authors:** Stephen Winter

**Comments:** 6 Pages.

1. WHAT IS THE UNIVERSE : Non-singularity . Singularity (non-existence) is logically not. . The universe consists of abstraction (and nothing else) . Physical constants can't be other than exactly tailored . The world is a sense machine . The Fourth-Bag-Problem . Perception is extremely blinding out

2. WHAT IS WRONG WITH TODAY'S SCIENCE OF THE UNIVERSE : The universe has no size . The origin of the universe is not a location . 'Dark energy' wouldn't effect anything . Big Voids and SMBlack Holes = source and sink . The light of the universe isn't observable . Most galaxies move a billion times faster than light . Conceptually misguided space missions . Into limitless divergence

**Category:** Relativity and Cosmology

[23] **viXra:1404.0431 [pdf]**
*submitted on 2014-04-19 16:43:19*

**Authors:** Mustafa A. Khan

**Comments:** 4 Pages.

This article deals with the most fundamental of the questions about the universe, namely, how it came into existence. In this article I use the famous mass/energy equation of Einstein and interpret it in a novel way which makes it possible for our universe to come into existence out of pure thoughts only. I also discuss how to calculate the probability for our type of universe to come into existence and find that the initial mass at the time of the Big Bang has to be within a certain range for the event to occur and give rise to our type of universe. This is similar to the concept of the goldilocks zone for the solar system for the existence of life.

**Category:** Relativity and Cosmology

[22] **viXra:1404.0258 [pdf]**
*replaced on 2015-05-07 14:15:18*

**Authors:** Sergey I. Kuznetsov

**Comments:** 10 Pages.

The proposed model-independent solution to the dark energy problem requires only redefining the redshift parameter z with no special assumptions of the physical mechanism of cosmological redshifting. The new definition of the redshift parameter finds its justification in cosmological models based on both special and general relativity. In this paper a Hubble diagram is produced from a sample of the SNe1a observational data, after recalculating measured redshifts according to the new definition with no change in corresponding magnitudes (apparent luminosities). A linear fit of the observational data obtained with the newly-defined redshift z* can be considered as an evidence for the non-accelerating Universe with no need for any dark energy.

**Category:** Relativity and Cosmology

[21] **viXra:1404.0202 [pdf]**
*submitted on 2014-04-16 06:23:32*

**Authors:** Victor L. Mironov, Sergey V. Mironov

**Comments:** 9 pages, 3 tables

In present paper we develop the description of massless fields on the basis of space-time algebra of sixteen-component sedeons. The generalized sedeonic second-order equation for unified gravito-electromagnetic (GE) field describing simultaneously weak gravity and electromagnetism is proposed. The relations for the GE field energy, momentum and Lorentz invariants are derived. The special case of GE field described by first-order sedeonic wave equation is also discussed.

**Category:** Relativity and Cosmology

[20] **viXra:1404.0196 [pdf]**
*submitted on 2014-04-15 23:17:07*

**Authors:** Temur Z. Kalanov.

**Comments:** 4 Pages.

The critical discussion of the theory of Big Bang is proposed. Methodological basis is the unity of formal logic and of rational dialectics. It is proved that the theory of Big Bang contains three fundamental logical errors.

**Category:** Relativity and Cosmology

[19] **viXra:1404.0123 [pdf]**
*replaced on 2014-05-28 07:08:53*

**Authors:** J. C. Perez Ramos

**Comments:** 16 Pages. Spanish (Version 2) and English (Version 3)

We show how the theory of relativity disagrees with the isotropy of the expanding universe and with the experimental arguments in favour of the existence of a preferred frame. We postulate a new heuristic principle, the invariance of the radius of the universe, deriving new transformation equations. Then we develop the geometric scenario and we prove how the universe equals an anisotropic inhomogeneous hyperboloid in four-space. The new model quite naturally incorporates the expanding universe, solves the cosmological horizon problem, explains the asymmetrical time dilation effect (for example, in the twin paradox) and describes the Big Bang in an original way by reducing the radius of the hypersphere to zero. The speed of light acquires a new geometrical meaning that justifies a varying speed of light (VSL) theory and clarifies unsolved problems in physics as the Pioneer anomaly, cosmological puzzles, the dark energy and the Loschmidt paradox.

