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

Sumanta Chakraborty, Krishnamohan Parattu, T. Padmanabhan

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


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.

Original languageEnglish
Article number97
JournalJournal of High Energy Physics
Issue number10
StatePublished - 1 Oct 2015
Externally publishedYes


  • Black Holes
  • Classical Theories of Gravity


Dive into the research topics of 'Gravitational field equations near an arbitrary null surface expressed as a thermodynamic identity'. Together they form a unique fingerprint.

Cite this