5
$\begingroup$

Why is the boundary term in the Einstein-Hilbert action, the Gibbons-Hawking-York term, generally "missing" in General Relativity courses, IMPORTANT from the variational viewpoint, geometrical setting and the needs of Black Hole Thermodynamics? Shouldn't it be also included in modern courses of General Relativity despite its global effect on the equations of motion is irrelevant (at least in the classical theory of relativistic gravity)?

$\endgroup$
  • 2
    $\begingroup$ Because it's distracting when you're first learning the topic, and easy enough to add back into discussions when it's relevant. Also, note that MTW, which is still the source book for many intro graduate GR courses, predates the publication of this term in the action. I'm sure others would disagree. $\endgroup$ – Jerry Schirmer Sep 16 '14 at 18:40
  • 1
    $\begingroup$ Eric Poisson's lecture notes on Advanced General Relativity (pdf), which formed the basis of his book Relativist's Toolkit, discusses this (in chapter 4)... $\endgroup$ – Alex Nelson Sep 16 '14 at 18:56
3
$\begingroup$

Two points. First, the variation of the GHY term is discussed in detail in this post:

Explicit Variation of Gibbons-Hawking-York Boundary Term

Second, the GHY term on its own is enough to render the boundary value problem well-defined, but it is not sufficient for a physically interesting variational principle. This requires additional surface terms in the action, discussed by Regge and Teitelboim in the Hamiltonian formulation

http://adsabs.harvard.edu/abs/1974AnPhy..88..286R

and by Mann and Marolf in the Lagrangian case

http://arxiv.org/abs/hep-th/0511096

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.