Questions tagged [kerr-metric]

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Normal vector field of costant time Kerr slice

The the Kerr metric of the Kerr spacetime in Boyer-Lindquist coordinates is given by $$ds^2=-\left(1-\frac{2mr}{\Sigma}\right)dt^2+\frac{\Sigma}{\Delta}dr^2+\Sigma d\theta^2+\left(r^2+a^2+\frac{2mra^2}...
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Can the effective singularity radius of a rotating black hole be measured?

Can the angular velocity of a black hole be measured? I found this article explaining how to measure the spin of a black hole can be measured, though I'm unclear whether 'spin' means angular velocity ...
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Second fundamental form of Kerr timeslice in BL-coordinates

I want to compute the coefficients of the second fundamental form $K$ of a timeslice $\lbrace t=0\rbrace$ in the Kerr metric in Boyer-Lindquist coordinates. I tried to do this via the definition of ...
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Massless Kerr black hole

Kerr metric has the following form: $$ ds^2 = -\left(1 - \frac{2GMr}{r^2+a^2\cos^2(\theta)}\right) dt^2 + \left(\frac{r^2+a^2\cos^2(\theta)}{r^2-2GMr+a^2}\right) dr^2 + \left(r^2+a^2\cos(\...
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A question about transuvection in Kerr spacetime

We know there are Killing vectors in Kerr spacetime. I wonder when doing transuvection on Killing vector, like $\left(\frac{\partial}{\partial t}\right)^\mu \bullet (dt)_\mu$ why it equals to $g_{tt}$ ...
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Is ergosphere without singularity possible?

The ergosphere is created because of the twisting of spacetime by a fast-rotating black hole. Then what if we rotate a non-singular object (I mean just a normal object that is not a black hole) really ...
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Hadamard state in Kerr spacetime

I have heard of the fact (see e.g. here) that there exists no everywhere-regular Hadamard (vacuum) state for quantum field in Kerr spacetime. My understanding is that the Hadamard condition provides &...
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What's the inner ergosphere in a Kerr BH?

(My book uses the notation "ergosphere" as the hypersurface of static limit, "ergoregion" as the hypervolume within.) Studying the Kerr BH, I've come to the part about horizons and ...
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What do black holes spin relative to?

What do black holes spin relative to?In other words, what is black hole spin measured in relation to? Spinning black holes are different from non-spinning black holes. For instance, they have ...
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Radial outgoing null geodetic in Kerr spacetime

According to Poisson's book A relativist's toolkit, pag 52, with the Schwarzschild metric I can define outgoing radial null geodesic as follows: $$u=t-\int f(r)^{-1} dr$$ where $f(r)=1-\dfrac{2m}{r}$. ...
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Would there be a physical Boundary Condition on Event Horizon for a perturbed Fluid of a Kerr-BH Accretion Disk?

Let's say we have a Steady-State Disk (Fishbone 1976 HD, or an MHD disk). For simplicity, we focus only on $\theta = \pi/2$. If we perturb every physical quantity by the rule $A = A+ \delta A $ (...
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What is the physical shape of a rapidly spinning singularity?

Let's say I have a star 20x the mass of the sun. At the end of its life, it collapses into a black hole. Now correct me if I am wrong, but as it collapses it rotational speed dramatically increases ...
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Question on four-velocity condition for timelike observers

I am a bit rusty on GR, I have the condition $u_{\mu}u^{\mu} = -1 $, in some notes I am given that we can obtain: $$-1 = u^{2}_{t} [g_{tt} +2 \Omega g_{t \phi} + \Omega^{2} g_{\phi\phi}]. \tag{1} $$ ...
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Kerr Metric in Cartesian Coordinates

I have checked online and the Kerr metric never seems to be given in Cartesian coordinates (although there is a conversion factor from Cartesian to Boyer-Lindquist coordinates). Is there some reason ...
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1answer
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Do spinning object near a spinning black hole obey the equivalence principle?

According to the equivalence principle the path of an object should not depend on it's composition. But on the other hand a spinning object (e.g. an electron) moving past a rotating Kerr black hole ...
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1answer
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Kerr black hole evaporation time question

Is there any closed (even if complicated) formula por the Hawking evaporation time for a Kerr black hole (and more general black holes) just like the one \begin{equation} t_e=\dfrac{5120\pi G^2M_0^3}{\...
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Time dilatation of an observer falling towards a Kerr Black Hole

In a Kerr Black hole there is a region where the component $g_{t t}$ of the metric changes sign (the ergoregion). The surface where $g_{t t}=0$ is called the ergosphere. So, if we consider an observer ...
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What happens when two ergospheres of oppositely spinning black holes of the same mass, axis of rotation, and speed of rotation approach?

