Field Equations for Lovelock Gravity: An Alternative Route

2017/04/30 by Sumanta Chakraborty · 1 citation
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Curvature #Field equation #Gravitation #Gravitational field #Homogeneous space #Null (SQL) #Riemann curvature tensor #Riemann hypothesis #Tensor (intrinsic definition) #gr-qc #hep-th

paper · pdf · doi:10.1155/2018/6509045

published as Adv. High Energy Phys. 6509045 (2018) · Invited Article; 11 pages, no figures

openalex publication_date 2018/01/01 · arxiv created 2018/04/20 · arxiv updated 2018/04/23 · openalex created_date 2018/05/07 · openalex updated_date 2026/08/05

Abstract

We present an alternative derivation of the gravitational field equations for Lovelock gravity starting from Newton’s law, which is closer in spirit to the thermodynamic description of gravity. As a warm up exercise, we have explicitly demonstrated that, projecting the Riemann curvature tensor appropriately and taking a cue from Poisson’s equation, Einstein’s equations immediately follow. The above derivation naturally generalizes to Lovelock gravity theories where an appropriate curvature tensor satisfying the symmetries as well as the Bianchi derivative properties of the Riemann tensor has to be used. Interestingly, in the above derivation, the thermodynamic route to gravitational field equations, suited for null hypersurfaces, emerges quiet naturally.

Citations

• First Law of Thermodynamics and Friedmann Equations of Friedmann–Robertson–Walker Universe
• First law of thermodynamics and Friedmann-like equations in braneworld cosmology
• Friedmann Equations and Thermodynamics of Apparent Horizons
• Equipartition of energy in the horizon degrees of freedom and the emergence of gravity
• The atoms of space, gravity and the cosmological constant

Cited by

• Null boundary terms for Lanczos–Lovelock gravity