arXiv subjects

Samir D. Mathur

Publications and source records attributed to Samir D. Mathur.

At least 55 records · Page 3Linked to original sources

arXiv2016

Nature abhors a horizon

The information paradox can be resolved if we recognize that the wavefunctional in gravity $Ψ[g]$ should be considered on the {\it whole} of superspace, the space of possible $g$. The largeness of the Bekenstein entropy implies a vast space of gravitational solutions, which are conjectured to be fuzzball configurations. In the WKB approximation, the wavefunctional for a collapsing shell is oscillatory in a small region of superspace, and the classical approximation picks out this part. But the wavefunctional will be damped (`under the barrier') in the remainder of this vast superspace. We perform a simple computation to show that at the threshold of black hole formation, the barrier is lowered enough to make the latter part oscillatory; this alters the classical evolution and avoids horizon formation.

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arXiv2015

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.

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arXiv2015

Effect of the deformation operator in the D1D5 CFT

The D1D5 CFT gives a holographic dual description of a near-extremal black hole in string theory. The interaction in this theory is given by a marginal deformation operator, which is composed of supercharges acting on a twist operator. The twist operator links together different copies of a free CFT. We study the effect of this deformation operator when it links together CFT copies with winding numbers M and N to produce a copy with winding M+N, populated with excitations of a particular form. We compute the effect of the deformation operator in the full supersymmetric theory, firstly on a Ramond-Ramond ground state and secondly on states with an initial bosonic or fermionic excitation. Our results generalize recent work which studied only the bosonic sector of the CFT. Our findings are a step towards understanding thermalization in the D1D5 CFT, which is related to black hole formation and evaporation in the bulk.

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arXiv2015

A violation of the covariant entropy bound?

Several arguments suggest that the entropy density at high energy density $ρ$ should be given by the expression $s=K\sqrt{ρ/G}$, where $K$ is a constant of order unity. On the other hand the covariant entropy bound requires that the entropy on a light sheet be bounded by $A/4G$, where $A$ is the area of the boundary of the sheet. We find that in a suitably chosen cosmological geometry, the above expression for $s$ violates the covariant entropy bound. We consider different possible explanations for this fact; in particular the possibility that entropy bounds should be defined in terms of volumes of regions rather than areas of surfaces.

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arXiv2014

Effect of the twist operator in the D1D5 CFT

The D1D5 CFT has been very useful in the study of black holes. The interaction in this theory involves a twist operator, which links together different copies of a free CFT. For the bosonic fields, we examine the action of this twist when it links together CFT copies with winding numbers M and N to produce a copy with winding M+N. Starting with the vacuum state generates a squeezed state, which we compute. Starting with an initial excitation on one of the copies gives a linear combination of excitations on the final state, which we also compute. These results generalize earlier computations where these quantities were computed for the special case M=N=1. Our results should help in understanding the thermalization process in the D1D5 CFT, which gives the dual of black hole formation in the bulk.

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arXiv2014

Analyzing the squeezed state generated by a twist deformation

The D1D5 CFT has provided a useful microscopic model for studying black holes. The coupling in this theory is a twist deformation whose action on the vacuum generates a squeezed state. We give a new derivation of the expression for this squeezed state using the conformal Ward identity; this derivation provides an insight into several features of the state. We also examine the squeezed state in a continuum limit where we describe it in terms of position space correlations created by the twist.

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arXiv2014

Bogoliubov coefficients for the twist operator in the D1D5 CFT

The D1D5 CFT is a holographic dual of a near-extremal black hole in string theory. The interaction in this theory involves a twist operator which joins together different copies of a free CFT. Given a large number of D1 and D5 branes, the effective length of the circle on which the CFT lives is very large. We develop a technique to study the effect of the twist operator in the limit where the wavelengths of excitations are short compared to this effective length, which we call the 'continuum limit'. The method uses Bogoliubov coefficients to compute the effect of the twist operator in this limit. For bosonic fields, we use the method to reproduce recent results describing the effect of the twist operator when it links together CFT copies with windings M and N, producing a copy of winding M+N. We also comment on possible generalizations of our results. The methods developed here may help in understanding the twist interaction at higher orders. This in turn should provide insight into the thermalization process in the D1D5 CFT, which gives a holographic description of black hole formation.

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arXiv2014

An equation of state in the limit of high densities

We take string theory in a box of volume $V$, and ask for the entropy $S(E,V)$. We let $E$ exceed the value $E_{bh}$ corresponding to the largest black hole that can fit in the box. Several approaches in the past have suggested the expression $S\sim \sqrt{EV/G}$. We recall these arguments, and in particular expand on an argument that uses dualities of string theory. We require that expression for $S(E,V)$ be invariant under the T and S dualities, and that it agree with the black hole entropy when $E\sim E_{bh}$. These criteria lead to the above expression for $S$. We note that this expression had been obtained also by a imposing a quite different requirement -- that the entropy within a cosmological horizon be of order the Bekenstein entropy for a black hole of size the cosmological horizon. We recall the earlier proposed model of a `dense gas of black holes' to model this entropy, and discuss its realization as a set of intersecting brane states. Finally we speculate that the cosmological evolution of such a phase may depart from the evolution expected from the classical Einstein equations, since the very large value of the entropy can lead to novel effects similar to the fuzzball dynamics found in black holes.

