Traversable wormholes via a double trace deformation

A bstractAfter turning on an interaction that couples the two boundaries of an eternal BTZ black hole, we find a quantum matter stress tensor with negative average null energy, whose gravitational backreaction renders the Einstein-Rosen bridge traversable. Such a traversable wormhole has an interesting interpretation in the context of ER=EPR, which we suggest might be related to quantum teleportation. However, it cannot be used to violate causality. We also discuss the implications for the energy and holographic entropy in the dual CFT description.

[1]  C. S..  The ( 2 + 1 )-Dimensional Black Hole , 1995 .

[2]  Kar,et al.  Lorentzian wormholes in Einstein-Gauss-Bonnet theory. , 1992, Physical review. D, Particles and fields.

[3]  The (2 + 1)-dimensional black hole , 1995, gr-qc/9506079.

[4]  Onkar Parrikar,et al.  Modular Hamiltonians for deformed half-spaces and the averaged null energy condition , 2016, 1605.08072.

[5]  S. Raju,et al.  An infalling observer in AdS/CFT , 2012, 1211.6767.

[6]  T. Takayanagi,et al.  EPR pairs, local projections and quantum teleportation in holography , 2016, 1604.01772.

[7]  Aron C. Wall.  Ten proofs of the generalized second law , 2009, 0901.3865.

[8]  D. Marolf,et al.  Eternal black holes and superselection in AdS/CFT , 2012, 1210.3590.

[9]  Non-Local Effects of Multi-Trace Deformations in the AdS/CFT Correspondence , 2005, hep-th/0504177.

[10]  J. Maldacena,et al.  Conformal collider physics: energy and charge correlations , 2008, 0803.1467.

[11]  Null Energy Condition in Dynamic Wormholes , 1998, gr-qc/9802048.

[12]  S. Chekanov,et al.  Scaled momentum distributions of charged particles in dijet photoproduction at HERA , 2009 .

[13]  David Poland,et al.  A proof of the conformal collider bounds , 2016, 1603.03771.

[14]  Entropies of scalar fields on three-dimensional black holes , 1994, hep-th/9412144.

[15]  L. Susskind,et al.  Cool horizons for entangled black holes , 2013, 1306.0533.

[16]  T. Takayanagi,et al.  Holographic Derivation of Entanglement Entropy from AdS/CFT , 2006, hep-th/0603001.

[17]  Thorne,et al.  Wormholes, time machines, and the weak energy condition. , 1988, Physical review letters.

[18]  Mario Ubeda Garcia,et al.  Measurement of the CKM angle $\gamma$ using $B^\pm \to D K^\pm$ with $D \to K^0_{\rm S} \pi^+\pi^-, K^0_{\rm S} K^+ K^-$ decays , 2014 .

[19]  T. Takayanagi,et al.  Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence. , 2006, Physical review letters.

[20]  Xi Dong,et al.  Holographic entanglement beyond classical gravity , 2013, 1306.4682.

[21]  J. Maldacena,et al.  Eternal black holes in anti-de Sitter , 2001, hep-th/0106112.

[22]  Aron C. Wall,et al.  Holographic proof of the averaged null energy condition , 2014, 1408.3566.

[23]  Aron C. Wall.  Proving the achronal averaged null energy condition from the generalized second law , 2009, 0910.5751.

[24]  M. Smedbäck.  Pulsating strings on Ads(5) x S(5) , 2004 .

[25]  T. Takayanagi,et al.  A covariant holographic entanglement entropy proposal , 2007, 0705.0016.

[26]  K. Thorne,et al.  Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity , 1988 .

[27]  S. Solodukhin.  Restoring unitarity in the Banados-Teitelboim-Zanelli black hole , 2005 .

[28]  D. Marolf,et al.  A coarse-grained generalized second law for holographic conformal field theories , 2015, 1509.00074.

[29]  Marcelo Botta-Cantcheff,et al.  Lorentzian AdS geometries, wormholes, and holography , 2010, 1012.4478.

[30]  A. Sever,et al.  `Double-trace' deformations, boundary conditions and spacetime singularities , 2001, hep-th/0112264.

[31]  Matt Visser,et al.  Lorentzian Wormholes: From Einstein to Hawking , 1995 .

[32]  Quantum Bousso bound , 2003, hep-th/0303067.

[33]  Michael J. Schlosser,et al.  Multiple Hypergeometric Series: Appell Series and Beyond , 2013, 1305.1966.

[34]  R. Bousso,et al.  Prepared for submission to JHEP A Quantum Focussing Conjecture , 2015 .

[35]  Werner Israel,et al.  Thermo-field dynamics of black holes☆ , 1976 .

[36]  Stefan Leichenauer,et al.  Holographic Proof of the Quantum Null Energy Condition , 2015, 1512.06109.

[37]  S. Shenker,et al.  Black holes and the butterfly effect , 2013, Journal of High Energy Physics.

[38]  Black hole in three-dimensional spacetime. , 1992, Physical review letters.

[39]  J. Maldacena,et al.  Causality constraints on corrections to the graviton three-point coupling , 2014, Journal of High Energy Physics.

[40]  W. Unruh.  Notes on black-hole evaporation , 1976 .

[41]  P. Hayden,et al.  Black holes as mirrors: Quantum information in random subsystems , 2007, 0708.4025.

[42]  K. Olum,et al.  Proof of the averaged null energy condition in a classical curved spacetime using a null-projected quantum inequality , 2015, 1507.00297.

[43]  Aitor Lewkowycz,et al.  Quantum corrections to holographic entanglement entropy , 2013, 1307.2892.

[44]  D. Amati,et al.  Effective action and all-order gravitational eikonal at planckian energies , 1993 .

[45]  R. Wald,et al.  Proof of classical versions of the Bousso entropy bound and of the generalized second law , 1999, hep-th/9908070.

[46]  K. Olum,et al.  Averaged null energy condition in a classical curved background , 2012, 1212.2290.

[47]  Zanelli,et al.  Geometry of the 2+1 black hole. , 1993, Physical review. D, Particles and fields.

[48]  Restoring Unitarity in BTZ Black Hole , 2005, hep-th/0501053.

[49]  Xi Dong,et al.  Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality. , 2016, Physical review letters.

[50]  Aron C. Wall.  A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices , 2011, 1105.3445.

[51]  R. Bousso.  A covariant entropy conjecture , 1999, hep-th/9905177.

[52]  Leonard Susskind,et al.  ER=EPR, GHZ, and the consistency of quantum measurements , 2014, 1412.8483.

[53]  Netta Engelhardt,et al.  Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime , 2014, 1408.3203.

[54]  L. Parker,et al.  Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity , 2009 .

[55]  Rudolf Haag,et al.  On the equilibrium states in quantum statistical mechanics , 1967 .

[56]  N. Graham,et al.  Achronal averaged null energy condition , 2007, 0705.3193.

[57]  M. Thibeault,et al.  Thin-shell wormholes in Einstein–Maxwell theory with a Gauss–Bonnet term , 2005, gr-qc/0512029.

[58]  Aron C. Wall.  Corrigendum: The generalized second law implies a quantum singularity theorem , 2010, 1010.5513.

[59]  D. Freedman,et al.  Stability in Gauged Extended Supergravity , 1982 .