Black hole as topological insulator

In summary, the black hole can be considered as a kind of topological insulator. This has far-reaching implications on our understanding of quantum black hole and the nature of gravity.
  • #1
shuijing
4
0
Hi, is anyone familiar with topological insulator? I read an interesting paper:
http://arxiv.org/abs/1703.09365,
Black hole as topological insulator

Abstract: Black holes are extraordinary massive objects which can be described
classically by general relativity, and topological insulators are new phases of
matter that could be use to built a topological quantum computer. They seem to
be different objects, but in this paper, we claim that the black hole can be
considered as a kind of topological insulator. For BTZ black hole in three
dimensional $AdS_3$ spacetime we give two evidences to support this claim: the
first evidence comes from the black hole "membrane paradigm", which says that
the horizon of black hole behaves like an electrical conductor. On the other
hand, the vacuum can be considered as an insulator. The second evidence comes
from the fact that the horizon of BTZ black hole can support two chiral
massless scalar field with opposite chirality. Those are two key properties of
2D topological insulator. For higher dimensional black hole the first evidence
is still valid. So we conjecture that the higher dimensional black hole can
also be considered as higher dimensional topological insulators. This
conjecture will have far-reaching influences on our understanding of quantum
black hole and the nature of gravity.

I am familiar with black hole but not topological insulator. Can anyone explain it to me?
 
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  • #2
You're barking at the wrong tree.

Topological insulator is a topic in condensed matter physics, and a very active one too. There have been a few threads started in the condensed matter forum on topological insulators. So you may want to browse that forum first, or ask this question there (see if a Mentor will move this thread for you).

Zz.
 
  • #3
Wow this sounds interesting! btw, Zapperz, this is the condensed matter forum, right? :D An insulator is simply a material which doesn't conduct electricity. In the system's band structure, the valence and conduction bands are separated by an energy gap which (assuming it is large enough) prevents electrons from jumping between bands. In condensed matter we use the Hamiltonian to describe a system; a few years ago the idea came around to classify these Hamiltonians according to their topology. This is usually done by considering [itex] H = h(k)\tilde{\sigma}[/itex], and using the [itex] h(k)[/itex] (or some other vector, it is somewhat up to the physicist) and finding it's map onto a unit sphere. The number of times this vector wraps around the unit sphere during the momentum shifting from [itex] -\pi\rightarrow\pi[/itex] in the Brillouin zone (band structure) is known as the winding number, or Chern number (similar to a genus in pure mathematics).

It was discovered that in certain systems, predicting the topology can correspond to protected edge states. So in some insulators which were previously thought to contain no conductance, two edge modes appear (under certain parameters) which are protected (not affected by disorder and giving conductance quantized similar to the quantum hall conductance) and move antiparallel to each other (chiral). A VERY nice review on the topic can be found in Topological Insulators, by Hasan and Kane.

Regarding the vacuum question, this is addressed directly in the Hasan and Kane review. The idea is that a vacuum is an insulator, with a gap separating the particle and antiparticle states. So if a black hole is a vacuum with chiral edge modes around the perimeter, the author's should be suggesting that this system can be classified topologically; it is an overall insulator but contains currents propagating in antiparallel directions on the edge. Whether these are protected states would interesting to see. Check out that review!
 
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  • #4
DeathbyGreen said:
Wow this sounds interesting! btw, Zapperz, this is the condensed matter forum, right? :D

The thread was moved from where it was originally posted.

Zz.
 
  • #5
Here's a nice 2 min video on topological insulators
 
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What is a black hole as a topological insulator?

A black hole as a topological insulator is a theoretical concept where the event horizon of a black hole behaves as a boundary between two distinct topological phases. This means that the laws of physics inside the event horizon are different from those outside, making the black hole an insulator that blocks the flow of particles and energy.

How does a black hole act as a topological insulator?

The gravitational pull of a black hole causes space and time to warp, creating a curved spacetime. This curvature can be described by a mathematical concept called topology, which studies the properties of objects that remain unchanged under continuous deformations. The event horizon of a black hole is a boundary where the topology of spacetime changes, making it act as a topological insulator.

What is the significance of black holes as topological insulators?

The concept of black holes as topological insulators has implications for our understanding of the fundamental laws of physics. It suggests that the laws of physics may not be the same everywhere in the universe and can change depending on the topology of space. This could potentially help us reconcile the theories of general relativity and quantum mechanics, which currently have discrepancies at the quantum level.

Can we observe black holes as topological insulators?

At this point, the concept of black holes as topological insulators is still a theoretical idea that has not been directly observed. However, there have been some studies that have shown evidence of topological properties in black holes, such as the presence of topological defects in the form of magnetic monopoles. Further research and observations are needed to confirm the existence of black holes as topological insulators.

What are the potential applications of black holes as topological insulators?

If confirmed, the concept of black holes as topological insulators could have significant implications for technologies such as quantum computing and communications. The distinct topological phases within the event horizon could be harnessed to manipulate and control the flow of particles and information in ways that are not possible with conventional materials. However, more research is needed to fully understand the potential applications of this concept.

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