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Jul
30
comment Gedanken experiment: Does it collapse to a black hole or not?
The mass of a Schwarzschild black hole depends on the force exerted on a test particle at infinity, which does not change in your example.
Jul
16
comment Why does locking the rear tires on a vehicle cause it to spin?
When the tyres lock, static friction decreases significantly. This is the reason cars have ABS.
Jul
15
comment Are (active vs. passive) and (covariant vs. contravariant) related?
Active/passive transformation is related to whether we effect a change on the function and preserve the coordinate system, as opposed to the change on the coordinate system, while the function remains the same. A tensor can be covariant or contravariant regardless of whether the transformation is active or not.
Jul
12
comment Generalised velocities enough to be deterministic in Lagrangian mechanics?
Where does the dependence of $\ddot{q}$ on $(q, \dot{q})$ come from? This is not valid in the general case.
Jul
8
comment Classical models with unbounded particle number
The Boltzmann equation is about the distribution of particles in phase space. It allows for different kinds of particles that change from one form into another, which implies particle creation and destruction. It has applications in plasma physics.
Jun
20
comment How do you take the derivative with respect to a rank two tensor?
Every index combination indicates a different function. The derivative of a function w.r.t another functionally independent function, which is the case for functions with different indices, is zero and the only non-zero case is when the function to be derived and the one to be derived with are the same.
Jun
11
comment Is there a scientific term for the right-hand-(grip-)rule?
This is known as orientation. There are two orientations depending on the order of the basis vectors and only one of them can be used to define the volume element with positive sign.
May
10
comment If the electrostatic potential is zero, why doesn't the electric field have to be zero?
Do you mean $V$ is zero identically or that there's a value of $\vec{x}$, so that $V=0$?
Oct
27
comment Why to write the Navier-Stokes equation with dimensionless quantities?
Dimensionless quantities make it easier to define scales in some cases, such as this one, which allows us to derive physical meaning more easily. Also, they are especially suited for numerical simulations if the quantities have extreme values, because fast computer arithmetic has finite precision.
Oct
18
comment Why does gravitational collapse occur suddenly in a supernova progenitor?
I'm not arguing whether electron degeneracy is essential for stellar equilibrium or not, I'm just claiming that one needs to decide at what depth to extend an answer and assume certain knowledge by the OP, otherwise answering becomes a very time-consuming process. The core consists of Fe mainly (not Ni), because it has the maximum binding energy per nucleon. The model with a second shock wave is known as delayed hydrodynamic explosion. You're right about the free-fall time-scale; what I wrote is correct about the outer layers of the core.
Oct
18
comment Why does gravitational collapse occur suddenly in a supernova progenitor?
I didn't write about electron degeneracy pressure, because the question is about the process after the hydrostatic equilibrium condition ceases to be valid. I had assumed that the OP is aware of the process that keeps the stars in equilibrium.
Oct
18
comment Why does gravitational collapse occur suddenly in a supernova progenitor?
Since the time-scale of free-fall collapse is decreasing as the density increases, the outer layers fall faster than the inner ones and separate completely from the rest of the star as they reach supersonic speed. Splitting Fe reduces Fe's mass (the core is primarily Fe; products of its reactions eventually escape). The free-fall time-scale is essential here, because we have loss of hydrostatic equilibrium. The explosion does not always occur in a single stage; it is possible for part of the iron core to remain after the bounce, which triggers a second shock wave.
Aug
7
comment Unknown Function in the Tolman-Bondi-de Sitter Metric
$e^{-2\Psi}$ is a function that allows you to express a spherically symmetric metric in its most general form. It takes specific values depending on extra assumptions you make, e.g. static Einstein, Friedmann etc. The reprinted article has more examples.
Aug
7
comment Does a square wave “smooth out” in the air?
Try plotting it: a square wave is formed by the infinite sum of waves with integral multiples of the fundamental frequency. The more frequencies you add, the more the sine shape resembles a square. Since air is dispersive, the square will be deformed, especially for the higher frequencies. Higher frequencies affect the edges of the waveform, therefore the edges will soften as you lose supersonic frequencies.
Jul
29
comment Why does Pluto's orbit cross Neptune's orbit?
The solar system is not stable, as it demonstrates chaotic behaviour on time-scale of order of ten million years, as indicated by numerical simulations. In particular, the probability of collision is ~1% before the Sun dies. See this for details.
Jul
29
comment Is it possible that black holes are also neutron stars, but so dark that we cannot see them?
@RobJeffries Yes, sorry. I wrote that the Schwarzschild radius is of order 1 km, meaning that in general it is smaller than the radius of a neutron star, which is one order higher. I was giving rough estimates, because the equation of state is not known and exact values may change in the future. The range you give is realistic.
Jul
29
comment Is it possible that black holes are also neutron stars, but so dark that we cannot see them?
@RobJeffries According to p.12,15, of this, it is 7-11 km with the most conservative estimate being 9 km. This estimate hasn't changed much since Shapiro & Teukolsky was published.
Jul
25
comment Calculate loudness of sound: why am I getting contradictory answers?
Also, the temperature gradient in the vertical direction is known to affect the propagation of sound waves significantly.
Jul
22
comment Counting Problems in Physics
Non-trivial counting is often done in group theory.
Jul
21
comment Show that getting parallel transported does not change angle between them- Tensors
If you use google, there are lots of lecture notes on GR, but they require understanding of calculus, linear algebra, mechanics, differential geometry, differential equations etc.