Geometric Model of Black Hole Quantum N-portrait, Extradimensions and Thermodynamics

Recently a short scale modified black hole metric, known as holographic metric, has been proposed in order to capture the self-complete character of gravity. In this paper we show that such a metric can reproduce some geometric features expected from the quantum $N$-portrait beyond the semi-classical limit. We show that for a generic $N$ this corresponds to having an effective energy momentum tensor in Einstein equations or, equivalently, non-local terms in the gravity action. We also consider the higher dimensional extension of the metric and the case of an AdS cosmological term. We provide a detailed thermodynamic analysis of both cases, with particular reference to the repercussions on the Hawking-Page phase transition.

[1]  Deforming regular black holes , 2015, 1508.06701.

[2]  Renormalization group improved black hole spacetimes , 2000, hep-th/0002196.

[3]  Marco Cavaglia.  Black Hole and Brane Production in TeV Gravity , 2002 .

[4]  G. Dvali,et al.  Ultra-high energy probes of classicalization , 2012, 1205.2540.

[5]  M. Kowalski,et al.  Black holes at neutrino telescopes , 2002, hep-ph/0201139.

[6]  S. Park.  Black holes and the LHC: A review , 2012, 1203.4683.

[7]  R. Mann,et al.  P − V criticality of charged AdS black holes , 2012, 1205.0559.

[8]  L. Modesto.  Loop quantum black hole , 2005, gr-qc/0509078.

[9]  A. Barvinsky.  Dark energy and dark matter from nonlocal ghost-free gravity theory , 2011, 1107.1463.

[10]  L. Susskind.  Twenty Years of Debate with Stephen , 2002, hep-th/0204027.

[11]  X. Calmet.  A Review of Quantum Gravity at the Large Hadron Collider , 2010, 1005.1805.

[12]  G. Magli.  A simple model of a black-hole interior , 1997 .

[13]  G. Landsberg,et al.  Black holes at the Large Hadron Collider. , 2001 .

[14]  Stephen W. Hawking,et al.  Particle Creation by Black Holes , 1993, Resonance.

[15]  D. Lüst,et al.  Black Hole Formation and Classicalization in Ultra-Planckian 2 ! N Scattering , 2014, 1409.7405.

[16]  P. Provero,et al.  MINIMUM PHYSICAL LENGTH AND THE GENERALIZED UNCERTAINTY PRINCIPLE IN STRING THEORY , 1990 .

[17]  G. Veneziano.  A Stringy Nature Needs Just Two Constants , 1986 .

[18]  P. Nicolini,et al.  Holographic Screens in Ultraviolet Self-Complete Quantum Gravity , 2012, 1210.0015.

[19]  B. Dolan.  Where is the PdV term in the fist law of black hole thermodynamics , 2012, 1209.1272.

[20]  Pisin Chen,et al.  Black Hole Remnants and the Information Loss Paradox , 2014, 1412.8366.

[21]  M. Isi,et al.  Self-completeness and the generalized uncertainty principle , 2013, Journal of High Energy Physics.

[22]  P. Nicolini,et al.  Mini-review on mini-black holes from the mini-Big Bang , 2014, 1403.0944.

[23]  M. Vahidinia,et al.  Extended phase space thermodynamics and P-V criticality of black holes with a nonlinear source , 2012, 1212.6128.

[24]  F. Scardigli,et al.  Horizon wave function for single localized particles: GUP and quantum black-hole decay , 2013, 1306.5298.

[25]  J. Bekenstein.  Black Holes and Entropy , 1973, Jacob Bekenstein.

[26]  G. Calcagni,et al.  Super-accelerating bouncing cosmology in asymptotically free non-local gravity , 2013, 1306.5332.

[27]  J. Maldacena.  The Large-N Limit of Superconformal Field Theories and Supergravity , 1997, hep-th/9711200.

[28]  G. Dvali,et al.  Black Hole Macro-Quantumness , 2012, 1212.0765.

[29]  R. Mann,et al.  Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization , 2012, Journal of High Energy Physics.

[30]  R. Mann,et al.  Cosmological production of noncommutative black holes , 2011, 1102.5096.

[31]  Scott D. Thomas,et al.  High-energy colliders as black hole factories: The End of short distance physics , 2001, hep-ph/0106219.

[32]  Stephen W Hawking,et al.  Soft Hair on Black Holes. , 2016, Physical review letters.

