praveen said:
...
i read some physics in my Engineering education days. Surprisingly, i am getting more & more attracted to Physics , particularly astrophysics ( relativity ,...etc ).
I read that Earth has gravity G with certain value. Per Einstein, space is curved with presence of Huge object(mass) . My question is does Earth have gravitation because of it's mass ? If so , what is the relation between Mass of a Object and Gravitation ? i mean to ask , how does a object with certain mass makes the space around it to be curved ?
...
We should be able to think of better books for you, praveen.
the books so-far suggested are not mathematical.
but you have had college calculus (as normal part of engineer education)
so a good approach for you could have some formulas in it.
http://math.ucr.edu/home/baez/relativity.html
http://www.math.ucr.edu/home/baez/einstein/
http://math.ucr.edu/home/baez/RelWWW/tutorial.html
http://math.ucr.edu/home/baez/gr/gr.html
the key equation for you to understand is the einstein equation which relates curvature in a region to the density of mass and pressure in that region.
the curvature is on the lefthand side of the equation and the
"stress-energy" tensor is on the righthand side.
the righthand side is usually dominated by a mass density
but mass can be thought of as a form of energy so (just multiplying
mass by c
2) the righthand side can be all put into form
of energy density (joules per cubic meter)
a very small role is played by pressure (which has the same units as energy density----joules per cubic meter is same as Newton per sq.meter)
It is actually true that if material is squeeze so it has more pressure inside this contributes a tiny tiny tiny extra gravity----almost always negligible.
amazingly einstein included even this extremely small effect of pressure.
so it is not just mass-energy on the righthand side.
this equation is very simple and elegant, and it would be fortunate if we could find a book which would present it to you in a way that pleased you
and made it easy for you to understand.
John Baez has a tutorial on the einstein equation at his website. this is an introductory simplified approach to the main equation of Gen Rel. and it also does not cost money. I already gave the link. I will give it again:
http://www.math.ucr.edu/home/baez/einstein/
It is called "the meaning of the einstein equation"
It is very simplified but maybe it would be suitable as a beginning.
this stuff has equations and expects you to know simple college calculus,
but they are not HARD equations and there are not so many.
So nobody who has had engineer education should be worried!
he also has a collection of links to Gen Rel resources on the WW Web.
he also recommends BOOKS
Like Ian Kenyon 1991 Oxford Univ. Press text called "General Relativity"
and also he suggests popular books (but not by Stephen Hawking as it happens)
Now I will have my say and tell you a little about the UNITS of the einstein equation. at one point I will use a letter K for curvature instead of the usual letter G (which is confusing because same letter as the Newton gravitational constant G) otherwise this is pretty standard.
the units of curvature is inverse distance square------that is 1/sq meter.
(time must be multiplied by c and measured as distance---cdt---to have all units same)
that is because curvature is a second derivative----d
2/dx
2
so think about the units of the Einsteinequation. On the lefthhand side it must be curvature---inverse square distance---- meters
-2
and on the righthand it must be energy density----joule meters
-3------which is same units as pressure-----Newton meter
-2
Guess what do you multiply the RHS by to get the LHS? the answer is 8pi G/c
4
where c is speed of light and G is the (Newtonian) universal grav. const. which has units
meters
3second
-2kilogram
-1
Amazingly, G/c
4 has units 1/Newton!
this is just what is needed so you can multiply by it Newton meter
-2 and get the right thing, namely meter
-2!
so einstein eqn. (main eqn. of Gen Rel) says simply
K = 8pi G/c
4 T
where K is curvature on LHS and T is energy density (officially "stress-energy tensor") on RHS.
(careful, people use various different letters in their notation, often use G for curvature, confusing since also have letter G for grav. const!)
Now I suggest that you go to
John Baez website and try to understand this equation more deeply, with his examples.
After that there will turn up some respectable book, like Ian Kenyon or the classic difficult Misner Thorne Wheeler or something----see what other PF people say---also see if
John Baez has a recommendation
Also BTW I thought everything NateTG said was good advice---but he did not recommend any book. I think he said do to PF "General Relativity" forum and ask. That is a good suggestion also.
You say you had an engineer education and then later in life got interested in fundamental things like the universe and why there are forces and matter and so on. this is a good transition and i sympathize.
I hope that in the next few years the actual REASONS why concentration of energy in a region causes curvature will begin to emerge. I think I see signs of this in Quantum Gravity research. But in any case we must first understand the Einstein Equation because that describes the way it goes even tho it cannot explain the mechanism connecting them
matter tells spacetime how to bend
spacetime shape tells matter how to flow
have fun learning
