Abstract
A possible source of black hole entropy could be the entanglement of quantum fields in and out the horizon. The entanglement entropy of the ground state obeys the area law. However, a correction term proportional to a fractional power of area results when the field is in a superposition of ground and excited states. Inspired by the power-law corrections to entropy and adopting the viewpoint that gravity emerges as an entropic force, we derive modified Newton's law of gravitation as well as the corrections to Friedmann equations. In a different approach, we obtained power-law corrected Friedmann equation by starting from the first law of thermodynamics at apparent horizon of a FRW universe, and assuming that the associated entropy with apparent horizon has a power-law corrected relation. Our study shows a consistency between the obtained results of these two approaches. We also examine the time evolution of the total entropy including the power-law corrected entropy associated with the apparent horizon together with the matter field entropy inside the apparent horizon and show that the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon.
Highlights
Verlinde [1] demonstrated that gravity can be interpreted as an entropic force caused by the changes in the information associated with the positions of material bodies
In this way the authors of [19] showed that the black hole entropy is proportional to the area of the sphere when the field is in its ground state, but a correction term proportional to a fractional power of area results when the field is in a superposition of ground and excited states. These corrections are relatively small and the area law is recovered. Applying this power-law corrected entropy, we obtain the corrections to Newton’s law as well as modified Friedmann equation by adopting the viewpoint that gravity emerges as an entropic force
It was argued that a possible source of black hole entropy could be the entanglement of quantum fields in and out the horizon [19]
Summary
Verlinde [1] demonstrated that gravity can be interpreted as an entropic force caused by the changes in the information associated with the positions of material bodies. Modified Newton’s law of gravitation has been studied in [13], while, modified Friedmann equations have been constructed in [14, 15] In all these cases [13,14,15] the corrected entropy has the logarithmic term which arises from the inclusion of quantum effects, motivated from the loop quantum gravity and is due to the thermal equilibrium fluctuations and quantum fluctuations [17]. By considering the quantum corrections to the area law of black hole entropy, the modified forms of Poisson’s equation of gravity, MOND theory of gravitation and Einstein field equations were derived using the entropic force interpretation of gravity [18]. These corrections are relatively small and the area law is recovered Applying this power-law corrected entropy, we obtain the corrections to Newton’s law as well as modified Friedmann equation by adopting the viewpoint that gravity emerges as an entropic force.
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