[33]  P. Nicolini,et al.  Noncommutative geometry inspired Schwarzschild black hole , 2005, gr-qc/0510112.

[34]  Eric G. Brown,et al.  Instability of the noncommutative geometry inspired black hole , 2010, 1012.4787.

[35]  I. Dymnikova.  Vacuum nonsingular black hole , 1992 .

[36]  M. B. Sedra,et al.  On Thermodynamics of AdS Black Holes in Arbitrary Dimensions , 2012, 1210.4617.

[37]  E. Spallucci,et al.  Maxwellʼs equal-area law for charged Anti-de Sitter black holes , 2013, 1305.3379.

[38]  Samir D. Mathur,et al.  AdS / CFT duality and the black hole information paradox , 2001, hep-th/0109154.

[39]  A. Barvinsky,et al.  Nonlocal action for long-distance modifications of gravity theory , 2003 .

[40]  V. M. Ghete,et al.  Search for resonances and quantum black holes using dijet mass spectra in proton-proton collisions at sqrt(s) = 8 TeV , 2015, 1501.04198.

[41]  B. Dolan.  The cosmological constant and black-hole thermodynamic potentials , 2011 .

[42]  J. Moffat.  Ultraviolet complete quantum gravity , 2010, 1008.2482.

[43]  B. Carr,et al.  The Compton-Schwarzschild correspondence from extended de Broglie relations , 2015, 1505.06994.

[44]  C. Rovelli,et al.  On the effective metric of a Planck star , 2014, 1412.6015.

[45]  B. Dolan.  Compressibility of rotating black holes , 2011, 1109.0198.

[46]  A. DeBenedictis.  Developments in black hole research: Classical, semi-classical, and quantum , 2007, 0711.2279.

[47]  F. Scardigli,et al.  Quantum hoop conjecture: Black hole formation by particle collisions , 2013, 1311.5698.

[48]  Metric of the multiply wound rotating string , 2001, hep-th/0105136.

[49]  R. Casadio,et al.  Horizon Quantum Mechanics: a hitchhiker's guide to quantum black holes , 2015, 1512.04071.

[50]  G. Gibbons.  What is the Shape of a Black Hole , 2012, 1201.2340.

[51]  S. Hayward.  Formation and evaporation of nonsingular black holes. , 2005, Physical review letters.

[52]  D. Lüst,et al.  Gravitational black hole hair from event horizon supertranslations , 2016, 1601.03725.

[53]  Anshul Saini,et al.  Radiation from a collapsing object is manifestly unitary. , 2015, Physical review letters.

[54]  G. Landsberg,et al.  Black Holes at the LHC , 2001, hep-ph/0106295.

[55]  N. Krasnikov.  Nonlocal gauge theories , 1987 .

[56]  D. Stojkovic,et al.  Inner horizon of the quantum Reissner-Nordström black holes , 2015, 1503.01888.

[57]  P. Nicolini,et al.  Non-commutative geometry inspired higher-dimensional charged black holes , 2008, 0801.3519.

[58]  Samir D. Mathur.  The Fuzzball proposal for black holes: An Elementary review , 2005 .

[59]  E. Spallucci,et al.  Semi-classical approach to quantum black holes , 2014, 1410.1706.

[60]  Clifford V. Johnson,et al.  Charged AdS black holes and catastrophic holography , 1999, hep-th/9902170.

[61]  P. Nicolini,et al.  Hawking emission from quantum gravity black holes , 2011, 1108.4419.

[62]  G. Dvali,et al.  Self-Completeness of Einstein Gravity. , 2010, 1005.3497.

[63]  D. Stojkovic,et al.  Horizon Wave-Function and the Quantum Cosmic Censorship , 2015, 1503.02858.

[64]  B. Dolan.  Pressure and volume in the first law of black hole thermodynamics , 2011, 1106.6260.

[65]  L. Randall,et al.  A Large mass hierarchy from a small extra dimension , 1999, hep-ph/9905221.

[66]  Anshul Saini,et al.  Nonlocal (but also nonsingular) physics at the last stages of gravitational collapse , 2014, 1401.6182.

[67]  R. Casadio.  Localised particles and fuzzy horizons: A tool for probing Quantum Black Holes , 2013, 1305.3195.

[68]  K. Nozari,et al.  Noncommutative Geometry Inspired Charged Black Holes in Extra Dimensions , 2007 .

