Borun Chowdhury - Profile on Academia.edu (original) (raw)

Papers by Borun Chowdhury

It is possible to construct a special family of nonextremal black hole microstates. These microst... more It is possible to construct a special family of nonextremal black hole microstates. These microstates are unstable, and emit radiation at a rate which is found to exactly equal the Hawking radiation rate predicted for them by the dual CFT. In this paper we analyze in more detail the nature of the radiation created by these unstable modes. The energy and angular momentum of the mode is found to be localized in two regions: one near infinity corresponding to the emitted quanta, and the other in the ergoregion which is deep inside the interior of the geometry. The energy and angular momenta are equal and opposite for these two contributions, as expected for emission from ergoregions. We conjecture that more general nonextremal microstates will possess ergoregions (with no axial symmetry), and radiation from these regions can be part of the general Hawking emission for the microstates.

We compute the gravitational entropy of “spherical Rindler space”, a time-dependent, spherically ... more We compute the gravitational entropy of “spherical Rindler space”, a time-dependent, spherically symmetric generalization of ordinary Rindler space, defined with reference to a family of observers traveling along non-parallel, accelerated trajectories. All these observers are causally disconnected from a spherical region H (a “hole”) located at the origin of Minkowski space. The entropy evaluates to S = A/4G, where A is the area of the spherical acceleration horizon, which coincides with the boundary of H. We propose that S is the entropy of entanglement between quantum gravitational degrees of freedom supporting the interior and the exterior of the sphere H.

An example of entropy enigma with a controlled CFT dual was recently studied in [1]. The enigmati... more An example of entropy enigma with a controlled CFT dual was recently studied in [1]. The enigmatic bulk configurations, considered within the STU model, can be mapped under spectral flow into black rings with three monopole and dipole charges. Even though the bulk and CFT configurations existed in the same region of parameter space, the Bekenstein-Hawking entropy of the bulk configurations was found to be lower than the microscopic entropy from the CFT. While it is possible that the difference in entropy is due to the bulk and boundary configurations being at different points in the moduli space, it is also possible that the bulk configurations embeddable within the STU model are not the most entropic. New families of BPS black ring solutions with four electric and four dipole magnetic charges have recently been explicitly constructed in [2]. These black rings are not embeddable within the STU model. In this paper we investigate if these black rings can be entropically dominant over the STU model black rings. We find that the new black rings are always entropically subdominant to the STU-model black rings. However, for small fourth dipole charge these black rings continue to be dominant over the BMPV in a small region of parameters and are thus enigmatic. Contents 1 Introduction 1 2 Review of moulting black holes 4 2.1 The new phase at the orbifold point in the D1-D5 CFT 4 2.2 The new phase at the supergravity point in the STU model 6 3 New black ring with entropy maximized 8 4 Discussion 11

Abstract: It is generally believed that the eternal AdS black hole is dual to two confor-mal fiel... more Abstract: It is generally believed that the eternal AdS black hole is dual to two confor-mal field theories with compact spatial sections that are together in a thermofield double state. We argue that this proposal is incorrect, and by extension so are the “entangle-ment=geometry ” proposal of Van Raamsdonk and “ER=EPR ” proposal of Maldacena and Susskind. We show that in the bulk there is an interaction needed between the two halves of the Hilbert space for connectivity across the horizon; however, there is no such interaction between the CFTs. This rules out the possibility of the dual to the CFTs being the eternal AdS black hole. We argue the correct dual “geometries ” resemble the exterior of the black hole outside the stretched horizon but cap off before the global horizon. This disallows the possibility of a shared future (and past) wedge where Alice falling from one side can meet Bob falling from the other. We expect that in the UV complete theory the aforementioned caps will...

Abstract: We study the fate of two-centered D1-D5 systems on T 4 away from the singular supergrav... more Abstract: We study the fate of two-centered D1-D5 systems on T 4 away from the singular supergravity point in the moduli space. We do this by considering a background D1-D5 black hole with a self-dual B-field moduli turned on and treating the second center in the probe limit in this background. We find that in general marginal bound states at zero moduli become metastable at finite B-moduli, demonstrating a breaking of supersymmetry. However, we also find evidence that when the charges of both centers are comparable, the effects of supersymmetry breaking become negligible. We show that this effect is independent of string coupling and thus it should be possible to reproduce this in the CFT at weak coupling. We comment on the implications for the fuzzball proposal.

