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Finite entanglement entropy from the zero-point-area of spacetime · Around

2010

Finite entanglement entropy from the zero-point-area of spacetime

Padmanabhan, T.

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The calculation of entanglement entropy S of quantum fields in spacetimes with horizon shows that, quite generically, S (a) is proportional to the area A of the horizon and (b) is divergent.

I argue that this divergence, which arises even in the case of Rindler horizon in flat spacetime, is yet another indication of a deep connection between horizon thermodynamics and gravitational dynamics.
In an emergent perspective of gravity, which accommodates this connection, the fluctuations around the equipartition value in the area elements will lead to a minimal quantum of area, of the order of L_P^2, which will act as a regulator for this divergence.
In a particular prescription for incorporating L_P^2 as zero-point-area of spacetime, this does happen and the divergence in entanglement entropy is regularized, leading to S proportional to (A/L_P^2) in Einstein gravity.

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D.Kothawala, L.Sriramkumar, (2008) unpublished
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T. Padmanabhan, Phys.Rev

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