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Made by: Jochem Knuttel Manus Visser
Alex Kieft
Tijmen Veltman (University of Amsterdam, 2014)


Black holes and the Firewall paradox


Black holes have always been mysterious objects in our universe. Their gravitational force is so strong that once coming to close there is no turning back. This radius of no return is called the horizon of the black hole and has been a serious subject of discussion among physicists for the last decades. The discussion all started with the introduction of Hawking radiation by Stephen Hawking: despite its strong gravitational field, a black hole is able to emit particles. These emitted particles are called radiation and occurs at the horizon because of particle pair creation. In normal vacuum particles from such a pair creation would immediately interact with each other and disappear again. In the presence of a black hole however, one of the two particles will be sucked in the black hole and the other would be free to fly away. This new kind of radiation led to a fundamental problem in physics: the information loss paradox.


 To understand the information loss paradox, we have to carry out the following thought experiment. Two black holes are originated by a MacBook and a ball with both the same mass. After a while both black holes evaporate into hawking radiation. These two radiations will exactly be the same. It appears that information is lost.


To conclude that this information indeed is lost, two important assumptions have been made. First of all we need to assume that we can trust the theory that we use to describe a black hole, which we call the effective field theory. This theory implies that hawking radiation is the only radiation (and therefore the only information) that escapes from a black hole.  Since Hawking explained in his article that Hawking radiation only exists of thermal radiation, we can almost say that everything that falls in a black hole will come out as thermal radiation. We need to however make a second assumption: nothing special happens at the horizon. For very strong physical reasons, which we will not touch here for simplicity, this will imply that the whole black hole will eventually disappear. These two assumptions together with the result of our conducted thought experiment inevitably lead to the conclusion that information is lost. Or, in correct physics language, we conclude that there is a violation of unitarity.


A strong objection against this loss of unitarity was however made by Gerard ‘t Hoofd, with his holographic principle. This can be simply explained that what happens inside a black hole is described by a quantum theory that ‘lives’ on the horizon. Since the most fundamental law in quantum mechanics is the existence of unitarity, It seams reasonable to turn our previous reasoning around: we start with unitarity and see what we can conclude.


To start with this new reasoning we first have to understand how Hawking radiation works in a quantum theory. When two particles are created as happens with Hawking radiation, they become entangled. There is very fundamental property of entanglement called monogamy: particles can only entangle ones. This leads to a problem in our theory of black holes. When a black hole has lost half of its mass, there are no particles left for the Hawking radiation to entangle with. When particles are not able to entangle when being created, something special happens: an exited state will arise at the horizon. We will call an exited state at the horizon a firewall.


We can therefore state a second contention: when a black hole loses half its mass a firewall will form at the event horizon. As already highlighted, the main reason the black hole cannot entangle with all its emitted radiation. To properly understand this reasoning, the hidden assumptions have to be made explicit. First, the black hole needs to be entangled with all its radiation to form a vacuum state and second, if there is no vacuum state at the horizon there has to be a firewall. To explain why a black hole can not entangle with all its radiation we have to make a distinction. If Hawking radiation is emitted before a black hole has lost half its mass we call it early radiation, and after this moment we call it late radiation. The fundamental assumptions that are made lead to a different result as in the information loss paradox. Effective field theory now specifically states that the two particles created by Hawking radiations need to be entangled. The monogamy of entanglement then results in the fact that a black hole cannot entangle with its late radiation. Together with unitarity, which states that the entire black hole will be emitted as Hawking radiation, this leads to the conclusion that a black hole cannot entangle with all its radiation. And so we end up with the conclusion that there is a firewall at the horizon.


We see what the reasoning maps have made apparent to us, different assumptions lead to different conclusions in the evaluation of paradoxes concerning the horizons of black holes. The reasoning maps have proved to be very useful in outlining a difficult problem in physics.

Used resources for group assignment on Firewall Paradox.



-        Sean Carroll, “Spacetime and Geometry: An Introduction to General Relativity” (2003), Addison Wesley

-        Daniel Schroeder, "An Introduction to Thermal Physics", (1999), Addison Wesley



-        A. AlmheiriD. Marolf, J. PolchinskiJ. Sully, Black Holes: Complementarity or Firewalls?” arXiv:1207.3123[hep-th]

-        V. Coffman, J. Kundu, W. K. Wootters, "Distributed entanglement," Phys. Rev. A 61, 052306 (2000)

-        S. Hawking, "Pair Creation by Black Holes," Phys. 43, 199-220 (1975)

-        J. Hartle, S. Hawking, (1983). "Wave function of the Universe". Physical Review D 28 (12): 2960.

-        G. 't Hooft (1993). Dimensional Reduction in Quantum Gravity. p. 10026. arXiv:gr-qc/9310026





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