It is shown that exp(−2 Im ( ∫ p dr)) is not invariant under canonical transformations in general... more It is shown that exp(−2 Im ( ∫ p dr)) is not invariant under canonical transformations in general. Specifically for shells tunneling out of black holes, this quantity is not invariant under canonical transformations. It can be interpreted as the transmission coefficient only in the cases in which it is invariant under canonical transformations. Although such cases include alpha decay, they do not include the tunneling of shells from black holes. The simplest extension to this formula which is invariant under canonical transformations is proposed. However it is shown that this gives half the correct temperature for black holes. 1

[

It is shown that exp(−2 Im ( ∫ p dr)) is not invariant under canonical transformations in general... more It is shown that exp(−2 Im ( ∫ p dr)) is not invariant under canonical transformations in general. Specifically for shells tunneling out of black holes, this quantity is not invariant under canonical transformations. It can be interpreted as the tunneling probability only in the cases in which it is invariant under canonical transformations. Although such cases include alpha decay, they do not include the tunneling of shells from black holes. This demonstrates that this naive expression for tunneling probability does not hold for the case of shells tunneling out of black holes.

It is shown that in general the quantity exp(−2Im ( ∫ p dr)) is not invariant under canonical tra... more It is shown that in general the quantity exp(−2Im ( ∫ p dr)) is not invariant under canonical transformations. It can be interpreted as the tunneling probability only in specific cases which include the text book example of alpha decay but do not include a shell crossing a black hole horizon. With specific examples it is shown that this quantity is different for different canonically equivalent actions thus demonstrating that its interpretation as tunneling probability for black hole emission is questionable.

arXiv: High Energy Physics - Theory, 2013

It is generally believed that the eternal AdS black hole is dual to two conformal field theories ... more It is generally believed that the eternal AdS black hole is dual to two conformal field theories with compact spatial sections that are together in a thermofield double state. We argue that this proposal is incorrect, and by extension so are the "entanglement=geometry" proposal of Van Raamsdonk and "ER=EPR" proposal of Maldacena and Susskind. We show that in the bulk there is an interaction needed between the two halves of the Hilbert space for connectivity across the horizon; however, there is no such interaction between the CFTs. This rules out the possibility of the dual to the CFTs being the eternal AdS black hole. We argue the correct dual "geometries" resemble the exterior of the black hole outside the stretched horizon but cap off before the global horizon. This disallows the possibility of a shared future (and past) wedge where Alice falling from one side can meet Bob falling from the other. We expect that in the UV complete theory the aforement...

These lecture notes present an introduction to the fuzzball proposal and emission from the D1-D5 ... more These lecture notes present an introduction to the fuzzball proposal and emission from the D1-D5 system which is geared to an audience of graduate students and others with little background in the subject. The presentation begins with a discussion of the Penrose process and Hawking radiation. The fuzzball proposal is then introduced, and the twoand three-charge systems are reviewed. In the three-charge case details are not discussed. A detailed discussion of emission calculations for D1-D5-P black holes and for certain nonextremal fuzzballs from both the gravity and CFT perspectives is included. We explicitly demonstrate how seemingly different emission processes in gravity, namely, Hawking radiation and superradiance from D1-D5-P black holes, and ergoregion emission from certain non-extremal fuzzballs, are only different manifestations of the same phenomenon in the CFT.

Monthly Notices of the Royal Astronomical Society

Non-vanishing parity-odd correlators of gamma-ray arrival directions observed by Fermi-LAT indica... more Non-vanishing parity-odd correlators of gamma-ray arrival directions observed by Fermi-LAT indicate the existence of a helical intergalactic magnetic field with strength B ∼ 10 −14 G on ∼10 Mpc scales. We successfully test this hypothesis using more stringent cuts of the data, Monte Carlo simulations with Fermi-LAT time exposure information, separate analyses for the Northern and Southern galactic hemispheres, and confirm predictions made in Tashiro & Vachaspati. With some further technical assumptions, we show how to reconstruct the magnetic helicity spectrum from the parity-odd correlators.