What happens when two ergospheres of oppositely spinning black holes of the same mass, axis of rotation, and speed of rotation approach each other? What would happen to the black holes in question?
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How to show if a world line is null for a particular metric [closed]

For the Kerr metric, with line element $$ ds^2 = -\frac{\Delta-a^2\sin^2\theta}{\rho^2}dt^2 - \frac{4Mar\sin^2\theta}{\rho^2}dtd\phi +\frac{(r^2+a^2)^2-a^2\Delta\sin^2\theta}{\rho^2}\sin^2\theta d\phi^...
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Doubt on the precise definition of a general stationary rotating metric: the metric coefficients have which form?

Considering the following metric tensor $[1]$, with signature $(-,+,+,+)$, coordinates $(x^{0},x^{1},x^{2},x^{3})\equiv (t,r,\theta,\phi)$ and $c=1$: $$ds^{2} = g_{00}dt^{2} + g_{11}dr^{2} + g_{22}d\...
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Gravitational Redshift in Kerr Spacetime

Well, suppose then Schwarschild black holes. Following the $[1]$, we have the redshift factor: $$d\tau = \sqrt{1-\frac{2M}{r}}dt. \tag{1}$$ This factor have an physical interpretation to be the ...
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Spin rotation of masses in a rotating gravitational field around a black hole

If a rotational gravitational field affects masses in the way the frame and body velocities are added together does it mean that as the rotation of the frame has a gradient of the perpendicular ...
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Science of Kerr Black holes, can naked singularity form? Does it lead to another universe?

In the science fiction series, XeeLee Sequence, Stephen Baxter had used quite a lot of accurate physics in this hard science fiction. I was able to follow and determined which ones are true of our ...
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Horizons and other special surfaces on Kerr metric

The Kerr metric is \begin{equation} ds^2 = - \big(1-\frac{2GMr}{\rho^2}\big)dt^2-\frac{2GMra}{\rho^2}\sin^2 \theta \big(dtd\phi+d\phi dt\big)+ \frac{\rho^2}{\Delta}dr^2+\rho^2 d\theta^2 + \frac{\sin^...
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Trying to determine physically meaningful initial conditions for test particle around a Kerr black hole

I am working on some code for a test particle orbiting a Kerr black hole. I am trying to determine what the initial $ \frac{d t}{d\tau} $ would be. On Wikipedia https://en.wikipedia.org/wiki/...
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Symmetries of quasinormal modes of Kerr black hole

I have been reading this following paper on numerical evolution of the Teukolsky equation (see e.g. Eq 1 in their paper) for spin -2 fields about a spinning black hole (Kerr) solution. As the ...
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Gravitational waves from collapsing rotating mass? [closed]

According to the Birkhoff’s theorem, a non-rotating mass does not radiate gravitational waves during a spherically symmetric collapse. There is, however, no equivalent of the Birkhoff’s theorem for a ...
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Why do angular velocity deviates from Keplerian value close to a black hole?

The energy-momentum conservation equation in General Relativity is expressed as $T^{\mu\nu}_{\;\;;\nu}=0$ and by projecting this equation into the space normal to the four-velocity, we obtain the ...
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Does matter take infinite time to leave a black hole?

To this question: Can a sufficiently large black hole be singularity-free? about the possibility of a sufficiently large black hole not containing a singularity John Rennie posted an answer ...
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Some doubts regarding the effective potential for Kerr geometry

In the review Foundations of Black Hole Accretion Disk Theory, the authors defines an effective potential for Kerr geometry as (Chap. 2, eqn. 23) $$\Phi_{eff}=-\frac{1}{2}\ln\left|g^{tt}-2lg^{t\phi}+l^...
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Anatomy of a black hole: which are its layers?

I'm trying to find out how a Kerr-type black hole is structured (that is, a black hole with non-zero angular momentum but no net electrical charge). According to the information I have found, the ...
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What is the volume inside the inner event horizon of a Kerr black hole?

(Dokuchaev 2011) found periodic orbits of particles and photons inside a Kerr-Newman black hole with a maximally extended global geometry. They orbit inside the inner horizon $r<r_-$ where the $r$ ...
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What is the radius of the ringlike singularity of a Kerr BH?

For a rotating (Kerr) Black Hole the radius of the ring singularity is evaluated mathematically as R = a, see Metric diameter of a ring singularity. This means that R is always greater (or equal) to ...
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Where is the singularity located in a Kerr black hole?

