**A dimensional analysis activity to perform in the classroom**

**Jorge Pinochet**

In this paper we present a simple dimensional analysis exercise that allows us to derive the equation for the Hawking temperature of a black hole. The exercise is intended for high school students, and it is developed from a chapter of Stephen Hawking’s bestseller A Brief History of Time.

Read more at https://arxiv.org/pdf/2004.11850.pdf

# Tag Archives: Hawking

# Here’s What Stephen Hawking’s Final Paper Was Actually About

…. His final paper, entitled A Smooth Exit from Eternal Inflation? (preprint here), focuses on the birth of the Universe as we know it….

# Soft Hair on Black Holes

**Stephen W. Hawking, Malcolm J. Perry, and Andrew Strominger**

It has recently been shown that BMS supertranslation symmetries imply an infinite number of conservation laws for all gravitational theories in asymptotically Minkowskian spacetimes. These laws require black holes to carry a large amount of soft (i.e. zero-energy) supertranslation hair. The presence of a Maxwell field similarly implies soft electric hair. This paper gives an explicit description of soft hair in terms of soft gravitons or photons on the black hole horizon, and shows that complete information about their quantum state is stored on a holographic plate at the future boundary of the horizon. Charge conservation is used to give an infinite number of exact relations between the evaporation products of black holes which have different soft hair but are otherwise identical. It is further argued that soft hair which is spatially localized to much less than a Planck length cannot be excited in a physically realizable process, giving an effective number of soft degrees of freedom proportional to the horizon area in Planck units.

Read more at https://arxiv.org/pdf/1601.00921v1.pdf

Read also: “Gary T. Horowitz, **Black Holes Have Soft Quantum Hair**“

# Information Preservation and Weather Forecasting for Black Holes

**S. W. Hawking**

It has been suggested [1] that the resolution of the information paradox for evaporating black holes is that the holes are surrounded by firewalls, bolts of outgoing radiation that would destroy any infalling observer. Such firewalls would break the CPT invariance of quantum gravity and seem to be ruled out on other grounds.

A different resolution of the paradox is proposed, namely that gravitational collapse produces apparent horizons but no event horizons behind which information is lost. This proposal is supported by ADS-CFT and is the only resolution of the paradox compatible with CPT.

The collapse to form a black hole will in general be chaotic and the dual CFT on the boundary of ADS will be turbulent.

Thus, like weather forecasting on Earth, information will effectively be lost, although there would be no loss of unitarity.

Some time ago [2] I wrote a paper that started a controversy that has lasted until the present day. In the paper I pointed out that if there were an event horizon, the outgoing state would be mixed. If the black hole evaporated completely without leaving a remnant, as most people believe and would be required by CPT, one would have a transition from an initial pure state to a mixed final state and a loss of unitarity. On the other hand, the ADS-CFT correspondence indicates that the evaporating black hole is dual to a unitary conformal field theory on the boundary of ADS. This is the information paradox.

Recently there has been renewed interest in the information paradox [1]. The authors of [1] suggested that the most conservative resolution of the information paradox would be that an infalling observer would encounter a firewall of outgoing radiation at the horizon.

There are several objections to the firewall proposal. First, if the firewall were located at the event horizon, the position of the event horizon is not locally determined but is a function of the future of the spacetime.

Another objection is that calculations of the regularized energy momentum tensor of matter fields are regular on the extended Schwarzschild background in the Hartle-Hawking state [3, 4]. The outgoing radiating Unruh state differs from the Hartle-Hawking state in that it has no incoming radiation at infinity. To get the energy momentum tensor in the Unruh state one therefore has to subtract the energy momentum tensor of the ingoing radiation from the energy momentum in the Hartle-Hawking state. The energy momentum tensor of the ingoing radiation is singular on the past horizon but is regular on the future horizon. Thus the energy momentum tensor is regular on the horizon in the Unruh state.

So no firewalls.

For a third objection to firewalls I shall assume that if firewalls form around black holes in asymptotically flat space, then they should also form around black holes in asymptotically anti deSitter space for very small lambda. One would expect that quantum gravity should be CPT invariant. Consider a gedanken experiment in which Lorentzian asymptotically anti deSitter space has matter fields excited in certain modes. This is like the old discussions of a black hole in a box [5]. Non-linearities in the coupled matter and gravitational field equations will lead to the formation of a black hole [6]. If the mass of the asymptotically anti deSitter space is above the Hawking-Page mass [7], a black hole with radiation will be the most common configuration. If the space is below that mass the most likely configuration is pure radiation.

Whether or not the mass of the anti deSitter space is above the Hawking-Page mass the space will occasionally change to the other configuration, that is the black hole above the Hawking-Page mass will occasionally evaporate to pure radiation, or pure radiation will condense into a black hole. By CPT the time reverse will be the CP conjugate. This shows that, in this situation, the evaporation of a black hole is the time reverse of its formation (modulo CP), though the conventional descriptions are very different. Thus if one assume quantum gravity is CPT invariant, one rules out remnants, event horizons, and firewalls.