Physical Review D, 2016

In the AdS/CFT correspondence, CFTs are identified by asymptotic boundary surfaces and the bounda... more In the AdS/CFT correspondence, CFTs are identified by asymptotic boundary surfaces and the boundary conditions imposed on those surfaces. However, AdS can be foliated in various ways to give different boundaries. We show that the CFTs obtained using certain distinct foliations are different. This difference arises because the asymptotic region of a foliation overlaps with the deep interior region of another. In particular we focus on the CFTs defined on surfaces of large constant radius in global coordinates, Rindler-AdS coordinates, and Poincaré coordinates for AdS 3 . We refer to these as global-CFT, Rindler-CFT and Poincaré-CFT respectively. We demonstrate that the correlators for these CFTs are different and argue that the bulk duals to these should agree up to very close to the respective horizons but then start differing. Since the BTZ black hole is obtained as a quotient of AdS 3 , we discuss the implications of our results for bulk duals of periodically-identified Poincaré and Rindler-CFTs. Our results are consistent with some recent proposals suggesting a modification of the semi-classical BTZ geometry close to the horizons.

A hole-ographic spacetime

We embed spherical Rindler space -- a geometry with a spherical hole in its center -- in asymptot... more We embed spherical Rindler space -- a geometry with a spherical hole in its center -- in asymptotically AdS spacetime and show that it carries a gravitational entropy proportional to the area of the hole. Spherical AdS-Rindler space is holographically dual to an ultraviolet sector of the boundary field theory given by restriction to a strip of finite duration in time. Because measurements have finite durations, local observers in the field theory can only access information about bounded spatial regions. We propose a notion of Residual Entropy that captures uncertainty about the state of a system left by the collection of local, finite-time observables. For two-dimensional conformal field theories we use holography and the strong subadditivity of entanglement to propose a formula for Residual Entropy and show that it precisely reproduces the areas of circular holes in AdS3. Extending the notion to field theories on strips with variable durations in time, we show more generally that ...

It is generally believed that the eternal AdS black hole is dual to two conformal field theories ... more It is generally believed that the eternal AdS black hole is dual to two conformal field theories with compact spatial sections that are together in a thermofield double state. We argue that this proposal is incorrect, and by extension so are the "entanglement=geometry" proposal of Van Raamsdonk and "ER=EPR" proposal of Maldacena and Susskind. We show that in the bulk there is an interaction needed between the two halves of the Hilbert space for connectivity across the horizon; however, there is no such interaction between the CFTs. This rules out the possibility of the dual to the CFTs being the eternal AdS black hole. We argue the correct dual "geometries" resemble the exterior of the black hole outside the stretched horizon but cap off before the global horizon. This disallows the possibility of a shared future (and past) wedge where Alice falling from one side can meet Bob falling from the other. We expect that in the UV complete theory the aforement...

In the AdS/CFT correspondence, CFTs are identified by asymptotic boundary surfaces and the bounda... more In the AdS/CFT correspondence, CFTs are identified by asymptotic boundary surfaces and the boundary conditions imposed on those surfaces. However, AdS can be foliated in various ways to give different boundaries. We show that the CFTs obtained using certain distinct foliations are different. This difference arises because the asymptotic region of a foliation overlaps with the deep interior region of another. In particular we focus on the CFTs defined on surfaces of large constant radius in global coordinates, Rindler-AdS coordinates, and Poincar\'e coordinates for AdS$_3$. We refer to these as global-CFT, Rindler-CFT and Poincar\'e-CFT respectively. We demonstrate that the correlators for these CFTs are different and argue that the bulk duals to these should agree up to very close to the respective horizons but then start differing. Since the BTZ black hole is obtained as a quotient of AdS$_3$, we discuss the implications of our results for bulk duals of periodically-identif...

