Thermodynamics of a Non-Stationary Black Hole Based on Generalized Uncertainty Principle

Mustari Mustari, Yuant Tiandho


In the general theory of relativity (GTR), black holes are defined as objects with very strong gravitational fields even light can not escape. Therefore, according to GTR black hole can be viewed as a non-thermodynamic object. The worldview of a black hole began to change since Hawking involves quantum field theory to study black holes and found that black holes have temperatures that analogous to black body radiation. In the theory of quantum gravity there is a term of the minimum length of an object known as the Planck length that demands a revision of Heisenberg's uncertainty principle into a Generalized Uncertainty Principle (GUP). Based on the relationship between the momentum uncertainty and the characteristic energy of the photons emitted by a black hole, the temperature and entropy of the non-stationary black hole (Vaidya-Bonner black hole) were calculated. The non-stationary black hole was chosen because it more realistic than static black holes to describe radiation phenomena. Because the black hole is dynamic then thermodynamics studies are conducted on both black hole horizons: the apparent horizon and its event horizon. The results showed that the dominant correction term of the temperature and entropy of the Vaidya-Bonner black hole are logarithmic.


Black hole; thermodynamics; generalized uncertainty principle

Full Text:



Alder, R., Chen, P., & Santiago, I. (2001). The generalized uncertainty principle and black hole remnants. General Relativity and Gravitation , 33, no 12, 2101-2108.

Bekenstein, J. D. (1973). Black holes and entropy. Physical Review D , 7, no 8, 2333-2346.

Camelia, A., Arzano, M., & Procaccini, A. (2004). Severe constraints on the loop-quantum-gravity energy-momentum dispersion relation from the black-hole area-entropy law,. Physical Review , 70, 107201.

Frolov, V. P., & Novikov, I. D. (1998). Black Hole Physics: Basic Concepts And New Developments. Netherland: Kluwer Publishing.

Gambini., R., & Pullin, J. (1999). Nonstandar optics from quantum space time. Physical Review. D , 59, 124021.

Hawking, S. W. (1975). Particle Creation by Black Hole . Commun. Math Phys , 43, 199-220.

Ibohal, N., & Kapil, L. (2010). Charged black holes in Vaidya backgrounds: Hawking radiation. Int. J. Mod. Phys. , 19 (4), 437-464.

Kim, S. W., Choi, E. Y., Kim, S., & & Yang, J. Black hole radiation in the Vaidya metric, . Phys , Lett. A 141, 238-241.

L.J. Garay. (1995). Quantum gravity and minimum length. International Journal of Modern Physics , 10, no 2, 145-165.

Liu, X. &. (2011). Apparent horizon and event horizon thermodynamics of a Vaidya Black hole using Damour -Ruffini method. Astrophys. space., 331, 237-241.

Medved, A. J., & Vagenas, E. C. (2004). When conceptual worlds collide: the generalized uncertainty prinsiple and the Bekenstein-hawking entropy. Physical Review , 70, 124021.

Niu, Z. F., & Liu, W. B. (2010). Hawking radiation and thermodynamics of a Vaidya-Bonner black hole. Research in Astronomy and Astrophysics , 10, 33-38.

Parikh, M. K. & Wilczek, F. (2000). Hawking radiation as tunneling. Phys. Rev. Lett. 85, 5042.

Srinivasan, K., & Padmanabhan, T. (1999). Particle production and complex path analysis. Phys. Rev. D 60 , 024007.

Tiandho, Y. (2017). Mesin Panas Foto-Carnot Lubang Hitam Non-Stasioner. Jurnal Sains Dasar , 1, 17-25.

Yang, Z. (1995). study of hawking effect in Vaidya-Bonner Black hole by means of second quantization. Acta Physica Sinica , 141, 241-247.

Zheng, Z., & Xianxin, D. (1992). A new method with Hawking effects of evaporating black holes. Modern Physics Letters A , 7 (20), 1771-1778.


  • There are currently no refbacks.