Further evidence against firewalls comes from considering asymptotically anti deSitter to the metrics that fit in an S1 cross S2 boundary at infinity. There are two such metrics: pe- riodically identified anti deSitter space, and Schwarzschild anti deSitter. Only periodically identified anti deSitter space contributes to the boundary to boundary correlation func- tions because the correlation functions from the Schwarzschild anti deSitter metric decay exponentially with real time [8, 9]. I take this as indicating that the topologically trivial periodically identified anti deSitter metric is the metric that interpolates between collapse to a black hole and evaporation. There would be no event horizons and no firewalls.

The absence of event horizons mean that there are no black holes – in the sense of regimes from which light can’t escape to infinity. There are however apparent horizons which persist for a period of time. This suggests that black holes should be redefined as metastable bound states of the gravitational field. It will also mean that the CFT on the boundary of anti deSitter space will be dual to the whole anti deSitter space, and not merely the region outside the horizon.

The no hair theorems imply that in a gravitational collapse the space outside the event horizon will approach the metric of a Kerr solution. However inside the event horizon, the metric and matter fields will be classically chaotic. It is the approximation of this chaotic metric by a smooth Kerr metric that is responsible for the information loss in gravitational collapse. The chaotic collapsed object will radiate deterministically but chaotically. It will be like weather forecasting on Earth. That is unitary, but chaotic, so there is effective information loss. One can’t predict the weather more than a few days in advance.

[1] A. Almheiri, D. Marolf, J. Polchinski, J. Sully, Black Holes: Complementarity or Firewalls?, J. High Energy Phys. 2, 062 (2013)

[2] S. W. Hawking, Breakdown of Predicatability in Gravitational Collapse, Phys. Rev. D 14, 2460 (1976)

[3] M. S. Fawcett, The Energy-Momentum Tensor near a Black Hole Commun. Math. Phys. 89, 103-115 (1983)

[4] K. W. Howard, P. Candelas, Quantum Stress Tensor in Schwarzschild Space-Time, Physical Review Letters 53, 5 (1984)

[5] S. W. Hawking, Black holes and Thermodynamics, Phys. Rev. D 13, 2 (1976)

[6] P. Bizon, A. Rostworowski, Weakly Turbulent Instability of Anti-de Sitter Space, Phys. Rev. Lett. 107, 031102 (2011)

[7] S. W. Hawking, D. N. Page, Thermodynamics of Black Holes in Anti-de Sitter Space, Commun. Math. Phys. 87, 577-588 (1983)

[8] J. Maldacena, Eternal black holes in anti-de Sitter, J. High Energy Phys. 04, 21 (2003) [9] S. W. Hawking, Information Loss in Black Holes, Phys. Rev. D 72, 084013 (2005)

…. Read more at http://arxiv.org/pdf/1401.5761v1.pdf

Read also: **Stephen Hawking questions nature of black holes** and **Stephen Hawking’s new theory offers black hole escape**

# Stephen Hawking: physics would be ‘more interesting’ if Higgs boson hadn’t been found

Physics would have been “far more interesting” if scientists had been unable to find the Higgs boson at the Large Hadron Collider (LHC) in Cern, according to Stephen Hawking, who has admitted to losing a bet as a result of the discovery in July last year.

The world-famous cosmologist was speaking at an event to mark the launch of a new exhibit on the LHC at London’s Science Museum and, in a speech, discussing the unanswered questions at the edges of modern physics as part of a history of his own work in the field.

Though the Higgs boson was predicted by theory in the early 1960s, not everyone believed it would be found. If it had not been found, physicists would have had to go back to the drawing board and rethink many of their fundamental ideas about the nature of particles and forces – an exciting prospect for some scientists.

“Physics would be far more interesting if it had not been found,” said Hawking. “A few weeks ago, Peter Higgs and François Englert shared the Nobel Prize for their work on the boson and they richly deserved it. Congratulations to them both. But the discovery of the new particle came at a personal cost. I had a bet with Gordon Kane of Michigan University that the Higgs particle wouldn’t be found. The Nobel Prize cost me $100.”

Hawking hoped the LHC would now move on from the Higgs boson to looking for evidence of more fundamental theories that explain the nature universe and, in particular, he hoped it would find the first evidence for the M theory, which is the best candidate that physicists have to unify all the four fundamental forces of nature. It unites gravity (which rules at the largest scales of the universe) with quantum mechanics (which controls the behaviour atoms and below). As yet there has been no incontrovertible experimental evidence to show that M theory is correct.