A simple classical consideration of black hole formation and evaporation times as measured by an ... more A simple classical consideration of black hole formation and evaporation times as measured by an observer at infinity demonstrates that an infall cutoff outside the event horizon of a black hole must be imposed in order for the formation time of a black hole event horizon to not exceed its evaporation time. We explore this paradox quantitatively and examine possible cutoff scales and their relation to the Planck scale. Our analysis suggests several different possibilities, none of which can be resolved classically and all of which require new physics associated with even large black holes and macroscopic event horizons:(1) an event horizon never forms, for example due to radiation during collapse (resolving the information loss problem), (2) and/or quantum effects may affect space-time near an event horizon in ways which alter infall as well as black hole evaporation itself.

Journal of High Energy Physics, 2012

We find a family of novel supersymmetric phases of the D1-D5 CFT, which in certain ranges of char... more We find a family of novel supersymmetric phases of the D1-D5 CFT, which in certain ranges of charges have more entropy than all known ensembles. We also find bulk BPS configurations that exist in the same range of parameters as these phases, and have more entropy than a BMPV black hole; they can be thought of as coming from a BMPV black hole shedding a "hair" condensate outside of the horizon. The entropy of the bulk configurations is smaller than that of the CFT phases, which indicates that some of the CFT states are lifted at strong coupling. Neither the bulk nor the boundary phases are captured by the elliptic genus, which makes the coincidence of the phase boundaries particularly remarkable. Our configurations are supersymmetric, have non-Cardy-like entropy, and are the first instance of a black hole entropy enigma with a controlled CFT dual. Furthermore, contrary to common lore, these objects exist in a region of parameter space (between the "cosmic censorship bound" and the "unitarity bound") where no black holes were thought to exist.

Journal of High Energy Physics, 2015

It is conventional to study the entanglement between spatial regions of a quantum field theory. H... more It is conventional to study the entanglement between spatial regions of a quantum field theory. However, in some systems entanglement can be dominated by "internal", possibly gauged, degrees of freedom that are not spatially organized, and that can give rise to gaps smaller than the inverse size of the system. In a holographic context, such small gaps are associated to the appearance of horizons and singularities in the dual spacetime. Here, we propose a concept of entwinement, which is intended to capture this fine structure of the wavefunction. Holographically, entwinement probes the entanglement shadow -the region of spacetime not probed by the minimal surfaces that compute spatial entanglement in the dual field theory. We consider the simplest example of this scenario -a 2d conformal field theory (CFT) that is dual to a conical defect in AdS 3 space. Following our previous work, we show that spatial entanglement in the CFT reproduces spacetime geometry up to a finite distance from the conical defect. We then show that the interior geometry up to the defect can be reconstructed from entwinement that is sensitive to the discretely gauged, fractionated degrees of freedom of the CFT. Entwinement in the CFT is related to non-minimal geodesics in the conical defect geometry, suggesting a potential quantum information theoretic meaning for these objects in a holographic context. These results may be relevant for the reconstruction of black hole interiors from a dual field theory.

International Journal of Modern Physics D, 2013

In this paper, we examine the implications of the ongoing black holes versus firewalls debate for... more In this paper, we examine the implications of the ongoing black holes versus firewalls debate for the thermo-field dynamics of black holes by analyzing a conformal field theory (CFT) in a thermal state in the context of anti-de Sitter/CFT. We argue that the thermo-field doubled copy of the thermal CFT should be thought of not as a fictitious system, but as the image of the CFT in the heat bath. In case of strong coupling between the CFT and the heat bath, this image allows for free infall through the horizon and the system is described by a black hole. Conversely, firewalls are the appropriate dual description in case of weak interaction of the CFT with its heat bath.

Physical Review D, 2013

Recently, Almheiri, Marolf, Polchinski and Sully (AMPS) have suggested a Gedankenexperiment to te... more Recently, Almheiri, Marolf, Polchinski and Sully (AMPS) have suggested a Gedankenexperiment to test black hole complementarity. They claim that the postulates of black hole complementarity are mutually inconsistent and choose to give up the 'absence of drama' for an infalling observer. According to them the black hole is shielded by a firewall no later than Page time. This has generated some controversy. We find that an interesting picture emerges when we take into account objections from the advocates of fuzzballs. We reformulate AMPS' Gedankenexperiment in the decoherence picture of quantum mechanics and find that low energy wave packets interact with the radiation quanta rather violently while high energy wave packets do not. This is consistent with Mathur's recent proposal of fuzzball complementarity for high energy quanta falling into fuzzballs.

