TY - JOUR

T1 - Gravitational field equations near an arbitrary null surface expressed as a thermodynamic identity

AU - Chakraborty, Sumanta

AU - Parattu, Krishnamohan

AU - Padmanabhan, T.

N1 - Publisher Copyright:
© 2015, The Author(s).

PY - 2015/10/1

Y1 - 2015/10/1

N2 - Abstract: Previous work has demonstrated that the gravitational field equations in all Lanczos-Lovelock models imply a thermodynamic identity T δλS = δλE + P δλV (where the variations are interpreted as changes due to virtual displacement along the affine parameter λ) in the near-horizon limit in static spacetimes. Here we generalize this result to any arbitrary null surface in an arbitrary spacetime and show that certain components of the Einstein’s equations can be expressed in the form of the above thermodynamic identity. We also obtain an explicit expression for the thermodynamic energy associated with the null surface. Under appropriate limits, our expressions reduce to those previously derived in the literature. The components of the field equations used in obtaining the current result are orthogonal to the components used previously to obtain another related result, viz. that some components of the field equations reduce to a Navier-Stokes equation on any null surface, in any spacetime. We also describe the structure of Einstein’s equations near a null surface in terms of three well-defined projections and show how the different results complement each other.

AB - Abstract: Previous work has demonstrated that the gravitational field equations in all Lanczos-Lovelock models imply a thermodynamic identity T δλS = δλE + P δλV (where the variations are interpreted as changes due to virtual displacement along the affine parameter λ) in the near-horizon limit in static spacetimes. Here we generalize this result to any arbitrary null surface in an arbitrary spacetime and show that certain components of the Einstein’s equations can be expressed in the form of the above thermodynamic identity. We also obtain an explicit expression for the thermodynamic energy associated with the null surface. Under appropriate limits, our expressions reduce to those previously derived in the literature. The components of the field equations used in obtaining the current result are orthogonal to the components used previously to obtain another related result, viz. that some components of the field equations reduce to a Navier-Stokes equation on any null surface, in any spacetime. We also describe the structure of Einstein’s equations near a null surface in terms of three well-defined projections and show how the different results complement each other.

KW - Black Holes

KW - Classical Theories of Gravity

UR - http://www.scopus.com/inward/record.url?scp=84944321802&partnerID=8YFLogxK

U2 - 10.1007/JHEP10(2015)097

DO - 10.1007/JHEP10(2015)097

M3 - Article

AN - SCOPUS:84944321802

VL - 2015

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 10

M1 - 97

ER -