Abstract
In this chapter we will review some earlier results, which will be helpful for the later parts of the thesis. This includes some interesting results in general relativity, definition of Noether current and gravitational momentum etc. We have also reviewed Lanczos-Lovelock models of gravity as it will find extensive use in subsequent chapters. We have also provided a discussion on a particular coordinate system adapted to null surfaces, known as Gaussian Null Coordinates, which will be very useful for our thermodynamic considerations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
T. Padmanabhan, Gravitation: Foundations and Frontiers (Cambridge University Press, Cambridge, UK, 2010)
M.V. Ostrogradsky, Memoires de lAcademie Imperiale des Science de Saint-Petersbourg, 4, 385 (1850)
J. York, Role of conformal three geometry in the dynamics of gravitation. Phys. Rev. Lett. 28, 1082–1085 (1972)
G. Gibbons, S. Hawking, Action integrals and partition functions in quantum gravity. Phys. Rev. D 15, 2752–2756 (1977)
J. Charap, J. Nelson, Surface integrals and the gravitational action. J. Phys. A: Math. Gen. 16 1661 (1983)
C. Lanczos, Z. Phys. 73, 147 (1932)
C. Lanczos, Electricity as a natural property of Riemannian geometry. Rev. Mod. Phys. 39, 716–736 (1932)
C. Lanczos, Z. Phys. 39, 842 (1938)
C. Lanczos, A remarkable property of the Riemann-Christoffel tensor in four dimensions. Annals Math. 39, 842–850 (1938)
D. Lovelock, The Einstein tensor and its generalizations. J. Math. Phys. 12, 498–501 (1971)
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 (Jun, 2013). arXiv:gr-qc/1303.1535 [gr-qc], doi:10.1103/PhysRevD.87.124011
A. Eddington, The Mathematical Theory of Relativity, 2nd edn. (Cambridge University Press, Cambridge, UK, 1924)
E. Schrodinger, Space-Time Structure (Cambridge Science Classics. Cambridge University Press, Cambridge, UK, 1950)
A. Einstein, B. Kaufman, A new form of the general relativistic field equations. Annals Math. 62, 128–138 (1955)
A. Einstein, B. Kaufman, A new form of the general relativistic field equations. Annals Math. 62, 128–138 (1955), http://www.jstor.org/stable/2007103
T. Padmanabhan, Momentum density of spacetime and the gravitational dynamics. arXiv:1506.03814 [gr-qc]
T. Padmanabhan, Holographic gravity and the surface term in the Einstein-Hilbert action. Braz. J. Phys. 35, 362–372 (2005). arXiv:gr-qc/0412068 [gr-qc]
A. Mukhopadhyay, T. Padmanabhan, Holography of gravitational action functionals. Phys. Rev. D 74, 124023 (2006). arXiv:hep-th/0608120
S. Kolekar, T. Padmanabhan, Holography in action. Phys. Rev. D 82, 024036 (2010). arXiv:1005.0619 [gr-qc]
C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation, 3rd edn. (W. H. Freeman and Company, 1973)
H. Goldstein, C. Poole, J. Safko, Classical Mechanics. 3rd edn. (Pearson Education, 2007)
A. Palatini, Deduzione invariantiva delle equazioni gravitazionali dal principio di hamilton. Rend. Circ. Mat. Palermo 43, 203–212 (1919)
T. Padmanabhan, General relativity from a thermodynamic perspective. Gen. Rel. Grav. 46, 1673 (2014). arXiv:1312.3253 [gr-qc]
N. Dadhich, Characterization of the Lovelock gravity by Bianchi derivative. Pramana. 74, 875–882 (2010). arXiv:0802.3034 [gr-qc]
D.G. Boulware, S. Deser, String generated gravity models. Phys. Rev. Lett. 55, 2656 (1985)
L. Randall, R. Sundrum, A Large mass hierarchy from a small extra dimension. Phys. Rev. Lett. 83, 3370–3373 (1999). arXiv:hep-ph/9905221 [hep-ph]
