Questions tagged [reissner-nordstrom-metric]
The reissner-nordstrom-metric tag has no usage guidance.
58
questions
2
votes
1
answer
115
views
Magnetic Reissner-Nordstrom Black holes
I am studying the RN black hole from Carroll, but i have a hard time following his explanations given in page 254.
To solve for the purely electrically charged black hole, one introduces the four-...
- 2,420
0
votes
0
answers
33
views
Mass/Charge ratio of a black hole
Which order of mass/charge ratio must a black hole have to become overfed?
- 1
0
votes
1
answer
91
views
How close does a charged particle have to be “attracted” to a charged black hole?
Let’s say see have a “mildly charged” black hole ($r_q \ll r_s$),
and an electron or positive that has the same charge.
While the charge to mass ratio of the black hole is orders of magnitude below ...
- 2,830
5
votes
0
answers
246
views
Why are there multiple universes in the Reissner-Nordström solution?
I am trying to make sense of the Penrose diagram of a non extremal Reissner-Nordström spacetime, that is, the solution with two horizons. The coordinates are
$$ v'=\text{exp}\left(\frac{r_+-r_-}{2r_+^...
- 709
1
vote
1
answer
89
views
How can there be a naked singularity in the Reissner-Nordström (RN) geometry? [duplicate]
I recently read that, if the mass of a charged black hole is small (compared to its squared charge times some constant), than there is no event horizon, but there is still a (naked) singularity. My ...
- 360
0
votes
0
answers
145
views
In and out an (extremal) Reissner-Nordström black hole
The Reissner-Nordström metric is a charged black hole solution of the Einstein equations. When $M=|Q|$, the Reissner-Nordström metric is written
$$ds^2= -\left(1-\dfrac{M}{r} \right)^2 dt^2 + \left(1-\...
- 1
0
votes
0
answers
34
views
Electric field of a black hole with charges fall into from opposite directions [duplicate]
Take a black hole, drop in some protons into end and some electrons into the point directly opposite.
I am having a great deep of trouble understanding why this doesn’t turn the black hole into an ...
- 2,830
0
votes
1
answer
89
views
What is the formula for the radius of the photon sphere of a charge black hole? [closed]
What is the formula for the radius of the photon sphere of a charge black hole?
I've found the formula for a Schwarzschild black hole and a Kerr black hole but despite some googling but I can't find ...
- 2,830
0
votes
1
answer
52
views
What is $A'$ in the Reissner-Nordstrom metric?
So I was reading this paper on the Reissner-Nordstrom metric and on it they define $A$ as:
But they don't define $A'$. Yet $A'$ still ends up in other equations like defining the Ricci tensors:
So ...
- 33
5
votes
3
answers
976
views
Does a charged particle respond to a charged black hole both gravitationally and electromagnetically?
The Reissner–Nordström metric is given by:
$$ds^2= \Bigl( 1-\frac{r_s}{r}+\frac{r_Q^2}{r^2} \Bigr) c^2dt^2- \Bigl( 1-\frac{r_s}{r}+\frac{r_Q^2}{r^2} \Bigr)^{-1}dr^2-r^2d\Omega^2$$
Which is intuitive ...
- 1,302
1
vote
1
answer
96
views
How is electric charge acting as a negative mass in general relativity?
In a NASA script on negative masses, there was the following statement:
How is it understandable that, there, charge "acts negative on mass"?
In general relativity, all kinds of energy ...
- 235
5
votes
2
answers
625
views
Reissner–Nordström blackhole and irreducible mass
I'm learning the Reissner–Nordström metric and confused by the notion of irreducible mass $M_\text{irr}$. It is said that the "total mass" $M$ contains both the irreducible mass and the ...
- 669
2
votes
1
answer
66
views
Question on Einstein Field Equations: charged black holes and fluids
Introduction
Suppose then you're asked to find the metric of a charged black hole. Given a generic, static and spherically symmetric metric tensor,
$\text{d}s^{2} = A(r)\text{d}t^{2} + B(r)\text{d}r^{...
