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Black hole thermodynamics: entropy, information and beyond
(2015-12-16) Das, Saurya
We review some recent advances in black hole thermodynamics, including statistical mechanical origins of black hole entropy and its leading order corrections, from the viewpoints of various quantum gravity theories. We then examine the information loss problem and some possible approaches to its resolution. Finally, we study some proposed experiments which may be able to provide experimental signatures of black holes.
Entanglement as a source of black hole entropy
(2015-12-16) Das, Saurya; Shankaranarayanan, S.
We review aspects of black hole thermodynamics, and show how entanglement of a quantum field between the inside and outside of a horizon can account for the areaproportionality of black hole entropy, provided the field is in its ground state. We show that the result continues to hold for Coherent States and Squeezed States, while for Excited States, the entropy scales as a power of area less than unity. We also identify location of the degrees of freedom which give rise to the above entropy.
Entanglement entropy in all dimensions
(2015-12-15) Braunstein, Samuel L.; Das, Saurya; Shankaranarayanan, S.
It has long been conjectured that the entropy of quantum fields across boundaries scales as the boundary area. This conjecture has not been easy to test in spacetime dimensions greater than four because of divergences in the von Neumann entropy. Here we show that the R´enyi entropy provides a convergent alternative, yielding a quantitative measure of entanglement between quantum field theoretic degrees of freedom inside and outside hypersurfaces. For the first time, we show that the entanglement entropy in higher dimensions is proportional to the higher dimensional area. We also show that the R´enyi entropy diverges at specific values of the R´enyi parameter q in each dimension, but this divergence can be tamed by introducing a mass to the quantum field.
Is entanglement entropy proportional to area?
(2016-01-25) Ahmadi, Morteza; Das, Saurya; Shankaranarayanan, S.
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 outside the horizon. We examine this proposal carefully by including excited states, to check probable deviations from the area law.
Where are the black hole entropy degrees of freedom?
(2016-01-06) Das, Saurya; Shankaranarayanan, S.
Understanding the area-proportionality of black hole entropy (the ‘Area Law’) from an underlying fundamental theory has been one of the goals of all models of quantum gravity. A key question that one asks is: where are the degrees of freedom giving rise to black hole entropy located? Taking the point of view that entanglement between field degrees of freedom inside and outside the horizon can be a source of this entropy, we show that when the field is in its ground state, the degrees of freedom near the horizon contribute most to the entropy, and the area law is obeyed. However, when it is in an excited state, degrees of freedom far from the horizon contribute more significantly, and deviations from the area law are observed. In other words, we demonstrate that horizon degrees of freedom are responsible for the area law.
Where are the degrees of freedom responsible for black hole entropy?
(2015-12-15) Das, Saurya; Shankaranarayanan, S.; Sur, Sourav
Considering the entanglement between quantum field degrees of freedom inside and outside the horizon as a plausible source of black hole entropy, we address the question: where are the degrees of freedom that give rise to this entropy located? When the field is in ground state, the black hole area law is obeyed and the degrees of freedom near the horizon contribute most to the entropy. However, for excited state, or a superposition of ground state and excited state, power-law corrections to the area law are obtained, and more significant contributions from the degrees of freedom far from the horizon are shown.