[69]  G. Cognola,et al.  Thermodynamics of Kerr-Newman-AdS black holes and conformal field theories , 1999, hep-th/9908022.

[70]  Alex Casanova,et al.  TOPICAL REVIEW: TeV mini black hole decay at future colliders , 2005 .

[71]  D. Gross,et al.  String Theory Beyond the Planck Scale , 1988 .

[72]  D. Page,et al.  Thermodynamics of black holes in anti-de Sitter space , 1983 .

[73]  Israel,et al.  Inner-horizon instability and mass inflation in black holes. , 1989, Physical review letters.

[74]  J. Moffat,et al.  Black holes in an ultraviolet complete quantum gravity , 2010, 1010.0680.

[75]  E. Spallucci,et al.  Thermodynamical phases of a regular SAdS black hole , 2012, 1212.5044.

[76]  E. Ay'on-Beato,et al.  Regular black hole in general relativity coupled to nonlinear electrodynamics , 1998, gr-qc/9911046.

[77]  P. Nicolini,et al.  Minimum Length Effects in Black Hole Physics , 2014, 1405.1692.

[78]  Why the Length of a Quantum String Cannot Be Lorentz Contracted , 2013, 1309.7741.

[79]  Black holes and sub-millimeter dimensions , 1998, hep-th/9808138.

[80]  P. Nicolini.  Nonlocal and generalized uncertainty principle black holes , 2012, 1202.2102.

[81]  P. Kanti,et al.  Hawking Radiation from Higher-Dimensional Black Holes , 2014, 1402.3952.

[82]  Savas Dimopoulos,et al.  Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity , 1998, hep-ph/9807344.

[83]  G. Dvali,et al.  Classical limit of black hole quantum N-portrait and BMS symmetry , 2015, 1509.02114.

[84]  L. Randall,et al.  An Alternative to compactification , 1999, hep-th/9906064.

[85]  G. Gibbons,et al.  Black hole enthalpy and an entropy inequality for the thermodynamic volume , 2010, 1012.2888.

[86]  S. Hayward.  FORMATION AND EVAPORATION OF REGULAR BLACK HOLES , 2005 .

[87]  R. Casadio,et al.  Horizon of quantum black holes in various dimensions , 2015, 1509.09317.

[88]  G. Dvali,et al.  Black holes as critical point of quantum phase transition , 2012, The European physical journal. C, Particles and fields.

[89]  M. P. Casado,et al.  Search for new phenomena with photon+jet events in proton-proton collisions at s=13$$ \sqrt{s}=13 $$ TeV with the ATLAS detector , 2016 .

[90]  Alexis Larrañga,et al.  Geometric thermodynamics of a schwarzschild-AdS black hole with a cosmological constant as a state variable , 2011, 1108.2205.

[91]  P. Nicolini,et al.  Noncommutative geometry-inspired dirty black holes , 2009, 0902.4654.

[92]  G. Dvali,et al.  Black hole's quantum N‐portrait , 2011, 1112.3359.

[93]  Quantum Radiation from a 5-Dimensional Rotating Black Hole , 2002, gr-qc/0211055.

[94]  S. Hawking.  The Information Paradox for Black Holes. , 2015, 1509.01147.

[95]  P. Gaete,et al.  Un-graviton corrections to the Schwarzschild black hole , 2010, 1005.0234.

[96]  E. Witten.  Reflections on the Fate of Spacetime , 1996 .

[97]  P. Nicolini,et al.  Large extra dimensions and small black holes at the LHC , 2010, 1001.2211.

[98]  A Critique of Pure String Theory: Heterodox Opinions of Diverse Dimensions , 2003, hep-th/0306074.

[99]  P. Nicolini,et al.  Connecting horizon pixels and interior voxels of a black hole , 2014, 1409.5069.

[100]  Trevor Coward,et al.  Nova Science Publishers , 2013 .

[101]  How to create black holes on Earth , 2007, physics/0703062.

[102]  Jillian Bellovary,et al.  Black holes in the early Universe , 2012, Reports on progress in physics. Physical Society.

[103]  Willy Fischler,et al.  A Model for High Energy Scattering in Quantum Gravity , 1999 .

[104]  Hawking radiation from rotating brane black holes , 2007, 0708.2656.

[105]  Sabine Hossenfelder.  What Black Holes Can Teach Us , 2004 .

[106]  G. Hooft.  Quantum black holes , 1987 .