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arXiv2014

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.

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arXiv2014

Comments on black holes I: The possibility of complementarity

We comment on a recent paper of Almheiri, Marolf, Polchinski and Sully who argue against black hole complementarity based on the claim that an infalling observer 'burns' as he approaches the horizon. We show that in fact measurements made by an infalling observer outside the horizon are statistically identical for the cases of vacuum at the horizon and radiation emerging from a stretched horizon. This forces us to follow the dynamics all the way to the horizon, where we need to know the details of Planck scale physics. We note that in string theory the fuzzball structure of microstates does not give any place to 'continue through' this Planck regime. AMPS argue that interactions near the horizon preclude traditional complementarity. But the conjecture of 'fuzzball complementarity' works in the opposite way: the infalling quantum is absorbed by the fuzzball surface, and it is the resulting dynamics that is conjectured to admit a complementary description.

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arXiv2014

Oscillating supertubes and neutral rotating black hole microstates

The construction of neutral black hole microstates is an important problem, with implications for the information paradox. In this paper we conjecture a construction of non-supersymmetric supergravity solutions describing D-brane configurations which carry mass and angular momentum, but no other conserved charges. We first study a classical string solution which locally carries dipole winding and momentum charges in two compact directions, but globally carries no net winding or momentum charge. We investigate its backreaction in the D1-D5 duality frame, where this object becomes a supertube which locally carries oscillating dipole D1-D5 and NS1-NS5 charges, and again carries no net charge. In the limit of an infinite straight supertube, we find an exact supergravity solution describing this object. We conjecture that a similar construction may be carried out based on a class of two-charge non-supersymmetric D1-D5 solutions. These results are a step towards demonstrating how neutral black hole microstates may be constructed in string theory.

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arXiv2014

The flaw in the firewall argument

A lot of confusion surrounds the issue of black hole complementarity, because the question has been considered without discussing the mechanism which guarantees unitarity. Considering such a mechanism leads to the following: (1) The Hawking quanta with energy E of order the black hole temperature T carry information, and so only appropriate processes involving E>>T quanta can have any possible complementary description with an information-free horizon; (2) The stretched horizon describes all possible black hole states with a given mass M, and it must expand out to a distance s_{bubble} before it can accept additional infalling bits; (3) The Hawking radiation has a specific low temperature T, and infalling quanta interact significantly with it only within a distance s_{alpha} of the horizon. One finds s_{alpha} << s_{bubble} for E>>T, and this removes the argument against complementarity recently made by Almheiri et al. In particular, the condition E>>T leads to the notion of 'fuzzball complementarity', where the modes around the horizon are indeed correctly entangled in the complementary picture to give the vacuum.

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arXiv2014

What is the dual of two entangled CFTs?

It has been conjectured that the dual of the eternal black hole in AdS is two entangled but disconnected CFTs. We show that the entanglement created by the process of Hawking radiation creates several challenges for this conjecture. The nature of fuzzball states suggests a different picture, where the dual to two entangled CFTs is two entangled but disconnected spacetimes. We argue for a process of `quick tunneling' where the Einstein-Rosen bridge of the eternal hole tunnels rapidly into fuzzball states, preventing the existence of the eternal hole as a semiclassical spacetime. The regions behind the horizon then emerge only in the approximation of fuzzball complementarity, where one considers the impact of probes with energy $E\gg T$.

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arXiv2014

Fuzzballs and black hole thermodynamics

The fuzzball construction resolves the black hole information paradox by making spacetime end just before the horizon is reached. But if there is no traditional horizon, then do we lose the elegant relations of black hole thermodynamics? Using an argument similar to modular invariance, we argue that the answer is no; the completeness of fuzzball states implies that the generic fuzzball indeed reproduces the thermal properties attributed to the traditional hole.

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arXiv2013

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 $E\gg T$.

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arXiv2013

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.

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arXiv2013

D1-D5-P microstates at the cap

The geometries describing D1-D5-P bound states in string theory have three regions: flat asymptotics, an anti-de Sitter throat, and a 'cap' region at the bottom of the throat. We identify the CFT description of a known class of supersymmetric D1-D5-P microstate geometries which describe degrees of freedom in the cap region. The class includes both regular solutions and solutions with conical defects, and generalizes configurations with known CFT descriptions: a parameter related to spectral flow in the CFT is generalized from integer to fractional values. We provide strong evidence for this identification by comparing the massless scalar excitation spectrum between gravity and CFT and finding exact agreement.

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arXiv2012

A toy black hole S-matrix in the D1-D5 CFT

To model the process of absorption and emission of quanta by an extremal D1-D5 black hole in the dual CFT, we consider transitions between different Ramond vacua via absorption and emission of chiral primaries. We compute the probabilities to reach different CFT states starting with a special Ramond vacuum, using techniques of the orbifold CFT. It is found that the processes involving the change of angular momentum by $k$ units are suppressed as 1/N^k

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