2012/10/10 by Naresh Dadhich, Dadhich, Naresh
Physics and Astronomy · #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.1210.3022
latex, 5pages, Contribution to the Proceedings of the Conference, Relativity and Gravitation: 100 years after Einstein in Prague, June 25-28, 2012
arxiv created 2012/10/10 · arxiv updated 2012/10/12
Like the Lovelock Lagrangian which is a specific homogeneous polynomial in Riemann curvature, for an alternative derivation of the gravitational equation of motion, it is possible to define a specific homogeneous polynomial analogue of the Riemann curvature, and then the trace of its Bianchi derivative yields the corresponding polynomial analogue of the divergence free Einstein tensor defining the differential operator for the equation of motion. We propose that the general equation of motion is G(n)ab = -Λgab +κn Tab for d=2n+1, 2n+2 dimensions with the single coupling constant κn, and n=1 is the usual Einstein equation. It turns out that gravitational behavior is essentially similar in the critical dimensions for all n. All static vacuum solutions asymptotically go over to the Einstein limit, Schwarzschild-dS/AdS. The thermodynamical parameters bear the same relation to horizon radius, for example entropy always goes as rhd-2n and so for the critical dimensions it always goes as rh, rh2. In terms of the area, it would go as A1/n. The generalized analogues of the Nariai and Bertotti-Robinson solutions arising from the product of two constant curvature spaces, also bear the same relations between the curvatures k1=k2 and k1=-k2 respectively.