Black hole size and phase space volumes

For extremal black holes the fuzzball conjecture says that the throat of the geometry ends in a quantum `fuzz', instead of being infinite in length with a horizon at the end. For the D1-D5 system we consider a family of sub-ensembles of states, and find that in each case the boundary area of the fuzzball satisfies a Bekenstein type relation with the entropy enclosed. We suggest a relation between the `capped throat' structure of microstate geometries and the fact that the extremal hole was found to have zero entropy in some gravity computations. We examine quantum corrections including string 1-loop effects and check that they do not affect our leading order computations.Comment: 37 pages, 6 figures, Late

Effective information loss outside the horizon

If a system falls through a black hole horizon, then its information is lost to an observer at infinity. But we argue that the {\it accessible} information is lost {\it before} the horizon is crossed. The temperature of the hole limits information carrying signals from a system that has fallen too close to the horizon. Extremal holes have T=0, but there is a minimum energy required to emit a quantum in the short proper time left before the horizon is crossed. If we attempt to bring the system back to infinity for observation, then acceleration radiation destroys the information. All three considerations give a critical distance from the horizon $d\sim \sqrt{r_H\over \Delta E}$, where $r_H$ is the horizon radius and $\Delta E$ is the energy scale characterizing the system. For systems in string theory where we pack information as densely as possible, this acceleration constraint is found to have a geometric interpretation. These estimates suggest that in theories of gravity we should measure information not as a quantity contained inside a given system, but in terms of how much of that information can be reliably accessed by another observer.Comment: 7 pages, Latex, 1 figure (Essay awarded fourth prize in Gravity Research Foundation essay competition 2011

Is the Polyakov path integral prescription too restrictive?

In the first quantised description of strings, we integrate over target space co-ordinates $X^\mu$ and world sheet metrics $g_{\alpha\beta}$. Such path integrals give scattering amplitudes between the `in' and `out' vacuua for a time-dependent target space geometry. For a complete description of `particle creation' and the corresponding backreaction, we need instead the causal amplitudes obtained from an `initial value formulation'. We argue, using the analogy of a scalar particle in curved space, that in the first quantised path integral one should integrate over $X^\mu$ and world sheet {\it zweibiens}. This extended formalism can be made to yield causal amplitudes; it also naturally allows incorporation of density matrices in a covariant manner. (This paper is an expanded version of hep-th 9301044)Comment: 37 pages, harvma

A model with no firewall

We construct a model which illustrates the conjecture of fuzzball complementarity. In the fuzzball paradigm, the black hole microstates have no interior, and radiate unitarily from their surface through quanta of energy $E\sim T$. But quanta with $E\gg T$ impinging on the fuzzball create large collective excitations of the fuzzball surface. The dynamics of such excitations must be studied as an evolution in superspace, the space of all fuzzball solution $|F_i\rangle$. The states in this superspace are arranged in a hierarchy of `complexity'. We argue that evolution towards higher complexity maps, through a duality analogous to AdS/CFT, to infall inside the horizon of the traditional hole. We explain how the large degeneracy of fuzzball states leads to a breakdown of the principle of equivalence at the threshold of horizon formation. We recall that the firewall argument did not invoke the limit $E\gg T$ when considering a complementary picture; on the contrary it focused on the dynamics of the $E\sim T$ modes which contribute to Hawking radiation. This loophole allows the dual description conjectured in fuzzball complementarity.Comment: 45 pages, 18 figure

What happens at the horizon?

The Schwarzschild metric has an apparent singularity at the horizon r=2M. What really happens there? If physics at the horizon is 'normal' laboratory physics, then we run into Hawking's information paradox. If we want nontrivial structure at the horizon, then we need a mechanism to generate this structure that evades the 'no hair' conjectures of the past. Further, if we have such structure, then what would the role of the traditional black hole metric which continues smoothly past the horizon? Recent work has provided an answer to these questions, and in the process revealed a beautiful tie-up between gravity, string theory and thermodynamics.Comment: 6 pages, 3 figures (Essay awarded third prize in the Gravity Research Foundation essay competition 2013