It is possible to construct a special family of nonextremal black hole microstates. These microst... more It is possible to construct a special family of nonextremal black hole microstates. These microstates are unstable, and emit radiation at a rate which is found to exactly equal the Hawking radiation rate predicted for them by the dual CFT. In this paper we analyze in more detail the nature of the radiation created by these unstable modes. The energy and angular momentum of the mode is found to be localized in two regions: one near infinity corresponding to the emitted quanta, and the other in the ergoregion which is deep inside the interior of the geometry. The energy and angular momenta are equal and opposite for these two contributions, as expected for emission from ergoregions. We conjecture that more general nonextremal microstates will possess ergoregions (with no axial symmetry), and radiation from these regions can be part of the general Hawking emission for the microstates.

We compute the gravitational entropy of “spherical Rindler space”, a time-dependent, spherically ... more We compute the gravitational entropy of “spherical Rindler space”, a time-dependent, spherically symmetric generalization of ordinary Rindler space, defined with reference to a family of observers traveling along non-parallel, accelerated trajectories. All these observers are causally disconnected from a spherical region H (a “hole”) located at the origin of Minkowski space. The entropy evaluates to S = A/4G, where A is the area of the spherical acceleration horizon, which coincides with the boundary of H. We propose that S is the entropy of entanglement between quantum gravitational degrees of freedom supporting the interior and the exterior of the sphere H.

An example of entropy enigma with a controlled CFT dual was recently studied in [1]. The enigmati... more An example of entropy enigma with a controlled CFT dual was recently studied in [1]. The enigmatic bulk configurations, considered within the STU model, can be mapped under spectral flow into black rings with three monopole and dipole charges. Even though the bulk and CFT configurations existed in the same region of parameter space, the Bekenstein-Hawking entropy of the bulk configurations was found to be lower than the microscopic entropy from the CFT. While it is possible that the difference in entropy is due to the bulk and boundary configurations being at different points in the moduli space, it is also possible that the bulk configurations embeddable within the STU model are not the most entropic. New families of BPS black ring solutions with four electric and four dipole magnetic charges have recently been explicitly constructed in [2]. These black rings are not embeddable within the STU model. In this paper we investigate if these black rings can be entropically dominant over the STU model black rings. We find that the new black rings are always entropically subdominant to the STU-model black rings. However, for small fourth dipole charge these black rings continue to be dominant over the BMPV in a small region of parameters and are thus enigmatic. Contents 1 Introduction 1 2 Review of moulting black holes 4 2.1 The new phase at the orbifold point in the D1-D5 CFT 4 2.2 The new phase at the supergravity point in the STU model 6 3 New black ring with entropy maximized 8 4 Discussion 11

Abstract: It is generally believed that the eternal AdS black hole is dual to two confor-mal fiel... more Abstract: It is generally believed that the eternal AdS black hole is dual to two confor-mal field theories with compact spatial sections that are together in a thermofield double state. We argue that this proposal is incorrect, and by extension so are the “entangle-ment=geometry ” proposal of Van Raamsdonk and “ER=EPR ” proposal of Maldacena and Susskind. We show that in the bulk there is an interaction needed between the two halves of the Hilbert space for connectivity across the horizon; however, there is no such interaction between the CFTs. This rules out the possibility of the dual to the CFTs being the eternal AdS black hole. We argue the correct dual “geometries ” resemble the exterior of the black hole outside the stretched horizon but cap off before the global horizon. This disallows the possibility of a shared future (and past) wedge where Alice falling from one side can meet Bob falling from the other. We expect that in the UV complete theory the aforementioned caps will...

Abstract: We study the fate of two-centered D1-D5 systems on T 4 away from the singular supergrav... more Abstract: We study the fate of two-centered D1-D5 systems on T 4 away from the singular supergravity point in the moduli space. We do this by considering a background D1-D5 black hole with a self-dual B-field moduli turned on and treating the second center in the probe limit in this background. We find that in general marginal bound states at zero moduli become metastable at finite B-moduli, demonstrating a breaking of supersymmetry. However, we also find evidence that when the charges of both centers are comparable, the effects of supersymmetry breaking become negligible. We show that this effect is independent of string coupling and thus it should be possible to reproduce this in the CFT at weak coupling. We comment on the implications for the fuzzball proposal.

