What would happen to me if by accident, a leftover magnetic monopole from the inflationary period were to hit me? Would I even notice?
Just to add: Einstein's field equations are a bit like Newton's laws of motion. Newton's laws potentially describe anything that moves under the influence of a force, and Einstein's equations are the same. So, to start looking for solutions you need to decide what thing or class of things you want to look at. If you're not specific about it then the problem is just too general. For example, suppose you start with Newton's laws of motion and ask the particular question "What shape path does a ball follow when I throw it through the air?" To answer that question you need to plug some observations about the forces that act on the ball into Newton's equations, then mathematically work through the solutions to those equations to get a mathematical description of the path, which is the answer to your original question. That's like asking why Isaac Newton didn't solve his equations for the motion of every conceivable object. For a start, Newton didn't always know what specific questions to ask, even if he knew the general laws. And even if he had asked the questions the task of solving the equations is way too big for one man to do in one lifetime. I should say that all the general equations of physics describe whole sets of phenomena. For example, everything we know about (classical) electromagnetism is described by less than 10 electromagnetic equations. But that doesn't mean that as soon as we knew those 10 equations we were immediately able to invent radio and TV and electronic computers, even though everything that happens inside a radio, a TV or a computer is a "solution" to those same 10 equations.
tashja: Magnetic monopoles are completely theoretical right now. A little background: every magnet you ordinarily come across has two poles: a north pole and a south pole. If you take an ordinary bar magnet then one end is a north pole and the other is a south pole. Cut the magnet in half and you get two pieces of magnet. However, one piece is not a north pole and the other piece a south pole. What you get is two pieces that each have a north and a south pole. This cutting business works right down to the atomic level. Cut any magnetic substance and the pieces you end up with all have both a north and a south pole. Nothing you can do will ever leave you with just a north pole on its own or just a south pole on its own. A theoretical particle that has just a north magnetic pole, or just a south pole, on its own, is a magnetic monopole. No magnetic monopoles have ever been found in the real world. In theory, any particle could be a magnetic monopole, so its mass could be anything, and it could belong to any "family" of particles. But no particle ever observed has been found to be a monopole. I can't see any reason why they couldn't, if they exist. Of course, two "north" monopoles should always repel each other magnetically, and so should two "south" monopoles, though one north and one south would attract. I have no idea.
I was wondering if black holes grow in size just by been exposed to light. For example: the black hole at the center of the Milky Way is bombarded by starlight all the time. What happens to those photons? Do they add to its mass?
Yep, they sure do. If Hawking radiation is correct (and we have no reason to believe it's not) then black holes lose mass by radiating a thermal spectrum of particles. For black holes that are a result of the collapse of a star, the temperature of the Hawking radiation is a few 10's of micro Kelvins. Compare that with the CMB which is 2.7K and you can see that black holes absorb more radiation than they emit, meaning they gain a bit of mass.
Thanks, Prometheus. ''The Lie group of possible rotations in three spaces and one of time direction is Spin(1,3)-the Lie group of gravity. We feel the force of gravity because the gravitational spin connection field is rotating our frame as we move through time, attempting to steer us towards Earth's center.'' SciAm, December 2010 I don't understand this. How is the gravitational field rotating our frame?
Spin connections are perhaps a little too much to be biting off. They relate to how the gravitational field affects covariant derivatives when phrased in terms of vierbeins. You can relate the curved space-time metric g to the flat space-time metric (which allows you to define, if only for an instant, an inertial frame) \(\eta\) by the use of a veirbein e via \(g_{ab} = \eta_{\mu\nu}e^{\mu}_{a}e^{\nu}_{b}\). The space-time curvature dependency is then entirely contained within e, which then can be used to define a spin connection via something like \(\partial_{b}e_{a}^{\mu} = \omega^{\mu}_{ba}\), which then is added to the connection in a covariant derivative \(\nabla \to \nabla +\omega\) (if memory serves, its been a few years). Put in vaguely wordy terms it tells you how your inertial frame, associated to a flat space-time point of view, varies as you move through space. A special relativity based inertial frame doesn't allow for curved space-time but you can shoe-horn the special relativity notion into general relativity by using the spin connection to update your inertial frame's structure as you move through curved space-time.
Tha characterization of spin in a gravitational field I think goes like: objects with momentum can spin in space and in time, and there is an abstract system of coordinates with [an] axis for components of spin in time and in space, which is the Spin(1,3) Lie group. It's a way to package the curvature = gravity theory (which works pretty well); an object with momentum follows a geodesic path, and if spacetime is curved the path will 'rotate' because of the extrinsic curvature. The moon is rotating around the earth because the curvature of spacetime gives the moon 'spin' in (3,1) dimensions. Then of course, objects accelerate (rocket ships for instance), and rotate around their centres of mass, and there are tidal forces that deform the shape of gravitationally bound objects. Gravity is complicated because if gravity is acceleration this is equivalent to the intrinsic curvature of a geodesic.
So, do we feel gravity because we are falling towards the center of the Earth, or is it because the Earth is falling towards the center of the Sun, or is it both?
You feel because you are not falling. In other words you feel the pressure (or tension?) in your joints and muscles because they support your weight.
Sorry,Temur, let me reword my question. If the Sun were to disappear, would the gravity on Earth remain the same?
Your weight is a product of your mass and the strength of the gravitational field, W = mg. This says your "Newtonian" weight is an acceleration towards a centre of gravity. You don't think you're moving when you stand still, but you are moving through spacetime, the sun is too and the galaxy. What prevents your apparent motion is the surface and the stress and tension in it from all the motion in your comoving frame. If the surface wasn't rigid you would be in motion.
I'm trying to figure if the gravity that we have on our planet is generated by the Earth only and not by the curvature that the Sun makes in space.
The answer to that question is that the gravity you feel on earth is not due to any effect from the sun's mass, only the earths..
Tides are caused by the moon's and sun's influence on the earth as well as the rotation of the earth on its own axis, which gives rise to 'fictitious' forces.
Quarkhead makes a good point. Suppose we isolate the Earth from everything around it and toss it into intergalactic space far from any noticeable dimple in space-time like the Sun or the galaxy. I'm guessing that Earth will simply create its own gravity well and we would continue to experience gravity like always, right? A watermelon would fall to the floor at the same rate, and it would weight the same, no?