- 3,005
0
votes
1
answer
686
views
RN Black hole and an accelerated observer
If I use the spacetime geometry for the Reissner-Nordström case and try to see the black hole's effect on an accelerated charged observer nearby, can I use the covariant equation for a charge moving ...
- 219
3
votes
0
answers
124
views
Are Reissner-Nordström black holes repulsive?
I'm not sure if I understand how the charged black holes work. The Reissner-Nordström metric is defined as
$$ds^2=\left(1-\frac{2M}{r}+\frac{Q^2}{r^2}\right)dt^2-\left(1-\frac{2M}{r}+\frac{Q^2}{r^2}\...
- 323
3
votes
1
answer
132
views
With how much energy can a charged black hole launch a electron away with?
Let’s say with have a black hole with a strong negative charge, then a say a neutron falls towards it.
Just before the neutron reaches the black hole's event horizon it undergoes beta decay, this ...
- 2,830
0
votes
1
answer
209
views
Negative energy of infalling particle in a Reissner-Nordström black hole
If we have a Reissner-Nordström black hole with Q > 0, then what charge (positive or negative) must an infalling charged particle have in order for the particle to be able to obtain negative ...
- 133
1
vote
0
answers
41
views
Why does a charged black hole affect the trajectories and event horizon for uncharged particles? [duplicate]
I can get electric charge affecting the behavior of quarks, charged leptons, W bosons, and photons since they interact electromagnetically. However, why would it affect uncharged particles like the ...
0
votes
1
answer
54
views
Why doesn't the electrostatic repulsion potential energy contribute to the metric of the Reissner-Nordström metric?
In Reissner-Nordström black holes it's the electric field that contributes to the metric. shouldn't the elctrostatic repulsion energy contribute also? there is quite a bit involved when charges are ...
0
votes
1
answer
223
views
How does the electric field of a Reissner-Nordstrom black hole exist outside its event horizon if nothing can escape the event horizon? [duplicate]
I am learning Reissner-Nordstrom black holes and I have learnt that the black hole contains a net charges. The static field due to it ( through the Energy Momentum tensor) exists even outside the ...
- 2,727
1
vote
1
answer
429
views
How does Spherical Symmetry constraint the Components of the Vector Potential
I am a bit confused as to what form does the 4 vector potential and Electromagnetic field tensor $F_{\mu \nu}$ take in the presence of magnetic charges. I got confused in this while looking at the ...
- 2,727
3
votes
1
answer
324
views
Why is trace of energy-momentum tensor not a good candidate for the source of gravity?
The reason why I think trace of energy-momentum tensor can't be the source is that, in a static weak field $p$<<$\rho$
$$T^{\mu}_{\mu} \approx T^{0}_{0} = -\rho$$
and if in one system I have ...
- 3,424
1
vote
0
answers
110
views
Extremal Reissner-Nordström Black Holes and the Third Law
I am thinking about a way to design a process which makes a extremal Reissner-Nordström black hole out of a non extremal one, i.e. it would violate the third law of black hole thermodynamics.
...
- 173
1
vote
0
answers
210
views
Maximal analytic extension of Robinson-Bertotti geometry
I want to find a maximal analytic extension of the Robinson-Bertotti metric given by
$$ds^2 = - \lambda^2 dt^2 +Q^2 \frac{d\lambda^2}{\lambda^2}+Q^2d\Omega_{S^2}^2.$$
Where $Q$ is a constant charge ...
- 173
1
vote
0
answers
78
views
Does the no-hair theorem apply to non-stationary spacetimes?
Carroll (pg. 238) gives the follow statement of the no-hair theorem:
Stationary, asymptotically flat black hole solutions to general relativity coupled to electromagnetism that are nonsingular ...