It is shown that exp(−2 Im ( ∫ p dr)) is not invariant under canonical transformations in general... more It is shown that exp(−2 Im ( ∫ p dr)) is not invariant under canonical transformations in general. Specifically for shells tunneling out of black holes, this quantity is not invariant under canonical transformations. It can be interpreted as the transmission coefficient only in the cases in which it is invariant under canonical transformations. Although such cases include alpha decay, they do not include the tunneling of shells from black holes. The simplest extension to this formula which is invariant under canonical transformations is proposed. However it is shown that this gives half the correct temperature for black holes. 1

[

It is shown that exp(−2 Im ( ∫ p dr)) is not invariant under canonical transformations in general... more It is shown that exp(−2 Im ( ∫ p dr)) is not invariant under canonical transformations in general. Specifically for shells tunneling out of black holes, this quantity is not invariant under canonical transformations. It can be interpreted as the tunneling probability only in the cases in which it is invariant under canonical transformations. Although such cases include alpha decay, they do not include the tunneling of shells from black holes. This demonstrates that this naive expression for tunneling probability does not hold for the case of shells tunneling out of black holes.

It is shown that in general the quantity exp(−2Im ( ∫ p dr)) is not invariant under canonical tra... more It is shown that in general the quantity exp(−2Im ( ∫ p dr)) is not invariant under canonical transformations. It can be interpreted as the tunneling probability only in specific cases which include the text book example of alpha decay but do not include a shell crossing a black hole horizon. With specific examples it is shown that this quantity is different for different canonically equivalent actions thus demonstrating that its interpretation as tunneling probability for black hole emission is questionable.

arXiv: High Energy Physics - Theory, 2013

It is generally believed that the eternal AdS black hole is dual to two conformal field theories ... more It is generally believed that the eternal AdS black hole is dual to two conformal field theories with compact spatial sections that are together in a thermofield double state. We argue that this proposal is incorrect, and by extension so are the "entanglement=geometry" proposal of Van Raamsdonk and "ER=EPR" proposal of Maldacena and Susskind. We show that in the bulk there is an interaction needed between the two halves of the Hilbert space for connectivity across the horizon; however, there is no such interaction between the CFTs. This rules out the possibility of the dual to the CFTs being the eternal AdS black hole. We argue the correct dual "geometries" resemble the exterior of the black hole outside the stretched horizon but cap off before the global horizon. This disallows the possibility of a shared future (and past) wedge where Alice falling from one side can meet Bob falling from the other. We expect that in the UV complete theory the aforement...

These lecture notes present an introduction to the fuzzball proposal and emission from the D1-D5 ... more These lecture notes present an introduction to the fuzzball proposal and emission from the D1-D5 system which is geared to an audience of graduate students and others with little background in the subject. The presentation begins with a discussion of the Penrose process and Hawking radiation. The fuzzball proposal is then introduced, and the twoand three-charge systems are reviewed. In the three-charge case details are not discussed. A detailed discussion of emission calculations for D1-D5-P black holes and for certain nonextremal fuzzballs from both the gravity and CFT perspectives is included. We explicitly demonstrate how seemingly different emission processes in gravity, namely, Hawking radiation and superradiance from D1-D5-P black holes, and ergoregion emission from certain non-extremal fuzzballs, are only different manifestations of the same phenomenon in the CFT.

Monthly Notices of the Royal Astronomical Society

Non-vanishing parity-odd correlators of gamma-ray arrival directions observed by Fermi-LAT indica... more Non-vanishing parity-odd correlators of gamma-ray arrival directions observed by Fermi-LAT indicate the existence of a helical intergalactic magnetic field with strength B ∼ 10 −14 G on ∼10 Mpc scales. We successfully test this hypothesis using more stringent cuts of the data, Monte Carlo simulations with Fermi-LAT time exposure information, separate analyses for the Northern and Southern galactic hemispheres, and confirm predictions made in Tashiro & Vachaspati. With some further technical assumptions, we show how to reconstruct the magnetic helicity spectrum from the parity-odd correlators.

