# On one-loop renormalization of black-hole entropy

**Authors:** Dmitri V. Fursaev, Sergey N. Solodukhin  
**arXiv:** [hep-th/9412020](https://arxiv.org/abs/hep-th/9412020)  
**Date:** 1994-12-02  
**Summary page:** https://www.summarizepaper.com/en/paper/hep-th--9412020v2/

## Key points

- Dmitri V. Fursaev and Sergey N. Solodukhin explore quantum black holes and address one-loop divergences in their entropy.
- Adjusting gravitational constant and other coefficients using $R^2$-terms in the effective gravitational action can eliminate these divergences.
- Incorporating higher order curvature terms introduces deviations in entropy from the Bekenstein-Hawking formula within Einstein gravity.
- The deviations are linked to both internal and external geometry of the horizon surface around a black hole.
- Fursaev and Solodukhin establish a framework showing how higher order curvature terms shape the entropy of quantum black holes, contributing to our theoretical understanding of black hole thermodynamics.
- This research was published in Phys.Lett.B365 (1996) 51-55.

## Summary

In their paper titled "On one-loop renormalization of black-hole entropy," Dmitri V. Fursaev and Sergey N. Solodukhin delve into the intricate realm of quantum black holes and explore the elimination of one-loop divergences in their entropy through standard renormalization techniques. The authors demonstrate that by adjusting the gravitational constant and other coefficients using $R^2$-terms in the effective gravitational action, these divergences can be completely eradicated. This is a significant step forward in unraveling the mysteries surrounding black hole entropy and highlights the importance of considering advanced gravitational terms in theoretical frameworks aimed at describing these enigmatic cosmic entities. The crux of their proof lies in incorporating higher order curvature terms, which introduce deviations in the entropy from the well-known Bekenstein-Hawking formula within Einstein gravity. These deviations are intricately linked to both the internal and external geometry of the horizon surface surrounding a black hole. Through meticulous analysis and manipulation of equations, Fursaev and Solodukhin establish a robust framework for understanding how these higher order curvature terms play a crucial role in shaping the entropy of quantum black holes. Their findings not only contribute to our theoretical understanding of black hole thermodynamics but also shed light on the intricate interplay between gravity, quantum effects, and geometric properties at the event horizon. This research was published in Phys.Lett.B365 (1996) 51-55.