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Lanczos-Lovelock Gravity from a Thermodynamic Perspective

  • Sumanta ChakrabortyEmail author
Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

The deep connection between gravitational dynamics and horizon thermodynamics leads to several intriguing features in general relativity. In this chapter we provide a generalization of several of such results to Lanczos-Lovelock gravity. To our expectation it turns out that most of the results obtained in the context of general relativity generalize to Lanczos-Lovelock gravity in a straightforward but non-trivial manner. First, we provide an alternative and more general derivation of the connection between Noether charge for a specific time evolution vector field and gravitational heat density of the boundary surface. Taking a cue from this, we have introduced naturally defined four-momentum current associated with gravity and matter energy momentum tensor for both Lanczos-Lovelock Lagrangian. Then, we consider the concepts of Noether charge for null boundaries in Lanczos-Lovelock gravity by providing a direct generalization of previous results derived in the context of general relativity. Further we have shown that gravitational field equations for arbitrary static and spherically symmetric spacetimes with horizon can be written as a thermodynamic identity in the near horizon limit, transcending general relativity.

References

  1. 1.
    T. Padmanabhan, General relativity from a thermodynamic perspective. Gen. Relativ. Gravit. 46, 1673 (2014). arXiv:1312.3253 [gr-qc]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    D. Kothawala, T. Padmanabhan, Thermodynamic structure of Lanczos-Lovelock field equations from near-horizon symmetries. Phys. Rev. D 79, 104020 (2009). arXiv:0904.0215 [gr-qc]ADSCrossRefGoogle Scholar
  3. 3.
    A. Paranjape, S. Sarkar, T. Padmanabhan, Thermodynamic route to field equations in Lancos-Lovelock gravity. Phys. Rev. D 74, 104015 (2006). arXiv:hep-th/0607240 ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    S. Chakraborty, K. Parattu, T. Padmanabhan, Gravitational field equations near an arbitrary null surface expressed as a thermodynamic identity. JHEP 10, 097 (2015). arXiv:1505.05297 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    D. Kothawala, The thermodynamic structure of Einstein tensor. Phys. Rev. D 83, 024026 (2011). arXiv:1010.2207 [gr-qc]
  6. 6.
    S.A. Hayward, Unified first law of black hole dynamics and relativistic thermodynamics. Class. Quantum Gravity 15, 3147–3162 (1998). arXiv:gr-qc/9710089 [gr-qc]
  7. 7.
    D. Kastor, S. Ray, J. Traschen, Enthalpy and the mechanics of AdS black holes. Class. Quantum Gravity 26, 195011 (2009). arXiv:0904.2765 [hep-th]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    B.P. Dolan, Pressure and volume in the first law of black hole thermodynamics. Class. Quantum Gravity 28, 235017 (2011). arXiv:1106.6260 [gr-qc]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    D. Kubiznak, R.B. Mann, P-V criticality of charged AdS black holes. JHEP 07, 033 (2012). arXiv:1205.0559 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    A.M. Frassino, D. Kubiznak, R.B. Mann, F. Simovic, Multiple reentrant phase transitions and triple points in lovelock thermodynamics. JHEP 09, 080 (2014). arXiv:1406.7015 [hep-th]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    T. Jacobson, R.C. Myers, Black hole entropy and higher curvature interactions. Phys. Rev. Lett. 70, 3684–3687 (1993). arXiv:hep-th/9305016 [hep-th]
  12. 12.
    T. Clunan, S.F. Ross, D.J. Smith, On Gauss-Bonnet black hole entropy, Class. Quantum Gravity 21, 3447–3458 (2004). arXiv:gr-qc/0402044 [gr-qc]
  13. 13.
    R.M. Wald, Black hole entropy is the Noether charge. Phys. Rev. D 48, 3427–3431 (1993). arXiv:gr-qc/9307038 [gr-qc]
  14. 14.
    K. Parattu, B.R. Majhi, T. Padmanabhan, Structure of the gravitational action and its relation with horizon thermodynamics and emergent gravity paradigm, Phys. Rev. D 87, 124011 (2013). arXiv:gr-qc/1303.1535 [gr-qc], doi: 10.1103/PhysRevD.87.124011
  15. 15.
    S. Chakraborty, T. Padmanabhan, Geometrical variables with direct thermodynamic significance in Lanczos-Lovelock gravity. Phys. Rev. D 90(8), 084021 (2014). arXiv:1408.4791 [gr-qc]
  16. 16.
    B. Julia, S. Silva, Currents and superpotentials in classical gauge invariant theories. 1. Local results with applications to perfect fluids and general relativity. Class. Quantum Gravity 15, 2173–2215 (1998). arXiv:gr-qc/9804029 [gr-qc]
  17. 17.
    T. Regge, C. Teitelboim, Role of surface integrals in the Hamiltonian formulation of general relativity. Ann. Phys. 88, 286 (1974)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    S. Carlip, Entropy from conformal field theory at killing horizons, Class. Quantum Gravity 16, 3327–3348 (1999). arXiv:gr-qc/9906126 [gr-qc]
  19. 19.
    B.R. Majhi, T. Padmanabhan, Noether current, horizon Virasoro algebra and entropy. Phys. Rev. D 85, 084040 (2012). arXiv:1111.1809 [gr-qc]ADSCrossRefGoogle Scholar
  20. 20.
    B.R. Majhi, S. Chakraborty, Anomalous effective action, Noether current, virasoro algebra and horizon entropy. Eur. Phys. J. C 74, 2867 (2014). arXiv:1311.1324 [gr-qc]ADSCrossRefGoogle Scholar
  21. 21.
    K. Parattu, S. Chakraborty, B.R. Majhi, T. Padmanabhan, Null surfaces: counter-term for the action principle and the characterization of the gravitational degrees of freedom. arXiv:1501.01053 [gr-qc]
  22. 22.
    T. Padmanabhan, A. Paranjape, Entropy of null surfaces and dynamics of spacetime. Phys. Rev. D 75, 064004 (2007). arXiv:gr-qc/0701003 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsIndian Association for the Cultivation of ScienceJadavpur, KolkataIndia

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