Most number theorists will be familiar with the result conjectured in the 19th century and proved in the 20th century that the only square pyramidal numbers that are square numbers are 1 and 4900 (the sum of the squares from 1^2 to 24^2 = 70^2).
While discussing this, it was pointed out to me...
Imagine a perfectly reflecting box with a homogenous distribution of photons within it with total energy E (not entirely sure how close to possible this is, but don't worry about that).
I would have thought this box's gravitational field would be very much like the combination of the the box's...
It is well-known that associated with the Kerr solution which represents a rotating black hole, there can be a region of space-time where there are loops in space time (non simply connected paths which are navigable in principle). If this is so, it breaks causality and permits time travel in...
Hawking and others suggest that it is a very special deal that macroscopic black holes lose quantum information, but I only partially agree.
It is clearly important that they do not preserve most quantum numbers - black holes may be a way to break a lot of conservation laws of particle physics...
Suppose you have the simplest type of black hole - time independent, no angular momentum or charge, Schwarzschild solution, then you modify the situation by adding a stationary mass outside the event horizon (I imagined lowering this slowly on an idealised string).
The question is, does this...