PROPER ARTICLE IS AVAILABLE HERE
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STRUCTURE OF WORMHOLE,ITS COMPOSTION AND THE NATURE OF PHOTONS PASSING THROUGH IT-
This is a write up which I have completed uptil now. Its a 5 long paged. I am now working on Schwarzschild metry and Solutions to Theory of relativity which can fit in wormhole
By - A. Deoras
Introduction-
This write up deals with the possible explainations for the exsistence of shortcuts in the Universe popularly termed as Wormhole----
CHAPTER I
PREVIOUS STUDIES,RESULTS, AND CONCLUSIONS
*** The solutions to Einstein's Theory of Relativity coupled by Nathan Rosen's work led the foundation of Einstein-Rosen Bridge of Schwarzschild wormhole. Einstein-Rosen bridge are the Vacuum solutions to Einsteins' Field Equation combining the black hole and white hole model in the year 1935.However in 1962,J.Wheeler and R.Fuller published a paper showing that the wormhole so formed from the vacuum solutions is unstable and will disappear very soon as soon as it is formed. Schwarzschild concluded that his wormhole was a non traversable one!
Kip Thorne considered the throat of Schwarzschild wormhole as having Exotic matter.
In 1988, Morris,Thorne,Yurtsever worked to convert a wormhole traversing space into one traversing time. This has been disputed.
CHAPTER II
INTRODUCTION TO THE ARTICLE
The article deals with the environment required for existence of traversable wormholes by using the time dilation equation and conversion of inertial to non inertial frame of references.
The article also deals with the aspects of traversibility of wormholes.
The article also specifies the ideal composition of wormhole
CHAPTER III
SOLUTIONS TO SCHWARZSCHILD METRY
The solutions to the schwarzschild metry can be positive or negative. Solutions refer to Square roots inside the horizon. For Schwarzschild metrical solutions to wormhole, negative square root indicates negative properties relating to negative attraction and negative energy. The second of law of thermodynamics is violated by wormholes which acts as barrier for their mathematical existence. Negative square root of Black hole's solution indicates matter being released with tremendous speed outside the event horizon. The present models of Wormhole contain Black Hole for sucking matter and White hole for ejecting matter.
CHAPTER IV
STABILITY OF WORMHOLE
The mathematical models require an exotic matter at the throat of wormhole for stabilisation. Exotic matter is a matter with negative energy/pressure. The 2-D diagram will make a ring form at the throat of Black and White holes which will maintain the stability of wormhole.The shell is supposed to have a positive surface pressure and negative mass. These all features help the stability of wormhole
CHAPTER V
VIOLATION OF WHITE HOLE BY LAWS OF THERMODYNAMICS
The second law of thermodynamics is an expression of the universal principle of entropy, stating that the entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium; and that the entropy change dS of a system undergoing any infinitesimal reversible process is given by δq / T, where δq is the heat supplied to the system and T is the absolute temperature of the system.Wormhole has not this tendency so it might not exist.
CHAPTER VI
BLACK HOLE FORMATION AND WHITE HOLE FORMATION WITH THE PROPERTIES
Also As we know after a death of a star, Black holes are created if the mass of the star was more than CHANDRASHEKHAR LIMIT
HOW CAN A WORMHOLE EXIST. LET US TALK ON ITS PROPERTIES AS SUGGESTED BY SCHWARZSCHILD METRY.
THE WORMHOLE EJECTS MATTER. THIS MEANS THAT ITS GRAVITY IS NOT ZERO. IF IT HAS SOME MASS AT THE CENTER WHICH FORMS GRAVITY THEN HOW CAN AN ATOM BE EJECTED WITH SPEED. THIS MIGHT LEAD US TO THINK THAT THERE MIGHT BE A NEGATIVE ENERGY AT THE THROAT OF A WORMHOLE. I DISAGREE ON IT.
CHAPTER VII
MY VIEWS ON WORMHOLE
ON MY VIEWS OF A TRAVERSABLE WORMHOLES THERE MIGHT NOT BE SOMETHING AT THE OTHER END OF A WORMHOLE
CONTEMPLARY-
""A WORMHOLE ACTUALLY FOLDS THE UNIVERSE"""
IT IS A POPULAR STATEMENT.