**Category:** Relativity and Cosmology

[18] **viXra:1404.0107 [pdf]**
*submitted on 2014-04-12 18:17:51*

**Authors:** Michael Harney, Julie Seal

**Comments:** 8 Pages.

By modeling the Universe as a quantum well for standing waves and solving Schrodinger’s equation for a particle trapped in this well, the solutions for the allowable rest-energies of all particles in the Universe are obtained, from the mass of the photon up to the mass of the Universe. The quantum numbers that predict the allowable rest-energies of all particles are also found to quantize the distance over which gravity acts, ranging from the Planck length to the radius of the universe. The potential that is derived from the quantum well model is validated for gravitational, strong, weak and electromagnetic forces by confirming the mass of the vector particle for each force.

**Category:** Relativity and Cosmology

[17] **viXra:1404.0106 [pdf]**
*submitted on 2014-04-12 20:43:51*

**Authors:** Richard L. Amoroso

**Comments:** 6 Pages. Preprint from: "The Physics of Reality: Space, Time, Matter,Cosmos" (2013) RL Amoroso, LH Kauffman, P. Rowlands (eds.) Singapore: World Scientific Publishers, pp. 504-509

The concept of time in the 'clockwork' Newtonian world was irrelevant; and has generally been ignored until recently by several
generations of physicists since the implementation of quantum mechanics. We will set aside the utility of time as a property relating to
physical calculations of events relating to a metrics line element or as an aspect of the transformation of a particles motion/interaction
in a coordinate system or in relation to thermodynamics etc., i.e. we will discard all the usual uses of time as a concept used to
circularly define physical parameters in terms of other physical parameters; concentrating instead on time as an aspect of the
fundamental cosmic topology of our virtual reality especially as it inseparably relates to the nature and role of the observer in natural
science.

**Category:** Relativity and Cosmology

[16] **viXra:1404.0083 [pdf]**
*replaced on 2015-12-05 12:59:48*

**Authors:** Ramzi Suleiman

**Comments:** 14 Pages.

The Twin Paradox is one of the most fascinating paradoxes in physics. In Special Relativity, the paradox arises due to the nonexistence of a preferred frame of reference, resulting in both twins observing that he or she is younger than the other twin. Nonetheless, it is commonly agreed that the "traveling" twin returns younger than the "staying" twin. The prevailing solution is obtained by deviating from the relativity principle and assuming that the "staying" twin's frame is preferred over the "traveling" twin's frame. Here I describe a newly proposed relativity theory, termed Information Relativity (IR) and show that it solves the twin paradox symmetrically, with the twins aging equally.

**Category:** Relativity and Cosmology

[15] **viXra:1404.0076 [pdf]**
*submitted on 2014-04-09 21:41:25*

**Authors:** Richard J. Benish

**Comments:** 23 Pages.

Schiller has shown not only that a maximum force follows from General Relativity, he has also argued that General Relativity can be derived from the principle of maximum force. In the present paper an alternative derivation of maximum force is given. Inspired by the equivalence principle, the approach is based on a modification of the well known special relativity equation for the velocity acquired from uniform proper acceleration. Though in Schiller's derivation the existence of gravitational horizons plays a key role, in the present derivation this is not the case. In fact, though the kinematic equation that we start with does exhibit a horizon, it is not carried over to its gravitational counterpart. A few of the geometrical consequences and physical implications of this result are discussed.

**Category:** Relativity and Cosmology

[14] **viXra:1404.0074 [pdf]**
*replaced on 2014-06-15 22:53:35*

**Authors:** Richard Benish

**Comments:** 1 Page.

With respect to logarithmic scales spanning over 80 orders of magnitude of mass and over 70 orders of magnitude of density, this chart represents essentially all known bodies of matter in the Universe, including the Universe itself. A variety of essential cosmic relationships become immediately evident: the broad span of atomic matter, which branches toward increasing and decreasing density at the mass of stars; the Chandrasekhar limit mass; some curious ratios involving the fine structure constant; and the artificial, unnatural appearance of the Schwarzschild horizon line. Also displayed is a simple expression that defines Newton's constant G in terms of two key densities and three fundamental atomic constants

**Category:** Relativity and Cosmology

[13] **viXra:1404.0073 [pdf]**
*submitted on 2014-04-10 01:16:57*

**Authors:** Rodney Bartlett

**Comments:** 3 Pages.

First, I refer you to two statements in "Solving the mystery of COSMIC RAYS" by Angela Olinto (Astronomy magazine - April 2014):
a) In 2013, scientists discovered that cosmic rays - charged particles travelling near the speed of light - get their energy by travelling back and forth over the edges of supernova remnants ... The origins of the highest-energy cosmic rays, though, remain a mystery."
b) "Or are they (ultra-high-energy cosmic rays) accelerated in the explosive deaths of the massive stars that create black holes and neutron stars?"
Then I ask if the theories of Einstein suggest the origin of ultra-high-energy cosmic rays is, ultimately, gravitational?