Physical Review D, 2016

In the AdS/CFT correspondence, CFTs are identified by asymptotic boundary surfaces and the bounda... more In the AdS/CFT correspondence, CFTs are identified by asymptotic boundary surfaces and the boundary conditions imposed on those surfaces. However, AdS can be foliated in various ways to give different boundaries. We show that the CFTs obtained using certain distinct foliations are different. This difference arises because the asymptotic region of a foliation overlaps with the deep interior region of another. In particular we focus on the CFTs defined on surfaces of large constant radius in global coordinates, Rindler-AdS coordinates, and Poincaré coordinates for AdS 3 . We refer to these as global-CFT, Rindler-CFT and Poincaré-CFT respectively. We demonstrate that the correlators for these CFTs are different and argue that the bulk duals to these should agree up to very close to the respective horizons but then start differing. Since the BTZ black hole is obtained as a quotient of AdS 3 , we discuss the implications of our results for bulk duals of periodically-identified Poincaré and Rindler-CFTs. Our results are consistent with some recent proposals suggesting a modification of the semi-classical BTZ geometry close to the horizons.

A hole-ographic spacetime

We embed spherical Rindler space -- a geometry with a spherical hole in its center -- in asymptot... more We embed spherical Rindler space -- a geometry with a spherical hole in its center -- in asymptotically AdS spacetime and show that it carries a gravitational entropy proportional to the area of the hole. Spherical AdS-Rindler space is holographically dual to an ultraviolet sector of the boundary field theory given by restriction to a strip of finite duration in time. Because measurements have finite durations, local observers in the field theory can only access information about bounded spatial regions. We propose a notion of Residual Entropy that captures uncertainty about the state of a system left by the collection of local, finite-time observables. For two-dimensional conformal field theories we use holography and the strong subadditivity of entanglement to propose a formula for Residual Entropy and show that it precisely reproduces the areas of circular holes in AdS3. Extending the notion to field theories on strips with variable durations in time, we show more generally that ...

It is generally believed that the eternal AdS black hole is dual to two conformal field theories ... more It is generally believed that the eternal AdS black hole is dual to two conformal field theories with compact spatial sections that are together in a thermofield double state. We argue that this proposal is incorrect, and by extension so are the "entanglement=geometry" proposal of Van Raamsdonk and "ER=EPR" proposal of Maldacena and Susskind. We show that in the bulk there is an interaction needed between the two halves of the Hilbert space for connectivity across the horizon; however, there is no such interaction between the CFTs. This rules out the possibility of the dual to the CFTs being the eternal AdS black hole. We argue the correct dual "geometries" resemble the exterior of the black hole outside the stretched horizon but cap off before the global horizon. This disallows the possibility of a shared future (and past) wedge where Alice falling from one side can meet Bob falling from the other. We expect that in the UV complete theory the aforement...

In the AdS/CFT correspondence, CFTs are identified by asymptotic boundary surfaces and the bounda... more In the AdS/CFT correspondence, CFTs are identified by asymptotic boundary surfaces and the boundary conditions imposed on those surfaces. However, AdS can be foliated in various ways to give different boundaries. We show that the CFTs obtained using certain distinct foliations are different. This difference arises because the asymptotic region of a foliation overlaps with the deep interior region of another. In particular we focus on the CFTs defined on surfaces of large constant radius in global coordinates, Rindler-AdS coordinates, and Poincar\'e coordinates for AdS$_3$. We refer to these as global-CFT, Rindler-CFT and Poincar\'e-CFT respectively. We demonstrate that the correlators for these CFTs are different and argue that the bulk duals to these should agree up to very close to the respective horizons but then start differing. Since the BTZ black hole is obtained as a quotient of AdS$_3$, we discuss the implications of our results for bulk duals of periodically-identif...

A simple classical consideration of black hole formation and evaporation times as measured by an ... more A simple classical consideration of black hole formation and evaporation times as measured by an observer at infinity demonstrates that an infall cutoff outside the event horizon of a black hole must be imposed in order for the formation time of a black hole event horizon to not exceed its evaporation time. We explore this paradox quantitatively and examine possible cutoff scales and their relation to the Planck scale. Our analysis suggests several different possibilities, none of which can be resolved classically and all of which require new physics associated with even large black holes and macroscopic event horizons:(1) an event horizon never forms, for example due to radiation during collapse (resolving the information loss problem), (2) and/or quantum effects may affect space-time near an event horizon in ways which alter infall as well as black hole evaporation itself.