“There is still hope that we see the first evidence for M theory at the LHC particle accelerator in Geneva,” said Hawking. “From an M theory perspective, the collider only probes low energies, but we might be lucky and see a weaker signal of fundamental theory, such as supersymmetry. I think the discovery of supersymmetric partners for the known particles would revolutionise our understanding of the universe.”

Supersymmetry is the concept that each known particle – such as electrons, quarks and photons – has a heavier and as-yet-undetected “superpartner”. The superpartners of quarks and electrons, for example, are called squarks and selectrons; the superpartners of the Higgs, and of force carriers such as the photon, are the higgsino and photino. Experimental evidence for the idea has, however, been elusive.

In recalling the bet he made with physicist Gordon Kane about the Higgs boson, Hawking admitted to enjoying gambling. “Throughout my life, I have had a gambling problem. When I was 12, one of my friends bet another friend a bag of sweets that I would never come to anything. I don’t know if this bet was ever settled, and if so, which way it was decided. I had six or seven close friends, and we used to have long discussions and arguments about everything, from radio-controlled models to religion. One of the things we talked about was the origin of the universe, and whether it required a God to create it and set it going.”

Hawking is no stranger to losing bets about the nature of cosmos. Along with Kip Thorne, he bet John Preskill that information should be destroyed when something fell into a black hole. The so-called “information paradox” was troubling because Hawking’s calculations suggested that anything that fell into a black hole would be obliterated, including the information about what that stuff was. But destroying information is not allowed under the rules of quantum mechanics.

After 30 years of arguing, Hawking said he eventually found a resolution. “Information is not lost in black holes, but it is not returned in a useful way,” he said. “It is like burning an encyclopaedia. Information is not lost, but it is very hard to read.”

He gave Preskill a baseball encyclopaedia to concede his side of the bet. “Maybe I should have just given him the ashes. The fact that I used to think that information was destroyed in black holes was my biggest blunder. Well, at least it was my biggest blunder in science.”

Many of Hawking’s insights have come from studying the cosmos, and the scientist said people needed to get more interested in the space around us for more prosaic reasons. “We must also continue to go into space for the future of humanity. I don’t think we will survive another thousand years without escaping beyond our fragile planet. I therefore want to encourage public interest in space, and I’ve been getting my training in early,” he said. Hawking recently took part in a zero-gravity flight, which is part of the training for astronauts to experience the weightlessness of space.

Hawking said that the recent Nobel prize for Engelert and Higgs had been a reminder to him that it was “a glorious time to be alive, and doing research in theoretical physics. Our picture of the universe has changed a great deal in the last 50 years, and I’m happy if I have made a small contribution.”

He added: “So remember to look up at the stars and not down at your feet. Try to make sense of what you see and hold on to that childlike wonder about what makes the universe exist.”

Read more at http://www.theguardian.com/science/2013/nov/12/stephen-hawking-physics-higgs-boson-particle

# Stephen Hawking Looks Back

Stephen Hawking is known for his research into relativity, black holes, and quantum mechanics, as well as for the disease that has left him almost entirely paralyzed. But the theoretical cosmologist says that, were he to start from scratch, he wouldn’t focus on physics.

What would Stephen Hawking do with his life if he had to do it all over again? Hawking, as you know, was one of the world’s most illustrious physicists and science author. And now he’s out with a new book, a personal memoir entitled “My Brief History,” out this week from Bantam. He doesn’t give many interviews as his illness does not allow him to converse in real time, but he did agree to answer a few questions we put to him. And I think some of his responses may surprise you. Let me give you those right now. First, we asked him, are there any mysteries about the universe you think we may never be able to answer, questions beyond the reach of science?

STEPHEN HAWKING:** I believe there are no questions that science can’t answer about a physical universe**. Although we don’t yet have the full understanding of the laws of nature, I think we will eventually find a complete unified theory. Some people would claim that things like love, joy and beauty belong to a different category from science and can’t be described in scientific terms, but I think they can now be explained by the theory of evolution.

FLATOW: We asked him another question – and I think this gave us a really interesting answer. We asked him if you were to start your career over again now, starting now, what would you study and why?

HAWKING: If I were starting research now,** I might study molecular biology**, the science of life. Crick and Watson discovered the double helix structure of DNA and the genetic code in 1953. I did not realize its significance in 1957 when I had to choose a science to specialize in. In my school, the brightest boys did math and physics, the less bright did physics and chemistry and the least bright did biology. I wanted to do math and physics but my father made me do chemistry because he thought there would be no jobs for mathematicians.

FLATOW: And finally we asked him what scientific question outside of physics most intrigues you?

HAWKING: The biggest unsolved problem in science, outside physics, is** the origin of life**. Did it arrive spontaneously on Earth, and if so how, or did it come from another planet on a meteorite?

…

Read more at http://www.npr.org/2013/09/13/222101247/stephen-hawking-looks-back?sc=tw