**Category:** Relativity and Cosmology

[12] **viXra:1404.0067 [pdf]**
*replaced on 2014-05-26 21:36:53*

**Authors:** Kenneth Dalton

**Comments:** 5 Pages. Journal Ref: Hadronic J. 37(2), 241-245 (2014)

Many galaxies have a concentration of mass at their center. In what follows, the mass is attributed to a neutral gas of electrons and positrons. It is found that electron degeneracy pressure supports the smaller masses against gravity. The larger masses are supported by ideal gas and radiation pressure. Physical properties are calculated for the range 450 to 45 billion solar masses.
Keywords: model; supermassive black hole; active galaxy; quasar

**Category:** Relativity and Cosmology

[11] **viXra:1404.0058 [pdf]**
*replaced on 2015-12-22 10:59:16*

**Authors:** Sergey G. Fedosin

**Comments:** 6 pages. International Frontier Science Letters, ISSN: 2349 – 4484, 2014, Vol. 1, No 1, P. 41 – 46. http://dx.doi.org/10.18052/www.scipress.com/ifsl.1.41 .

The metric outside a charged body is calculated. As part of the given approach it is shown that the gravitational and electromagnetic fields are equally involved in the formation of the metric tensor components. And the contribution of fields in the metric is proportional to the energy of these fields. From equations for the metric it follows that the metric tensor components are determined up to two constants.

**Category:** Relativity and Cosmology

[10] **viXra:1404.0055 [pdf]**
*replaced on 2014-06-24 20:56:13*

**Authors:** Michael John Sarnowski

**Comments:** 4 Pages. Mass of Universe correlated with neutron.

The
113 PlanckPressure Pascals 4.63309*10
. In this paper the author proposes
that Planck Pressure could be the gravitational force of attraction between
two equal sized universes all concentrated on the tiny area of one fourth of
Planck Area. This paper shows that the Critical density of the Hubble Sphere
Universe gives the same exact mass of the universe as the Planck Pressure
requires between two Hubble Sphere Universes, attracted gravitationally and
applied to the one fourth of Planck Area. This shows, that for such an
enormous pressure, to be concentrated on such a small area results in an
extremely rigid components of space and implies that matter and its
properties could not entirely travel through space, but must be transmitted
mostly through another mechanism which, likely, is a wave mechanism.

**Category:** Relativity and Cosmology

[9] **viXra:1404.0053 [pdf]**
*submitted on 2014-04-07 10:52:42*

**Authors:** Miroslaw J. Kubiak

**Comments:** 6 Pages.

In the previous papers [1, 2] we presented the concept of the effective mass tensor the in General Relativity (GR). According to this concept under the influence of the gravitational field the bare mass tensor becomes the effective mass tensor. Assuming that there is a relationship between metric tensor and the effective mass tensor we obtained modified Einstein’s field equations, which gives new meaning to GR.

**Category:** Relativity and Cosmology

[8] **viXra:1404.0044 [pdf]**
*submitted on 2014-04-06 13:30:19*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 32 Pages. Published in International Frontier Science Letters, Vol. 1, pp. 47-63, Jul. 2014

It is shown that the Theory of Special Relativity is not a theory free of contradictions. Putting apart our ingenious idea about clocks in a point (infinitesimal clocks), it is proved there are contradictions deriving from the synchronism of clocks. Other contradictions refer to the concept of relativity of simultaneity. One of these contradictions is proved through the idea of idealized experience: a simultaneous emission of two photons. Simultaneity related to an inertial frame of reference (inertial system) considered in movement, but whose system in movement stops moving between the first and the second emissions with respect to the steadied system (stationary system), ending up the experience “beforehand”. Only one photon would have been emitted with respect to the system in movement, which would make our prior hypotheses contradictory.

**Category:** Relativity and Cosmology

[7] **viXra:1404.0043 [pdf]**
*submitted on 2014-04-06 13:56:22*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 5 Pages. English language.