AFTER PLOTTING TWO POINTS ON SPACE-TIME CO-ORDINATE SYSTEM, WHICH ARE SUPPOSED TO BE NEAR TO EACH OTHER
DUE TO FOLDING,THE CO-ORDINATES ARE SAME AS THEY WERE BEFORE< THEIR SHIFTS ARE RELATIVE TO ANY POINT OF REFRENCE IN THE SAME DIMENSIONAL UNIVERSE>
SO IT IS NOT THAT FOLDING OF SPACE IS A WORMHOLE
THIS IS FOR ANY PLANET.
THIS IMPLIES THAT TIME TRAVEL IS NOT GOING TO HAPPEN DUE TO FINITE SPACE-TIME CURVATURE AS DONE BY PLANETS AND THE FOLDING CONCEPT IS ENTIRELY WRONG
TWO UNIVERSES
CHAPTER VIII
ENVIRONMENT OF WORMHOLE
II ENVIRONMENT FOR SCHWARZSCHILD WORMHOLE--
REQUIREMENT- BLACK HOLE-
A BLACK HOLES CENTER HAS INFINITE SPACE-TIME CURVATURE. TO EXPLAIN IT HAS SINGULARITY OF INFINITY.
IF WE CONSIDER LIGHT-CONE DIAGRAM ANY TWO PARALLEL UNIVERSES ARE SEPARATED FROM EACH OTHER BY A HORIZONTAL LINE OF A LINE OF ZERO TIME AS THE Y CO-ORDINATE OF X-AXIS IS ZERO. I CALL THIS HORIZONTAL AS A LINE OF HORIZONTAL OF A LINE OF REFRENCE.
IF WE CONSIDER TWO PARREL UNIVERSES,ONE ABOVE THE LINE
THESE TWO UNIVERSES HAVE INDEPENDENT TIME. AT THE BLACK HOLE AREA, THE SPACE-TIME CURVATURE IS INFINITE.
ACCORDING TO ME IT JUST TOUCHES THE LINE OF HORIZONTAL BUT DOESN'T PASS BELOW IT.
THE SPACE-TIME FABRIC WILL TOUCH THE LINE AT A POINT WHICH AFTER SOME YEARS WILL BECOME A TRAVERSABLE HOLE.
DURING ITS LIFE, A BLACK HOLE SUCKS MATTER. SUPPOSE IT TAKEN IN AN ATOM, DUE TO STRONG G FORCE AT THE CENTER,IT WILL CONTINUE TO MOVE IN ORBIT INSIDE THE BLACK HOLE GRADUALLY COLLAPSING WITH ITS CENTER. BUT IF AT THIS MOMENT ONLY " BLACK HOLE EVAPORATION> STARTS BLACK HOLE WILL START LOSING ITS MASS
MY CALCULATIONS ARE SUGGESTING THAT IT WILL BE DIFFICULT FOR THAT ATOM TO AVOID THE COLLAPSE WITH THE CENTER OF THE BLACK HOLE BUT IF THAT ATOM HAS A STRONG INERTIA IT WILL FALL DOW. "
HOW I JUSTIFY THAT THE COLLAPSE WILL BE AVOIDED---------------
BLACK HOLE EVAPORATION MUST BEGIN AT LEAST A SECOND BEFORE THE ATOM REACHES THE MINIMUM SCHWARZSCHILD RADIUS. THIS WILL ALLOW THE ATOM TO GET SOME TIME TO AVOID COLLAPSE. IF SUCH HAPPENS, THE CORE OF BLACK HOLE WILL PASS THROUGH THE ATOM WITHOUT AFFECTING IT. PROBLEM COME CAN I JUSTIFY ON THE BASIS OF INERTIAL ONLY
MY VIEWS-
INTERTIAL MASS OF THE ATOM WILL BE MORE THAN THE MASS OF BLACK HOLE. THIS WILL ALLOW THE ATOM TO DOMINATE.