In a rotating Kerr black hole is the ringlike singularity situated between the inner and the outer event horizon of the black hole?
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The physical interpretation of the trip inside Kerr (black hole) spacetime

Consider then the Kerr metric$[1]$: $$ds^{2} = -\Bigg(1-\frac{2Mr}{\rho^2}\Bigg)dt^2 - \frac{2Marsin^2(\theta)}{\rho^2}[dt d\phi+d\phi dt] +$$ $$+\frac{\rho^2}{\Delta}dr^2+\rho^2d\theta^2+ \frac{sin^...
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Time Derivative defined by Fermi transport in Kerr Space-Time

I have been studying 3+1 GR the last weeks. I have tried to comprehend Electrodynamics in curved space-time: 3+1 formulation (1982) Thorne McDonald I have studied another 3+1 GR book but it didn'...
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Normal vectors and induced metric Kerr metric

Consider the Kerr metric given by: $$ds^2 = -(1-\frac{2GMr}{\rho^2})dt^2 - \frac{2GMar\sin^2{\theta}}{\rho^2}(dtd\phi+d\phi dt)+ \frac{\rho^2}{\Delta}dr^2+\rho^2d\theta^2+ \frac{\sin^2\theta}{\rho^2}[...
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Particle falling into a Kerr black hole

Let's say that a particle starts a radial free fall towards a Kerr black hole with zero initial energy at $r\rightarrow\infty$. The initial angular momentum of the particle is zero ($p_\phi = 0)$. ...
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River model of a Kerr black hole: What does it mean for the spatial metric to be sheared?

I am currently trying to understand the river model for a Kerr black hole. There is one concept I don't grasp yet. What does it mean for the spatial metric to be sheared in the given context. I am ...
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Teukolsky-Starobinsky identities

The Teukolsky-Starobinsky identites relate solutions of the two Newman-Penrose scalars $\Psi_0$ and $\Psi_4$ around Kerr black holes. For example (here I am quoting Theorem 1 in Sec 81 of ...
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Is the Kerr metric more symmetric than a normal type D spacetime?

The Kerr spacetime is of Petrov type D (see here for the Petrov classification of spacetimes). In the Newman-Penrose formalism, from the Goldberg-Sachs theorem we can conclude that there is a choice ...
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Derivation of Teukolsky equation

I have been trying to derive the Teukolsky equation via the Newman-Penrose formalism. I have derived the following formula (see Eq. (2.14) in Teukolsky's paper) \begin{equation} (*) \left[(\Delta +3\...
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ZAMO's trajectory near a Kerr Black Hole?

sorry for the "generic" question, just that the last month I have been studying GR from 0 and having problems understanding some of the concepts. Anyways, to the question I wanted to ask: From my ...
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1answer
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Effective potential for Kerr geometry

In the review Foundations of Black Hole Accretion Disk Theory, the authors defines an effective potential for Kerr geometry as (Chap. 2, eqn. 23) $$\mathcal{U}_{eff}=-\frac{1}{2}\ln\left|g^{tt}-2lg^{t\...
2
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1answer
200 views

What is exactly rotating in a rotating black hole?

I have read this: https://arxiv.org/abs/gr-qc/9404041 In General Relativity the black hole solutions which have so far been found form a four parameter family called the generalized Kerr-...
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How to derive the angular velocity of circular orbits in Kerr geometry?

I am trying to derive the angular velocity of a circular orbit in Kerr geometry, eqn.(2.16) in Bardeen et al (1972) which reads $$\Omega=\dfrac{1}{r^{3/2}+a}$$ (Note that I am using the units in which ...
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1answer
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Physical significance of angular velocity of orbits around Kerr black holes

For the Kerr metric $$ds^2=\left(g_{tt}-\frac{g_{t\phi}^2}{g_{\phi\phi}}\right)dt^2+g_{\phi\phi}\left(d\phi-\omega dt\right)^2+g_{rr}dr^2+g_{\theta\theta}d\theta^2$$ the angular momentum is defined as ...
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Zero mass Kerr metric

When mass in Kerr metric is put to zero we have $$ds^{2}=-dt^{2}+\frac{r^{2}+a^{2}\cos^{2}\theta}{r^{2}+a^{2}}dr^{2}+\left(r^{2}+a^{2}\cos^{2}\theta\right)d\theta^{2}+\left(r^{2}+a^{2}\right)\sin^{2}\...
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Metric for a rotating star

If we want to describe a static spherically symmetric star we can use a metric which matches the Schwarzschild solution with correct mass on the outside of the star but differs from Schwartzschild in ...
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Light-like normal vectors

Can someone please show me how to mathematically establish that the normal vector to the event horizon of a Kerr Black Hole is light-like?