Entropy density of spacetime from the zero point length

Abstract

It is possible to obtain the gravitational field equations in a large class of theories from a thermodynamic variational principle which uses the gravitational heat density ${\mathcal{S}}_g$ associated with null surfaces. This heat density is related to the discreteness of spacetime at Planck scale, $L_P^2=(G\hslash /c^3)$, which assigns $A_{\perp }/L_P^2$ degrees of freedom to any area $A_{\perp }$. On the other hand, it is also known that the surface term $K\sqrt{h}$ in the gravitational action principle correctly reproduces the heat density of the null surfaces. We provide a link between these ideas by obtaining ${\mathcal{S}}_g$, used in emergent gravity paradigm, from the surface term in the action in Einstein's gravity. This is done using the notion of a nonlocal qmetric -- introduced recently [arXiv:1307.5618, arXiv:1405.4967] -- which allows us to study the effects of zero-point-length of spacetime at the transition scale between quantum and classical gravity. Computing $K\sqrt{h}$ for the qmetric in the appropriate limit directly reproduces the entropy density ${\mathcal{S}}_g$ used in the emergent gravity paradigm.

8 pages; no figures

References in corpus (7)

• Entropy of Null Surfaces and Dynamics of Spacetime
• General Relativity from a Thermodynamic Perspective
• Holography of Gravitational Action Functionals
• Grin of the Cheshire cat: Entropy density of spacetime as a relic from quantum gravity
• Cosmological Constant from the Emergent Gravity Perspective
• Holography in Action
• The Physical Principle that determines the Value of the Cosmological Constant

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• Minimum-length Ricci scalar for null separated events
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• Normal coordinates based on curved tangent space
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