[107]  P. Nicolini.  Noncommutative Black Holes, The Final Appeal To Quantum Gravity: A Review , 2008, 0807.1939.

[108]  E. Spallucci,et al.  Kerrr black hole: The lord of the string , 2010, 1003.3918.

[109]  FOUR DIMENSIONALITY IN NON-COMPACT KALUZA–KLEIN MODEL , 1999, hep-ph/9904383.

[110]  B. Carr,et al.  Sub-Planckian black holes and the Generalized Uncertainty Principle , 2015, 1504.07637.

[111]  P. Nicolini,et al.  Fuzziness at the horizon , 2010, 1001.1158.

[112]  Jonathan L. Feng,et al.  Detecting microscopic black holes with neutrino telescopes , 2002, hep-ph/0202081.

[113]  Sarah Folkerts,et al.  Physics of trans-Planckian gravity , 2010, 1006.0984.

[114]  D. Amati,et al.  Can spacetime be probed below the string size , 1989 .

[115]  Savas Dimopoulos,et al.  The Hierarchy problem and new dimensions at a millimeter , 1998, hep-ph/9803315.

[116]  A. Mazumdar,et al.  Towards singularity- and ghost-free theories of gravity. , 2011, Physical review letters.

[117]  P. Nicolini,et al.  Could Any Black Holes Be Produced at the LHC , 2011, 1111.5830.

[118]  R. Adler.  Six easy roads to the Planck scale , 2010, 1001.1205.

[119]  Kostas Skenderis,et al.  The fuzzball proposal for black holes , 2008, 0804.0552.

[120]  S. Dimopoulos,et al.  THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS NEW DIMENSIONS AT A MILLIMETER TO A FERMI AND SUPERSTRINGS AT A TeV , 2005 .

[121]  G. Dvali,et al.  Black holeʼs 1/N hair , 2012, 1203.6575.

[122]  E. Spallucci,et al.  Planck's uncertainty principle and the saturation of Lorentz boosts by Planckian black holes , 2013, 1309.7186.

[123]  G. Dvali.  Non‐Thermal Corrections to Hawking Radiation Versus the Information Paradox ** , 2015, 1509.04645.

[124]  S. Hawking,et al.  Information Preservation and Weather Forecasting for Black Holes , 2014, 1401.5761.

[125]  Black hole production by cosmic rays. , 2001, Physical review letters.

[126]  G. Torrieri,et al.  The Hawking-Page crossover in noncommutative anti-deSitter space , 2011, 1105.0188.

[127]  H. Culetu.  On a Regular Charged black Hole with a Nonlinear Electric Source , 2014, 1408.3334.

[128]  S. Capozziello,et al.  Extended Theories of Gravity , 2011, 1108.6266.

[129]  Nonsingular black hole model as a possible end product of gravitational collapse , 2005, gr-qc/0506111.

[130]  Greg Landsberg.  Black holes at future colliders and beyond , 2006 .

[131]  D. Stojkovic,et al.  Quantum gravitational collapse: non-singularity and non-locality , 2008, 0802.4087.

[132]  Leonardo Modesto,et al.  Super-renormalizable Quantum Gravity , 2011, 1107.2403.

[133]  Y. Pang,et al.  AdS and Lifshitz black holes in conformal and Einstein-Weyl gravities , 2012, 1204.1062.

[134]  A. Frassino.  Phase Transitions of Regular Schwarzschild-anti-deSitter Black Holes , 2015, 1502.01305.

[135]  T. Rizzo.  Noncommutative Inspired Black Holes in Extra Dimensions , 2006, hep-ph/0606051.

[136]  Quasilocal thermodynamics of dilaton gravity coupled to gauge fields. , 1995, Physical review. D, Particles and fields.

[137]  Bogdan A. Dobrescu,et al.  Bounds on Universal Extra Dimensions , 2000, hep-ph/0012100.

[138]  P. Nicolini,et al.  Charged rotating noncommutative black holes , 2010, 1005.5605.

[139]  Superrenormalizable gauge and gravitational theories , 1997, hep-th/9702146.

[140]  Sourya Ray,et al.  Enthalpy and the mechanics of AdS black holes , 2009, 0904.2765.

[141]  P. Nicolini,et al.  Self-completeness and spontaneous dimensional reduction , 2012, The European Physical Journal Plus.

[142]  Panagiota Kanti.  Black Holes in Theories with Large Extra Dimensions , 2004 .