5,207 reputation
1632
bio website sites.google.com/site/…
location Cambridge, MA
age 26
visits member for 3 years
seen 1 hour ago

Physics Graduate student at Harvard University.


Apr
10
answered Why is $p_\phi$ conserved in a Schwarzschild orbit?
Apr
9
comment Problem in one step of deriving Einstein's Field Equation from Caroll's book
For any general metric, $g^{\mu\nu}$ is defined to be the inverse matrix of $g_{\mu\nu}$. Then $g^{\mu\nu} g_{\mu\nu}$ is always computing $\text{tr}(g^{-1}g)$ which is the dimension of the space-time, namely 4.
Apr
9
comment Problem in one step of deriving Einstein's Field Equation from Caroll's book
To answer your question (which I think you deleted) - $g^{\mu\nu}$ is the inverse of the matrix $g$. In matrix notation, then $g^{\mu\nu} g_{\mu\nu} = \text{tr} \left( g^{-1} g \right) = \text{tr} \left( {\bf 1} \right) = 4$.
Apr
9
comment Problem in one step of deriving Einstein's Field Equation from Caroll's book
$g^{\mu\nu} g_{\mu\nu} = 4$
Apr
8
awarded  Nice Question
Apr
6
answered How to calculate angular momentum (J) in the Kerr parameter equation?
Apr
6
comment Gravitational Wave Interference
They can interfere but not via linear superposition since the equations of GR are non linear.
Apr
5
comment From String Frame to Einstein Frame for 10D supergravity
Integrate by parts?
Apr
3
comment How do I prove that the del squared operator commutes with the angular momentum operator?
That is not how it works. I am not asking you to compute $(\nabla^2 {\hat L}_z) f(x,y,z)$. I am asking you to compute $\nabla^2 \left( {\hat L}_z f(x,y,z) \right)$
Apr
3
comment How do I prove that the del squared operator commutes with the angular momentum operator?
Why do you think so??
Apr
3
comment How do I prove that the del squared operator commutes with the angular momentum operator?
Compute $\nabla^2 {\hat L}_z f(x,y,z)$ where $f$ is any function. Then compute ${\hat L}_z \nabla^2 f(x,y,z)$. Show that both answers are the same. QED.
Apr
2
awarded  Popular Question
Mar
31
answered $\nabla^{\mu}\nabla_{\mu}$ in general relativity
Mar
30
comment $\nabla^{\mu}\nabla_{\mu}$ in general relativity
I'll give you a simpler formula for the Laplacian on scalars: $\nabla^\mu \nabla_\mu \phi = \frac{1}{\sqrt{-g}} \partial_\mu \left( \sqrt{-g} g^{\mu\nu} \partial_\nu \phi \right)$. Prove this formula first and then use this.
Mar
24
comment Operator Dimension and Field Transformation under Rescaling
How so? You end up getting $\lambda \phi (\lambda x) \sim a_{\lambda^{-1} p'}$ and this $\lambda$ does not come out of the integral.
Mar
24
comment Operator Dimension and Field Transformation under Rescaling
Shouldn't $a_p = a_{\lambda^{-1} p'}$?
Mar
23
reviewed Close Why is there such an interest in Helium-3 and Moon mining?
Mar
23
reviewed Close Maximum acceleration for a vehicle
Mar
23
reviewed Close Photo electron effect on free electron
Mar
23
reviewed Close Off-diagonal terms in metric for 4D space-time