- 46.6k
-1
votes
1
answer
111
views
Time dilation in the Reissner-Nordström metric [closed]
According to Wikipedia, the formula for gravitational time dilation in the vicinity of a charged mass is:
$$\varsigma = \sqrt{|g^{t t}|} = \sqrt{\frac{r^2}{Q^2+(r-2 M) r}}$$
However, if I plug in $M=...
- 880
1
vote
1
answer
107
views
Mass distribution inside inner horizon of a charged black hole
I am trying to understand the spatial geometry inside the inner horizon of a charged black hole. I assume the charge accumulates exactly on the inner horizon (https://jila.colorado.edu/~ajsh/bh/rn....
- 2,605
1
vote
1
answer
398
views
What is the electromagnetic 4-vector potential in Reissner-Nordström coordinates?
If you have the usual Reissner-Nordström metric of a charged black hole, is the electromagnetic potential of the black hole still:
$$A_0(r,\theta,\phi) = \frac{Q}{r}$$
in these units?
user84158
0
votes
1
answer
78
views
Can a Black hole only have negative EM charge?
I understand that Black holes can have EM charge, they can have EM fields around them.
But is that possible that a black hole has more positrons and protons inside it (or that these have more EM ...
- 27.9k
2
votes
1
answer
523
views
Irreducible mass of a charged black hole merger
The irreducible mass $ \rm m_{irr} $ of a black hole with charge $ \rm Q $ is (in natural units)
$$ \rm m_{irr} = \frac{r_{+}}{2} = \frac{M}{2} + \sqrt{\frac{M^2}{4} - \frac{Q^2}{4}} $$
which is ...
- 10.9k
2
votes
1
answer
169
views
Imaginary charge on black hole
I was wondering if one can put an imaginary charge on a black hole. What I mean is, take a Reissner-Nordstörm black hole and make the charge $Q$ and therefore also the imaginary potential pure ...
5
votes
1
answer
157
views
What is the reason for $g_{tt}g_{rr}=-1$?
Both Reissner Nordstrom and Schwarzschild solutions in GR exhibit the property that $g_{tt}g_{rr}=-1$.
What can we deduce from this property in terms of the gravitational field?
- 1,938
1
vote
0
answers
111
views
On destroying the horizon of a Reissner-Nordstrom black hole
Consider a Reissner-Nordstrom black hole with $Q<M$, so that it has a well defined event horizon, the metric for such a black hole is given by (for $\theta=0, and ~d\phi=0$):
$$ds^{2}~=~-g(r)dt^{2}+...
- 1,349
1
vote
0
answers
99
views
Naked Singularities Out of Extremal Black Holes?
Consider a pair of identical extremal black holes at rest. It is a fact that they exert no net force on each other and remain in static equilibrium. Now, clearly, each of the black holes is in ...
user87745
8
votes
1
answer
1k
views
Why Do Extremal Black Holes Not Radiate?
This might be a "metaphysical" question with no actual physics content and if such is the case then I apologize. Actually, to figure out whether or not it is an actual physics question is one of the ...
user87745
4
votes
1
answer
229
views
Correlation between gravitational and electromagnetic radiation from collision of Kerr-Newman black holes
When black holes collide, they produce a gravitational wave, as has been recently established by LIGO.
When a charge is accelerated, it creates an electromagnetic wave.
Does an accelerated massive ...
- 653
6
votes
3
answers
657
views
Does the Reissner-Nordstrom Metric Necessarily Represent a Charged Black-hole?
The Reissner-Nordstrom metric
$$ds^2 = - \bigg(1-\dfrac{2M}{r}+\dfrac{4\pi Q^2}{r^2}\bigg)dt^2 + \dfrac{1}{\bigg(1-\dfrac{2M}{r}+\dfrac{4\pi Q^2}{r^2}\bigg)} dr^2 + r^2 d\Omega_2^2 $$
is a solution of ...
user87745
1
vote
0
answers
64
views
Temperature of R-N Black Hole by Euclideanising the Metric [closed]
How to derive the temperature of the Reissner–Nordstrom black hole by euclideanising the metric?