BUT IF THE ATOM IS WELL ABOVE NR THE EVENT HORIZON, THEN THE PROCESS WILL BE IMPOSSIBLE. AS I RELATE MINIMUM SCHWARZSCHILD RADIUS, MAXIMUM CHANCE OF TRAVEL
ONCE THE MATTER FALLS INTO THE SECOND UNIVERSE, BY FORMULA
1/
CONCLUSIONS BASED ON WRITE UPS--
1] FOLDING OF SPACE IS NOT A WORMHOLE AND TIME TRAVEL
2] WORMHOLES ARE NOTHING BUT THE STAGE WHERE BLACK HOLES START EVAPORATING,THE ATOM NEAR ITS CENTER WILL PEEP BY VIRTUE OF INTERTIA
3] WORMHOLES DON'T REQUIRE WHITE HOLES FOR EXISTENCE
4] THE SPACE-TIME DIMENSION SAYS THERE IS A LINE OF HORIZONTAL WHOSE CO-ORDINATE
5] TIME TRAVEL TAKES PLACE WHEN THE POSITION OF A BODY ON SPACE-TIME CO-ORDINATE SYSTEM REVERSES
6] FOR A COSMIC TUNNEL, SPACE-TIME FABRIC DOESN'T EXIST. IT GETS CONVERTED TO TIME FABRIC BY FORMULA
OR BY 1/S = 1/T FOR EVERY LIGHT YEAR.SECOND OF UNIVERSE
7] MATTER BREAKS TO ATOMS DUE TO STORNG GRAVITY OF B.HOLE BUT IT DOESN'T GET CONVERTED BACK TO MATTER WHEN IT PASSES THROUGH BLACK HOLE.
SO WHITE HOLES ARE NOT REQUIRED
MATHEMATICAL ANALYSIS
SIMPLE GRAVITY FIELD EQUATIONS-
Fg=G x M1 x M2/ r
Fg refers to Force in terms of gravity,M1 and M2 are masses of objects kept at a certain distance r from each other.
Mb as Mass of Black hole and Mp as mass of photon
Photon away from event horizon and travelling at Velocity of light
Fg=G x Mb x Mp/r
Indicating force of gravitation between black hole and photon will be product of masses divided by square of distance between them. The maximum Tidal force will be when r will be just more than a collapse. We are considering Mb as mass of Black hole and r is distance of seperation. A photon and any other matter falling in the black hole will witness the maximum force of gravity just before the singularity.
FOR A NON ROTATING B.Hole
The gravitation equation will denote r as zero because the the singularity and photon will collide with each other. The eq. Will show ZERO in denominator denoting meaningless eq.
FOR ROTATING BLACK HOLE- Singularity due to rotation of black hole will shape up like a ring. The singularity will rotate around a fixed center point. Point is not traceble. There will be a constant change in the value of r as point will rotate
EQ>
Fg=G x Mb x Mp/r
as r will fluctuate and r will never be zero, The gravitational Tidal forces of Non rotating Black hole will be stronger than of a rotating one.
CHAPTER IX
LEVEL OF TIDAL FORCE ON A PHOTON TRAVELLING WORMHOLE
TO AVOID SINGULARITY, A ROTATING BLACK HOLE WILL BE SUPPORTIVE.
Assume at a point of space and time, a photon is 1km away from point of singularity
Assume mass of photon as 1kg,mass of black hole as 10kg
G~ 6.67x 10 raise to MINUS 11 N
Fg= 6.67 x 10 raised to Minus 11N{(m/Kg) square} X 10Kg X 1Kg/1Km
IT WILL BE EQUAL TO 66.7 X 10 raised to minus 11N. This is the GRAVITY OF BLACK HOLE ACTING ON PHOTON of mass 1Kg with mass of Black hole as 10kg and at a distance of 1Km from point of singularity.
For a non rotating black hole, photon will collide with singularity.
BLACK HOLE EVAPORTATION CAUES black hole to lose mass thereby reducing the gravity and normalising the curvature of space-time. After crossing the Event horizon, photon will accelerate as it moves towards dense mass. With no resistance due to motion, It will pass through the center around which singularity rotates. Photon will be transferred from one universe to another universe as the TIME CORDINATE of photon after avoiding singularity will be negative co-ordinate is north of Y-AXIS is positive.