The nature of the gravitational vacuum

The vacuum must contain virtual fluctuations of black hole microstates for each mass $M$. We observe that the expected suppression for $M\gg m_p$ is counteracted by the large number $Exp[S_{bek}]$ of such states. From string theory we learn that these microstates are extended objects that are resistant to compression. We argue that recognizing this `virtual extended compression-resistant' component of the gravitational vacuum is crucial for understanding gravitational physics. Remarkably, such virtual excitations have no significant effect for observable systems like stars, but they resolve two important problems: (a) gravitational collapse is halted outside the horizon radius, removing the information paradox; (b) spacetime acquires a `stiffness' against the curving effects of vacuum energy; this ameliorates the cosmological constant problem posed by the existence of a planck scale $\Lambda$.Comment: 7 pages, 2 figures (Essay awarded an honorable mention in the Gravity Research Foundation 2019 Awards for Essays on Gravitation

Falling into a black hole

String theory tells us that quantum gravity has a dual description as a field theory (without gravity). We use the field theory dual to ask what happens to an object as it falls into the simplest black hole: the 2-charge extremal hole. In the field theory description the wavefunction of a particle is spread over a large number of `loops', and the particle has a well-defined position in space only if it has the same `position' on each loop. For the infalling particle we find one definition of `same position' on each loop, but there is a different definition for outgoing particles and no canonical definition in general in the horizon region. Thus the meaning of `position' becomes ill-defined inside the horizon.Comment: 8 pages, 5 figures (this essay received an honorable mention in the 2007 essay competition of the Gravity Research Foundation

Remnants, Fuzzballs or Wormholes?

The black hole information paradox has caused enormous confusion over four decades. But in recent years, the theorem of quantum strong-subaddditivity has sorted out the possible resolutions into three sharp categories: (A) No new physics at $r\gg l_p$; this necessarily implies remnants/information loss. A realization of remnants is given by a baby Universe attached near $r\sim 0$. (B) Violation of the `no-hair' theorem by nontrivial effects at the horizon $r\sim M$. This possibility is realized by fuzzballs in string theory, and gives unitary evaporation. (C) Having the vacuum at the horizon, but requiring that Hawking quanta at $r\sim M^3$ be somehow identified with degrees of freedom inside the black hole. A model for this `extreme nonlocality' is realized by conjecturing that wormholes connect the radiation quanta to the hole.Comment: 7 pages, 4 figures (Essay awarded an honorable mention in the Gravity Research Foundation essay competition 2014

Can the universe be described by a wavefunction?

Suppose we assume that in gently curved spacetime (a) causality is not violated to leading order (b) the Birkoff theorem holds to leading order and (c) CPT invariance holds. Then we argue that the `mostly empty' universe we observe around us cannot be described by an exact wavefunction $\Psi$. Rather, the weakly coupled particles we see are approximate quasiparticles arising as excitations of a `fuzz'. The `fuzz' {\it does} have an exact wavefunction $\Psi_{fuzz}$, but this exact wavefunction does not directly describe local particles. The argument proceeds by relating the cosmological setting to the black hole information paradox, and then using the small corrections theorem to show the impossibility of an exact wavefunction describing the visible universe.Comment: 8 pages, 6 figures, Essay awarded an honorable mention in the Gravity Research Foundation 2018 Awards for Essays on Gravitatio

What does the information paradox say about the universe?

The black hole information paradox is resolved in string theory by a radical change in the picture of the hole: black hole microstates are horizon sized quantum gravity objects called `fuzzballs' instead of vacuum regions with a central singularity. The requirement of causality implies that the quantum gravity wavefunctional $\Psi$ has an important component not present in the semiclassical picture: virtual fuzzballs. The large mass $M$ of the fuzzballs would suppress their virtual fluctuations, but this suppression is compensated by the large number -- $Exp[S_{bek}(M)]$ -- of possible fuzzballs. These fuzzballs are extended compression-resistant objects. The presence of these objects in the vacuum wavefunctional alters the physics of collapse when a horizon is about to form; this resolves the information paradox. We argue that these virtual fuzzballs also resist the curving of spacetime, and so cancel out the large cosmological constant created by the vacuum energy of local quantum fields. Assuming that the Birkoff theorem holds to leading order, we can map the black hole information problem to a problem in cosmology. Using the virtual fuzzball component of the wavefunctional, we give a qualitative picture of the evolution of $\Psi$ which is consistent with the requirements placed by the information paradox.Comment: 31 pages, 8 figures, Expanded version of the proceedings of the conference `The Physical Universe', Nagpur, March 201