P. Horava, E. Witten, Eleven-dimensional supergravity on a manifold with boundary. Nucl. Phys. B 475, 94–114 (1996). arXiv:hep-th/9603142 [hep-th]
N. Arkani-Hamed, S. Dimopoulos, G. Dvali, The hierarchy problem and new dimensions at a millimeter. Phys. Lett. B 429, 263–272 (1998). arXiv:hep-ph/9803315 [hep-ph]
T. Padmanabhan, D. Kothawala, Lanczos-Lovelock models of gravity. Phys. Rept. 531, 115–171 (2013). arXiv:1302.2151 [gr-qc]
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 [hep-th]
A. Yale, T. Padmanabhan, Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions. Gen. Rel. Grav. 43, 1549–1570 (2011). arXiv:1008.5154 [gr-qc]
N. Kiriushcheva, S.V. Kuzmin, On Hamiltonian formulation of the Einstein-Hilbert action in two dimensions. Mod. Phys. Lett. A 21, 899–906 (2006). arXiv:hep-th/0510260 [hep-th]
T. Padmanabhan, Some aspects of field equations in generalised theories of gravity. Phys. Rev. D 84, 124041 (2011). arXiv:1109.3846 [gr-qc]
T. Padmanabhan, A physical interpretation of gravitational field equations. AIP Conf. Proc. 1241, 93–108 (2010). arXiv:0911.1403 [gr-qc]
R.M. Wald, Black hole entropy is the Noether charge. Phys. Rev. D 48, 3427–3431 (1993). arXiv:gr-qc/9307038 [gr-qc]
T. Padmanabhan, Thermodynamical aspects of gravity: new insights. Rept. Prog. Phys. 73, 046901 (2010). arXiv:0911.5004 [gr-qc]
B.R. Majhi, T. Padmanabhan, Noether current, horizon virasoro algebra and entropy. Phys. Rev. D 85, 084040 (2012). arXiv:1111.1809 [gr-qc]
V. Iyer, R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy. Phys. Rev. D 50, 846–864 (1994). arXiv:gr-qc/9403028 [gr-qc]
R.M. Wald, A. Zoupas, A general definition of ’conserved quantities’ in general relativity and other theories of gravity. Phys. Rev. D 61, 084027 (2000). arXiv:gr-qc/9911095 [gr-qc]
A. Strominger, C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy. Phys. Lett. B 379, 99–104 (1996). arXiv:hep-th/9601029 [hep-th]
A. Ashtekar, J. Baez, A. Corichi, K. Krasnov, Quantum geometry and black hole entropy. Phys. Rev. Lett. 80, 904–907 (1998). arXiv:gr-qc/9710007 [gr-qc]
J.M. Garcia-Islas, BTZ black hole entropy: a spin foam model description. Class. Quant. Grav. 25, 245001 (2008). arXiv:0804.2082 [gr-qc]
L. Bombelli, R.K. Koul, J. Lee, R.D. Sorkin, A quantum source of entropy for black holes. Phys. Rev. D 34, 373–383 (1986)
B.R. Majhi, T. Padmanabhan, Thermality and heat content of horizons from infinitesimal coordinate transformations. arXiv:1302.1206 [gr-qc]
V. Moncrief, J. Isenberg, Symmetries of cosmological cauchy horizons. Commun. Math. Phys. 89(3) 387–413 (1983). doi:10.1007/BF01214662
E.M. Morales, On a second law of black hole mechanics in a higher derivative theory of gravity (2008), http://www.theorie.physik.uni-goettingen.de/forschung/qft/theses/dipl/Morfa-Morales.pdf
P. Davies, Scalar particle production in Schwarzschild and Rindler metrics. J. Phys. A 8, 609–616 (1975)
W. Unruh, Notes on black hole evaporation. Phys. Rev. D 14, 870 (1976)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Chakraborty, S. (2017). Setting the Stage: Review of Previous Results. In: Classical and Quantum Aspects of Gravity in Relation to the Emergent Paradigm. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-63733-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-63733-4_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-63732-7
Online ISBN: 978-3-319-63733-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)