Jerry Schirmer

Energy conservation does work perfectly in general relativity. The overall Lagrangian is invariant under time translations and Noether's Theorem can be used to derive a non-trivial and exact conserved current for energy. The only thing that makes general relativity a little different from electromagnetism is that the time translation symmetry is part of a larger gauge symmetry so time is not absolute and can be chosen in many ways.

Those objects are orbiting closely to SgrA${}^{*}$, certainly, but they are not orbiting closely enough to exhibit significant time dilation effects. In particular, consider the Schwarzschild spacetime. The inner most stable circular orbit around the central obect is at $r = 6M$, three Schwarzschild radii away. This makes the time dilation factor:So, even the farthest in stable orbit is only running 18% slower than a distant clock.

The angular momentum and charge of an electron are both large enough that a black hole would not form. If you believe classical general relativity all the way down to the scale of an electron (and you really shouldn't), then the electron will form a naked singularity. More exactly, for the case of a spinning body, the horizon is at the zero ofWhere $a$ is the angular momentum divided by the mass (in $G = c = 1$ units), and $M$ is the black hole's mass.

To being able to reach a high fraction of the speed of light, you need also a significant fraction of your equivalent payload mass as mass-energy. According to the formula for energy (rest and kinetic)so, to reach $0.1c$, that means your gamma is $\gamma = (1-\beta^2)^{-1/2} = 0.99^{-1/2} = 1.01$, so that means that for each kilogram of payload you want to accelerate to $0.1c$ (c being the speed of light) you need 0.01 kilograms as energy.

Firstly I hope this question is appropriate to ask here. I am a third year studying Mathematics at the University of Oxford, with plans to continue to 4th year to complete the masters course. I have been considering many paths to take so far this year, I started off by looking into finance, this I found however incredibly unintellectuality stimulating.

I hope this question isn't too naive, but would it theoretically be possible to have a black hole with 2 singularities (or 2 black holes at the same location). If this is possible, would there be any significant differences on the effects of space time? What I am thinking of is if you were to have a spinning black hole that has a ring as your first singularity and in the center of that ring was yet another singularity (with no angular momentum).

23 years later (after Millers planet, Murph is now grown), Tom is already regulary losing 1/3 of his corn harvest yearly (it's mentioned in the film, dialogue between Tom and Murph at the beginning of her visit at his farm). And as predicted by Prof Brand (Amelias father), Murphs generation will be indeed the last one surviving on Earth, Toms second child is also ill already, his son will not survive on the surface. I don't see a slip-up here.