- 11
7
votes
2
answers
547
views
Would two Reissner-Nordstrom black holes with like charges repel or attract?
A few related side questions:
If the two oppositely-charged Reissner Nordstrom black holes collide
would their charge be negated and result in a regular Schwarzschild black hole?
Would a positively-...
- 435
2
votes
2
answers
128
views
Is it possible to turn a RN black hole with real r+- into one with naked singularity?
Let's say we initially have a RN black hole that has $Q^2<M^2$ where $Q$ and $M$ are its charge and mass respectively. Now if a particle goes into the blackhole is it possible for the new charge ...
- 385
1
vote
2
answers
655
views
Electromagnetic tensor trouble understanding
I'm running into trouble understanding what is going wrong, fooling around with the maxwell equations in tensor form, and playing with Cartesian and spherical coordinates.
To be more clear, I'm ...
- 113
1
vote
0
answers
649
views
Einstein Maxwell Lagrangian
If I take the Lagrangian
\begin{eqnarray} L= \frac{1}{2} R *1 - \frac{1}{2} F\wedge *F
\end{eqnarray}
I found $$ds^2 = -(1-\frac{2M}{R} +\frac{Q^2}{2r^2} )dt^2 + (1-\frac{2M}{R} +\frac{Q^2}{2r^2}...
- 441
1
vote
1
answer
185
views
Physical interpretation of the Reissner-Nordstrom metric for the special case
In the Reissner-Nordstrom metric
$$ \mathrm ds^2 = \left(1 - \frac{2GM}{r} + \frac{GQ^2}{4\pi\epsilon_0 r^2}\right)~\mathrm dt^2 - \left(1 - \frac{2GM}{r} + \frac{GQ^2}{4\pi\epsilon_0 r^2}\right)^{-1}...
- 11
4
votes
1
answer
212
views
Does the cosmic censorship conjecture limit the charge/mass ratio for particles?
For charged black holes, supposing true the cosmic censorship conjecture, this inequality must be verified (in natural units):
$GM^2 > Q^2$
Where of course $M$ and $Q$ are the mass and charge of ...
- 2,124
5
votes
2
answers
632
views
Does the charge of a black hole affect its space-time geometry?
Does a black-hole of a given mass and angular momentum have the same space-time geometry regardless of its charge? I'm pretty sure that an electric field can accelerate a charged particle but doesn't ...
- 1,648
6
votes
2
answers
3k
views
Derivation for the temperature of Reissner-Nordström (charged) black hole
A lot of the text for this is from "How does one correctly interpret the behavior of the heat capacity of a charged black hole?" but this concerns a different question. The Reissner-Nordström black ...
- 87
2
votes
1
answer
678
views
Physical interpretation of the Reissner-Nordström metric
The Reissner-Nordström metric (in spherical coordinates and $c = 1$) differs from the Schwarzschild metric in a additive term $$\frac{GQ^2}{4\pi\epsilon_0 r^2},$$ so the metric is
$$ds^2 = \left(1 - \...
- 405
1
vote
0
answers
135
views
What is the difference between Reissner-Nordstrom (RN) black hole and dyonic black hole?
A RN black hole is a black hole with electric charge, and a dyonic black hole with both electric charge and magnetic charge.
My Questions:
Is the above statement correct?
Is the charges the unique ...
- 369
11
votes
3
answers
682
views
Physical motivation for mathematically extending solutions to Einstein's equations
Sorry if this question gets a little long; I want to explain why I'm asking it.
The usual Schwarzchild metric
$$ds^2 = -\left(1-\frac{2M}{r}\right) dt^2 + \left(1-\frac{2M}{r}\right)^{-1} dr^2 + r^2(...
- 27.7k
0
votes
1
answer
789
views
What is unstable about the wormhole in the Reissner-Nordström solution?
In the conformal diagram for the Reissner-Nordström solution (included below), the inner horizon of the black hole leads to a wormhole which has a singularity, but it is possible to exit it through a ...
- 51