Journal of High Energy Physics, 2012

We find a family of novel supersymmetric phases of the D1-D5 CFT, which in certain ranges of char... more We find a family of novel supersymmetric phases of the D1-D5 CFT, which in certain ranges of charges have more entropy than all known ensembles. We also find bulk BPS configurations that exist in the same range of parameters as these phases, and have more entropy than a BMPV black hole; they can be thought of as coming from a BMPV black hole shedding a "hair" condensate outside of the horizon. The entropy of the bulk configurations is smaller than that of the CFT phases, which indicates that some of the CFT states are lifted at strong coupling. Neither the bulk nor the boundary phases are captured by the elliptic genus, which makes the coincidence of the phase boundaries particularly remarkable. Our configurations are supersymmetric, have non-Cardy-like entropy, and are the first instance of a black hole entropy enigma with a controlled CFT dual. Furthermore, contrary to common lore, these objects exist in a region of parameter space (between the "cosmic censorship bound" and the "unitarity bound") where no black holes were thought to exist.

Journal of High Energy Physics, 2015

It is conventional to study the entanglement between spatial regions of a quantum field theory. H... more It is conventional to study the entanglement between spatial regions of a quantum field theory. However, in some systems entanglement can be dominated by "internal", possibly gauged, degrees of freedom that are not spatially organized, and that can give rise to gaps smaller than the inverse size of the system. In a holographic context, such small gaps are associated to the appearance of horizons and singularities in the dual spacetime. Here, we propose a concept of entwinement, which is intended to capture this fine structure of the wavefunction. Holographically, entwinement probes the entanglement shadow -the region of spacetime not probed by the minimal surfaces that compute spatial entanglement in the dual field theory. We consider the simplest example of this scenario -a 2d conformal field theory (CFT) that is dual to a conical defect in AdS 3 space. Following our previous work, we show that spatial entanglement in the CFT reproduces spacetime geometry up to a finite distance from the conical defect. We then show that the interior geometry up to the defect can be reconstructed from entwinement that is sensitive to the discretely gauged, fractionated degrees of freedom of the CFT. Entwinement in the CFT is related to non-minimal geodesics in the conical defect geometry, suggesting a potential quantum information theoretic meaning for these objects in a holographic context. These results may be relevant for the reconstruction of black hole interiors from a dual field theory.

International Journal of Modern Physics D, 2013

In this paper, we examine the implications of the ongoing black holes versus firewalls debate for... more In this paper, we examine the implications of the ongoing black holes versus firewalls debate for the thermo-field dynamics of black holes by analyzing a conformal field theory (CFT) in a thermal state in the context of anti-de Sitter/CFT. We argue that the thermo-field doubled copy of the thermal CFT should be thought of not as a fictitious system, but as the image of the CFT in the heat bath. In case of strong coupling between the CFT and the heat bath, this image allows for free infall through the horizon and the system is described by a black hole. Conversely, firewalls are the appropriate dual description in case of weak interaction of the CFT with its heat bath.

Physical Review D, 2013

Recently, Almheiri, Marolf, Polchinski and Sully (AMPS) have suggested a Gedankenexperiment to te... more Recently, Almheiri, Marolf, Polchinski and Sully (AMPS) have suggested a Gedankenexperiment to test black hole complementarity. They claim that the postulates of black hole complementarity are mutually inconsistent and choose to give up the 'absence of drama' for an infalling observer. According to them the black hole is shielded by a firewall no later than Page time. This has generated some controversy. We find that an interesting picture emerges when we take into account objections from the advocates of fuzzballs. We reformulate AMPS' Gedankenexperiment in the decoherence picture of quantum mechanics and find that low energy wave packets interact with the radiation quanta rather violently while high energy wave packets do not. This is consistent with Mathur's recent proposal of fuzzball complementarity for high energy quanta falling into fuzzballs.