Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0705.2070 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Power-law corrections to entanglement entropy of horizons

Saurya Das, S. Shankaranarayanan, Sourav Sur

Published Mar 10, 2008• 138 citations
arXivHTMLPDF

Abstract

We reexamine the idea that the origin of black-hole entropy may lie in the entanglement of quantum fields between the inside and outside of the horizon. Motivated by the observation that certain modes of gravitational fluctuations in a black-hole background behave as scalar fields, we compute the entanglement entropy of such a field, by tracing over its degrees of freedom inside a sphere. We show that while this entropy is proportional to the area of the sphere when the field is in its ground state, a correction term proportional to a fractional power of area results when the field is in a superposition of ground and excited states. The area law is thus recovered for large areas. Further, we identify the location of the degrees of freedom that give rise to the above entropy.

DOI
10.1103/physrevd.77.064013

Related papers

Is entanglement entropy proportional to area?

Morteza Ahmadi, Saurya Das, S Shankaranarayanan

It is known that the entanglement entropy of a scalar field, found by tracing over its degrees of freedom inside a sphere of radius [Formula: see text], is proportional to the area of the sphere (and not its volume). This suggests that the origin of black-hole entropy, also proportional to its horizon area, may lie in the entanglement between the degrees of freedom inside and outside the horizon. We examine this proposal carefully by including excited states, to check probable deviations from the area law.PACS Nos.: 04.60.–m, 04.62, 04.70.–s, 03.65.Ud

arXiv:hep-th/0507228•Canadian Journal of Physics•Jan 15, 2006•9 citations

How robust is the entanglement entropy-area relation?

Saurya Das, S. Shankaranarayanan

We revisit the problem of finding the entanglement entropy of a scalar field on a lattice by tracing over its degrees of freedom inside a sphere. It is known that this entropy satisfies the area law---entropy proportional to the area of the sphere---when the field is assumed to be in its ground state. We show that the area law continues to hold when the scalar field degrees of freedom are in generic coherent states and a class of squeezed states. However, when excited states are considered, the entropy scales as a lower power of the area. This suggests that, for large horizons, the ground state entropy dominates, whereas entropy due to excited states gives power-law corrections. We discuss possible implications of this result to black hole entropy.

arXiv:gr-qc/0511066•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Jun 28, 2006•70 citations

Power law corrections to BTZ black hole entropy

Dharm Veer Singh

We study the quantum scalar field in the background of BTZ black hole and evaluate the entanglement entropy of the nonvacuum states. The entropy is proportional to the area of event horizon for the ground state, but the area law is violated in the case of nonvacuum states (first excited state and mixed states) and the corrections scale as power law.

arXiv:1406.3809•International Journal of Modern Physics D•Nov 11, 2014•8 citations

1 Is entanglement entropy proportional to area?

Morteza Ahmadi, Saurya Das, S. Shankaranarayanan

Abstract: It is known that the entanglement entropy of a scalar field, found by tracing over its degrees of freedom inside a sphere of radius R, is proportional to the area of the sphere (and not its volume). This suggests that the origin of black hole entropy, also proportional to its horizon area, may lie in the entanglement between the degrees of freedom inside and

•Jan 1, 2005•7 citations

How are the degree of freedom responsible for entropy in BTZ spacetime

Dharm Veer Singh, Shobhit Sachan

We are using entanglement entropy approach to study how the entropy depends upon the location of degrees of freedom near and far from the horizon. We consider quantum fields in the vicinity of black holes space-time, the entropy receives log- arithmic and power law corrections in area law. The power law corrections arises when the fields are in excited or mixed state (superposition of ground and excited state)a but logarithmic corrections are present in ground state. In this paper, we try to understand physically the deviation from the area law for the excited and mixed state. We show that the degrees of freedom near to the horizon contribute the total entropy, but when degrees of freedom far away from the horizon are more significant for excited/mixed state instead of ground state.

•Dec 29, 2016•0 citations

Entanglement entropy in loop quantum gravity

William Donnelly

The entanglement entropy between quantum fields inside and outside a black hole horizon is a promising candidate for the microscopic origin of black hole entropy. We show that the entanglement entropy may be defined in loop quantum gravity, and compute its value for spin network states. The entanglement entropy for an arbitrary region of space is expressed as a sum over punctures where the spin network intersects the region's boundary. Our result agrees asymptotically with results previously obtained from the isolated horizon framework, and we give a justification for this agreement. We conclude by proposing a new method for studying corrections to the area law and its implications for quantum corrections to the gravitational action.

arXiv:0802.0880•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•May 6, 2008•81 citations
We reexamine the idea that the origin of black-hole entropy may lie in the entanglement of quantum fields between the inside and outside of the horizon. Motivated by the observation that certain modes of gravitational fluctuations in a black-hole background behave as scalar fields, we compute the entanglement entropy of such a field, by tracing over its degrees of freedom inside a sphere. We show that while this entropy is proportional to the area of the sphere when the field is in its ground state, a correction term proportional to a fractional power of area results when the field is in a superposition of ground and excited states. The area law is thus recovered for large areas. Further, we identify the location of the degrees of freedom that give rise to the above entropy.
It is known that the entanglement entropy of a scalar field, found by tracing over its degrees of freedom inside a sphere of radius [Formula: see text], is proportional to the area of the sphere (and not its volume). This suggests that the origin of black-hole entropy, also proportional to its horizon area, may lie in the entanglement between the degrees of freedom inside and outside the horizon. We examine this proposal carefully by including excited states, to check probable deviations from the area law.PACS Nos.: 04.60.–m, 04.62, 04.70.–s, 03.65.Ud
We revisit the problem of finding the entanglement entropy of a scalar field on a lattice by tracing over its degrees of freedom inside a sphere. It is known that this entropy satisfies the area law---entropy proportional to the area of the sphere---when the field is assumed to be in its ground state. We show that the area law continues to hold when the scalar field degrees of freedom are in generic coherent states and a class of squeezed states. However, when excited states are considered, the entropy scales as a lower power of the area. This suggests that, for large horizons, the ground state entropy dominates, whereas entropy due to excited states gives power-law corrections. We discuss possible implications of this result to black hole entropy.
We are using entanglement entropy approach to study how the entropy depends upon the location of degrees of freedom near and far from the horizon. We consider quantum fields in the vicinity of black holes space-time, the entropy receives log- arithmic and power law corrections in area law. The power law corrections arises when the fields are in excited or mixed state (superposition of ground and excited state)a but logarithmic corrections are present in ground state. In this paper, we try to understand physically the deviation from the area law for the excited and mixed state. We show that the degrees of freedom near to the horizon contribute the total entropy, but when degrees of freedom far away from the horizon are more significant for excited/mixed state instead of ground state.
The entanglement entropy between quantum fields inside and outside a black hole horizon is a promising candidate for the microscopic origin of black hole entropy. We show that the entanglement entropy may be defined in loop quantum gravity, and compute its value for spin network states. The entanglement entropy for an arbitrary region of space is expressed as a sum over punctures where the spin network intersects the region's boundary. Our result agrees asymptotically with results previously obtained from the isolated horizon framework, and we give a justification for this agreement. We conclude by proposing a new method for studying corrections to the area law and its implications for quantum corrections to the gravitational action.