Using the Lorentz Transformations between (x, y, z, t) and (X, Y, Z, T) and the fact that it is impossible to have clocks in a unique point (infinitesimal clocks), more exactly, the fact that time measured in a system does not depend on format, dimensions and internal mechanism of clocks and any periodical process adopted in measurement, it is proved the simultaneity of events E1, “Time measured at the stationary system (S) is t.” (Or “Clocks X1, X2, X3, …, Xn at rest at the stationary system indicate or set time t in this system”, i.e., no matter the position (x’, y, z) of measurement of time t in S, even to x’ <> x), and E2, “Time (or schedule, instant, time instant) measured at the moving system (S’), through a stationary clock at this system and at position (X, Y, Z), is given by T.”. Such simultaneity is related to the system considered stationary, of coordinates (x, y, z, t), as well as of the system considered in movement with respect to the first one, of coordinates (X, Y, Z, T). Of this simultaneity that is contained in the Lorentz Transformations of the time is easy to prove that is contradictory the definition of Synchronism of Clocks, used in the Special Relativity.

**Category:** Relativity and Cosmology

[6] **viXra:1404.0042 [pdf]**
*submitted on 2014-04-06 14:10:58*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 3 Pages. English language.

Considering it is not possible to have infinitesimal clocks and based on the Lorentz’s Transformation between (x, y, z, t) and (X, Y, Z, T), it is proved there is a contradiction on Lorentz’s Transformation of Time used in the Theory of Special Relativity.

**Category:** Relativity and Cosmology

[5] **viXra:1404.0041 [pdf]**
*submitted on 2014-04-06 09:29:14*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 13 Pages. Portuguese language.

Is shown contradictions in special relativity theory related to the clocks synchronization, covariance of the equations of electromagnetism and time dilatation.

**Category:** Relativity and Cosmology

[4] **viXra:1404.0040 [pdf]**
*submitted on 2014-04-06 10:48:22*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 19 Pages. Published in International Frontier Science Letters, Vol. 3, pp. 19-31, Jan. 2015

It is shown that the special theory of relativity is not a theory free of contradictions, one of the contradictions related to the relativity of simultaneity. Another contradiction occurs when we calculate the speed of light relative to a moving reference frame by using the dilatation of the space and contraction of time, since it appears that the speed of light depends on the speed reference. Also shows that for low speeds, but large distances, the Lorentz transformation for time is not reduced to their respective transformation of Galileo, subject not explored in most science books, and even college.

**Category:** Relativity and Cosmology

[3] **viXra:1404.0039 [pdf]**
*submitted on 2014-04-06 08:47:33*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 20 Pages. Portuguese language. Article originally published in the Revista Brasileira de Ensino de Física, vol. 19, No. 3, September, 1997.

It is critically exposed the deduction of Lorentz transformations made by Einstein in 1905. The Lorentz transformations are deduced following a similar method to that of Einstein.

**Category:** Relativity and Cosmology

[2] **viXra:1404.0037 [pdf]**
*submitted on 2014-04-06 05:05:55*

**Authors:** Jan Helm

**Comments:** 34 Pages.

The Tolman-Oppenheimer-Volkov (TOV) equation is solved with a new ansatz: the external boundary condition with mass M0 and radius R1 is dual to the internal boundary condition with density rbc and inner radius ri , the two boundary conditions yield the same result.
The inner boundary condition is imposed with a density rbc and an inner radius ri, which is zero for the compact neutron stars, but non-zero for the shell-stars: stellar quasi-black-hole and galactic quasi-black-hole. Parametric solutions are calculated for neutron stars, stellar quasi-black-holes, galactic quasi-black-holes. From the results an M-R-relation and mass limits for these star models can be extracted. A new method is found for solving the Einstein equations for Kerr space-time with matter (extended Kerr space-time), i.e. rotating matter distribution in its own gravitational field. Then numerical solutions are calculated for several astrophysical models: white dwarf, neutron star, stellar quasi-black-hole, galactic quasi-black-hole. The results suggest that quasi-black-hole star models resemble the behaviour of abstract black holes, but have finite redshifts and escape velocity v<c and no singularity.

**Category:** Relativity and Cosmology

[1] **viXra:1404.0016 [pdf]**
*submitted on 2014-04-02 04:05:21*

**Authors:** R Santosh Kumar

**Comments:** 7 Pages.

The notion of a geodesic line (also: geodesic) is a geometric concept which
is a generalization of the concept of a straight line (or a segment of a straight line) in
Euclidean geometry to spaces of a more general type. In this paper I have derived the
geodesic equation for a 2 dimensional spherical surface following a local local minkowski
frame with the minkowski metric localized .

**Category:** Relativity and Cosmology