CHAPTER VII
EXTENSION TO CHAPTER V
THERMODYNAMICS AND BLACK/WHITE HOLES
THE SECOND LAW OF THERMODYNAMICS IS A VERY CRUCIAL LAW IN STABILITY AND EXISTENCE FOR UNIVERSE
SECOND LAW SAYS THAT- ENTROPY OF A SYSTEM WHICH IS NOT IN EQUILIBRIUM WILL TEND TO INCREASE INSTEAD OF DECREASING REACHING THE MAXIMUM AT THERMAL EQUILIBRIUM.
.. A SIMPLIFIED VERSION IS THAT ENTROPY OF SYSTEM CAN DECREASE ONLY WHEN IT INCREASES ENTROPY OF ANOTHER SYSTEM IF TWO SYSTEMS ARE IN THERMAL CONTACT WITH EACH OTHER AND NOT IN PERFECT EQUILIBRIUM.
PROF. STEPHEN HAWKING PROVED THAT BLACK HOLE IS A THERMODYNAMIC BLACK BODY WHICH CONTAINS ENTROPY. ENTROPY OF BLACK HOLE PROVES ITS INTERRACTION WITH UNIVERSE. BLACK BODY PRINCIPLE CAUSES BLACK HOLE TO LOSE ENERGY AND MASS AT A CERTAIN TEMPERATURE DEFINED AS HAWKING TEMPERATURE. THIS INDICATES THAT BLACK HOLE'S ENTROPY INCREASES OVER A PERIOD OF TIME AND THUS EXISTENCE OF BLACK HOLE IS PROVED
UNFORTUNATELY, FOR WHITE HOLES, THE SECOND LAW HAS BEEN A BARRIER. SINCE TOTAL ENTROPY OF WHITE HOLE WILL NOT INCREASE RATHER DECREASE. WHITE HOLES EQUATIONS DESCRIBE IT TO BE A RELEASER OF LIGHT AND MATTER which ARE DENSE ENERGY OBJECTS, THUS DUE TO CONTANT RELEASE, ENTROPY WILL DECREASE AND THUS VIOLATION OF 2ND LAW.
THE IDEAL BLACK HOLE WHICH TENDS TO MAKE A TIME TRAVEL AS MENTIONED ABOVE MUST FOLLOW THE 2ND LAW. A ROTATING BLACK HOLE DOES FOLLOW SECOND LAW.
CHAPTER VIII
ACCELERATION
THE KEY OF TIMETRAVEL LIES WITH THE ACCELERATION. AS PER THE GENERAL THEORY OF RELATIVITY, AN OBSERVER MUST TRAVEL AT THE VELOCITY OF LIGHT SO AS TO OVERCOME AGING AND THUS RELATIVE FAST TIME. IF AN OBSERVER MOVES AT VELOCITY OF LIGHT, HE WILL OBSERVE TIME AROUND HIM TO PROCEED AS NORMAL AS CAN BUT IN REALITY HE WILL BE MOVING IN SLOW TIME AREA..
ALTHOUGH, ACCHIEVING THE VELOCITY OF LIGHT IS NOT VERY EASY AND ESPECIALLY TO ACCELERATE TO SPEED OF LIGHT, TIME TRAVEL CAN ALSO HAPPEN WITH ANOTHER PHENOMENA OF GRAVITATION TIME DILATION
A PHOTON CROSSING THE EVENT HORIZON WILL WITNESS DIFFERENT RATE OF TIME. RATE OF TIME WILL BE VERY SLOW AS THE OBJECT MOVES TOWARDS POINT OF SINGULARITY. AS SINGULARITY CAN BE AVOIDED, THE OBJECT AGAIN WILL WITNESS FASTER TIME RATE. THUS THE GRAVITY IN TERMS WILL CAUSE TIME DILATION EFFECT AND NO SPECIFIC NEED FOR THE OBSERVER TO ACCELERATE AND MOVE AT VELOCITY OF LIGHT.
HOWEVER, WE ARE CONSIDERING A PHOTON WHICH MOVES AT SPEED OF LIGHT FOR TIME TRAVEL
CHAPTER IX
THE TUNNEL OF TIMETRAVEL
IF THE PHOTON MANAGES TO AVOID SINGULARITY, THEN IT WILL PASS THROUGH THE OTHER END OF BLACK HOLE.
To be completed>>>>
Akshay Deoras
