Thermodynamic route to field equations in Lanczos-Lovelock gravity

By A. Paranjape, Sudipta Sarkar, Thanu Padmanabhan. 2006

295 citations recorded by the source corpus.

Spacetimes with horizons show a resemblance to thermodynamic systems and one can associate the notions of temperature and entropy with them. In the case of Einstein-Hilbert gravity, it is possible to interpret Einstein's equations as the thermodynamic identity TdS=dE+PdV for a spherically symmetric spacetime and thus provide a thermodynamic route to understand the dynamics of gravity. We study this approach further and show that the field equations for the Lanczos-Lovelock action in a spherically symmetric spacetime can also be expressed as TdS=dE+PdV with S and E given by expressions previously derived in the literature by other approaches. The Lanczos-Lovelock Lagrangians are of the form L=Q{sub a}{sup bcd}R{sup a}{sub bcd} with {nabla}{sub b}Q{sub a}{sup bcd}=0. In such models, the expansion of Q{sub a}{sup bcd} in terms of the derivatives of the metric tensor determines the structure of the theory and higher order terms can be interpreted as quantum corrections to Einstein gravity. Our result indicates a deep connection between the thermodynamics of horizons and the allowed quantum corrections to standard Einstein gravity, and shows that the relation TdS=dE+PdV has a greater domain of validity than Einstein's field equations.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/10f4f21a41114b240f14172320c1e31f461a75cd

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Citations in the corpus

Friedmann Equations from Entropic Force (2010, methodology): “This observation was then extended to the cases of stationary axisymmetric horizons and evolving spherically symmetric horizons in Einstein gravity [12], static spherically symmetric horizons [13] and dynamical apparent horizons [14] in Lovelock gravity, and three dimensional BTZ black hole horizons”