scholarly journals Noether Current of the Surface Term of Einstein-Hilbert Action, Virasoro Algebra, and Entropy

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Bibhas Ranjan Majhi
Keyword(s):  
Virasoro Algebra ◽  
Surface Term ◽  
Hilbert Action ◽  
Noether Current ◽  
Cardy Formula

A derivation of Noether current from the surface term of Einstein-Hilbert action is given. We show that the corresponding charge, calculated on the horizon, is related to the Bekenstein-Hawking entropy. Also using the charge, the same entropy is found based on the Virasoro algebra and Cardy formula approach. In this approach, the relevant diffeomorphisms are found by imposing a very simple physical argument:diffeomorphisms keep the horizon structure invariant. This complements similar earlier results (Majhi and Padmanabhan (2012)) (arXiv:1204.1422) obtained from York-Gibbons-Hawking surface term. Finally we discuss the technical simplicities and improvements over the earlier attempts and also various important physical implications.

scholarly journals Noether current, horizon Virasoro algebra, and entropy

2012 ◽  
Vol 85 (8) ◽  
Author(s):  
Bibhas Ranjan Majhi ◽  
T. Padmanabhan
Keyword(s):  
Virasoro Algebra ◽  
Noether Current

scholarly journals KERR–BOLT SPACETIMES AND KERR/CFT CORRESPONDENCE

2012 ◽  
Vol 27 (08) ◽  
pp. 1250046 ◽  
Author(s):  
A. M. GHEZELBASH
Keyword(s):  
Field Theory ◽  
Boundary Condition ◽  
Black Hole ◽  
Conformal Field Theory ◽  
Virasoro Algebra ◽  
Conformal Field ◽  
Higher Dimensional ◽  
Dimensional Black Hole ◽  
Horizon Geometry ◽  
Cardy Formula

We study the extremal rotating spacetimes with a NUT twist in the context of recently proposed Kerr/CFT correspondence. The Kerr/CFT correspondence states that the near-horizon states of an extremal four (or higher) dimensional black hole could be identified with a certain chiral conformal field theory. The corresponding Virasoro algebra is generated with a class of diffeomorphism which preserves an appropriate boundary condition on the near-horizon geometry. We combine the calculated central charges with the expected form of the temperature, using the Cardy formula to obtain the microscopically entropy of the extremal rotating spacetimes with a NUT twist. All results are in agreement with the macroscopic entropy of the extremal spacetimes.

scholarly journals A NEW PERSPECTIVE ON GRAVITY AND DYNAMICS OF SPACE–TIME

2005 ◽  
Vol 14 (12) ◽  
pp. 2263-2269 ◽  
Author(s):  
T. PADMANABHAN
Keyword(s):  
Thermodynamic Limit ◽  
Space Time ◽  
Mathematical Framework ◽  
Surface Term ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Time Dynamics ◽  
New Perspective ◽  
Hilbert Action

The Einstein–Hilbert action has a bulk term and a surface term (which arises from integrating a four divergence). I show that one can obtain Einstein's equations from the surface term alone. This leads to: (i) a novel, completely self-contained, perspective on gravity and (ii) a concrete mathematical framework in which the description of space–time dynamics by Einstein's equations is similar to the description of a continuum solid in the thermodynamic limit.

A short note on the boundary term for the Hilbert action

2014 ◽  
Vol 29 (08) ◽  
pp. 1450037 ◽  
Author(s):  
T. Padmanabhan
Keyword(s):  
Variational Principle ◽  
Short Note ◽  
Extrinsic Curvature ◽  
Action Principle ◽  
Boundary Term ◽  
Surface Term ◽  
Simple Derivation ◽  
Total Action ◽  
Hilbert Action

One way to make the variational principle based on the Einstein–Hilbert action well-defined (i.e. functionally differentiable) is to add a surface term involving the integral of the trace of the extrinsic curvature. I provide a simple derivation of this result which is constructive in the sense that it starts from the variation of Einstein–Hilbert action and obtains the correct boundary term. This is to be contrasted with the usual derivations in which one first adds this term and then shows that the unwanted parts cancel out in the variation of the total action. The approach described here also clearly identifies the variables that need to be fixed in the boundary as the three-metric, directly from the action principle.

Sign in / Sign up

Export Citation Format

Share Document