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

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

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

Real Time Propagator in the First Quantised Formalism

We argue that a basic modification must be made to the first quantised formalism of string theory if the physics of `particle creation' is to be correctly described. The analogous quantisation of the relativistic particle is performed, and it is shown that the proper time along the world line must go both forwards and backwards (in the usual quantisation it only goes forwards). The matrix propagator of the real time formalism is obtained from the two directions of proper time. (Talk given at the Thermal Fields Workshop held at Banff, Canada (August 1993).)Comment: pages, plain te

What does strong subadditivity tell us about black holes?

It has been argued that small corrections to evolution arising from non-geometric effects can resolve the information paradox. We can get such effects, for example, from subleading saddle points in the Euclidean path integral. But an inequality derived in 2009 using strong sub-additivity showed that such corrections {\it cannot} solve the problem. As a result we sharpen the original Hawking puzzle: we must either have (A) new (nonlocal) physics or (B) construct hair at the horizon. We get correspondingly different approaches to resolving the AMPS puzzle. Traditional complementarity assumes (A); here we require that the AMPS experiment measures the correct vacuum entanglement of Hawking modes, and invoke nonlocal $A=R_B$ type effects to obtain unitarity of radiation. Fuzzball complementarity is in category (B); here the AMPS measurement is outside the validity of the approximation required to obtain the complementary description, and a effective regular horizon arises only for freely infalling observers with energies $E\gg T$.Comment: 12 pages, 8 figures, Expanded version of proceedings for Light Cone 2012, Delh

Losing information outside the horizon

Suppose we allow a system to fall freely from infinity to a point near (but not beyond) the horizon of a black hole. We note that in a sense the information in the system is already lost to an observer at infinity. Once the system is too close to the horizon it does not have enough energy to send its information back because the information carrying quanta would get redshifted to a point where they get confused with Hawking radiation. If one attempts to turn the infalling system around and bring it back to infinity for observation then it will experience Unruh radiation from the required acceleration. This radiation can excite the bits in the system carrying the information, thus reducing the fidelity of this information. We find the radius where the information is essentially lost in this way, noting that this radius depends on the energy gap (and coupling) of the system. We look for some universality by using the highly degenerate BPS ground states of a quantum gravity theory (string theory) as our information storage device. For such systems one finds that the critical distance to the horizon set by Unruh radiation is the geometric mean of the black hole radius and the radius of the extremal hole with quantum numbers of the BPS bound state. Overall, the results suggest that information in gravity theories should be regarded not as a quantity contained in a system, but in terms of how much of this information is accessible to another observer.Comment: 27 pages, 3 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