well or euclid introducing how they are is the decisions of the universe

my i don't really and i'm walking by

in july of nineteen forty nine the ingenious location kroger omission favourite five and example

of the type of all possible solution aligns find the integration of gravitation

in that it is this article to his friend all the time on the occasion

of seven is firstly

they actually miss traditional phonological solution is the existence of closed time occurs which make

it feasible to go one bodily injury into one own house

the main goal of our goal is to visualize this unusual space you

in general relativity like call diagrams are used to get the first idea about structure

of a space time you can see like on diagram of goodness universe image the

future like onset point almost time axis

as one increases distance to the origin light comes keel over and reach domain of

negative corner time along the existence of closed time like ours

understand the visual perception in this universe one has to know how like probably case

two shows too light rays emitted at the origin common to all like rate is

there have a construction stretch long as taxes so you reveals that all light rays

emanating from the origin are in contrast by a single decision trees mediated by the

rest circle with radius called critical good rate

what visualization of quilt universe use tracing a simple but powerful method

the basic idea is to trace back light rays from your server side to the

scene

in case the library is an object the corresponding pixel on the screen is coloured

accordingly

as a first example initialize the fusion at low seemed are not directly origin

there exist two possible ways

the orange and blue ones that light can take to reach the of a

these two possibilities need to me of inverting images of the glow in this annotation

it's one between is that this is not the glow from the origin the two

images come closer in finally marriage you the radius

we don't the critical going radius the global south side

we are now ready

two and bar on our mind boggling journey into the past

in order to go on such a my journey we have to find a proper

in a closed curve

by using a boundaries we can transform the simplest close time curve such that it

passes through the origin

well visualization we use exact is corrupted sense you on a trip back in time

the first phase of the journey of this here is addressed but also the time

t equals zero this year starts to move along closed time occurs after that returns

back to the origin but interface to the destructor sphere remains addressed media server

the visualisation of this scenario shows the error rates here and it's copies you to

the light phrase the first figured it should give the rice and

suddenly the older version of the c approaches the youngest here addressed

it reaches the origin at the same moment in time in which the red dispute

you are trendy along the clothes i-vector

why the refugees appears to prosecute the rights and its blue all the variations remains

addressed

in our project tracing to provide you perspective on the structure of the universe

and you know that it inspires further investigations of other curved space times using this

powerful technique