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Dr. Hussain Gohar
Assistant Professor
Department of Physics

National University of Sciences and Technology (NUST)
School of Natural Sciences,H-12, Islamabad, Pakistan
Tel : +92 51 9085 5576

General Relativity and Cosmology

Ph.D. Physics (Szczecin, Poland)

Dr. Hussain Gohar is a theoretical physicist working in the field of gravitation and cosmology. He completed his Ph.D. from the University of Szczecin in Poland under the supervision of Prof. Dr. Mariusz P. Dabrowski and Prof. Vincenzo Salzano in 2017.  He was also a visiting Ph.D. student at Tufts University in Medford, Massachusetts (USA) under the supervision of Prof. Alex Vilenkin. After his Ph.D., he worked at the University of Szczecin for one more year as a researcher and then he joined Quaid-i-Azam University on HEC’s IPFP program. He joined NUST in September, 2019.  He has published several research papers in his field of research. For his research work and current running research projects, please visit his Research and Publication pages. 

Dr. Gohar’s research interests and their brief introduction:

Ø  Quantum aspects and thermodynamics of black holes

In the 1970s, Bekenstein and Hawking conjectured relations between parameters of black holes and quantities in thermodynamics, and formulated the laws of black hole thermodynamics. The laws of black hole thermodynamics emerged similar as in standard thermodynamics. According to Hawking’s area law, the area of the event horizon of a black hole always increases: if two black holes merge, the area of the final event horizon is greater than the sum of the areas of the initial horizons. This poses the basis for the analogy between the area A of the event horizon of the black hole and the entropy S, which can be written as S = A/4. For a stationary black hole the surface gravity k is constant on the horizon, which is equivalent to the zeroth law in thermodynamics for two systems having same temperature which are in equilibrium. Therefore there is an associated temperature defined on the surface of a black hole. In this way, the sum of the black holes entropy would never decrease. More generally the sum of the black holes entropy and the entropy of the matter outside black holes would never decrease, which is equivalent to the second law of thermodynamics. Finally it is impossible by any procedure, no matter how idealized, to reduce k to zero by a finite sequence of operations.

Classically, black holes do not emit radiation but by incorporating quantum mechanics they do emit radiations, called Hawking radiation. Hawking radiation can be understood by fluctuations of vacuum in quantum field theory. In quantum field theory, the vacuum is contained by virtual pair of particles and antiparticles. Due to the gravitational field of the black hole at the event horizon, the real particle tunnels out as Hawking radiation while the antiparticle falls into the black hole with a net negative energy as measured at infinity. As a result, the black hole shrinks and evaporates completely. Interestingly Hawking showed that the final state of the evaporated black hole is a mix state. Such evolution of a pure state to a mixed state implies that the information is lost somewhere and this violates quantum mechanics, which keeps pure state pure. Since then the information loss problem started a new debate, which possibly could connect thermodynamics, general relativity and quantum theory.

One of the important features of the first law of black hole thermodynamics is the omission of a pressure-volume term PdV. This term is very common in ordinary thermodynamics. There is no concept of pressure or volume associated with a black hole. By associating pressure with a negative cosmological constant, one can introduce the ideas of pressure and volume for a black hole. As a consequence of introducing pressure and volume for a black hole, new phase behavior for black holes analogous to that seen in gels and polymers was found. Similarly triple points for black holes analogous to those in water were found. In this way black holes could be understand as heat engines and Van der Waals fluids.

Dr. Gohar’s papers related to this topic:

  1. ​​A. Alonso-Serrano, M.P. Dabrowski, H. Gohar "Generalized uncertainty principle onto the black hole information flux and the sparsity of Hawking radiation", Physical Review D 97, 044029 (2018)
  2. A. Ejaz, H. Gohar, H. Lin, K. Saifullah, S-T. Yau, "Quantum tunneling from three-dimensional black holes", Physics Letters. B 726 (4), 827-833 (2013)
  3.  H. Gohar and K. Saifullah, "Emission of scalar particles from cylindrical black holes", Astrophysics and Space Sciences. 343 (1), 181-185 (2013)

Reading material:

1) The Thermodynamics of Black Holes (Wald, R.M. Living Rev. in Rel. (2001) 4: 6. )

2) The Black Hole Information Problem by Joseph Polchinski (

3) Black Hole Remnants and the Information Loss Paradox ( )

4) Black hole chemistry: thermodynamics with Lambda ( )


Ø    Dark energy and alternatives to dark energy in cosmology

General Relativity is an established theory which explains the evolution of the universe on a large scale. Although it is not complete because it contains singularities, it explains the dynamics of the universe in a consistent way. Furthermore, the current phase of accelerated evolution of the universe has been discovered. In order to obtain this accelerated expansion, one has to put an extra term, the cosmological constant or dark energy into the Einstein Friedmann equations. The LCDM models are consistent models to explain this accelerated expansion, but the observational value of cosmological constant is over 120 orders of magnitude smaller than the value calculated in quantum field theory, where it is interpreted as vacuum energy. This motivates cosmologists to look for alternative models which can explain the effect. Recently, the entropic cosmology based on the notion of the entropic force was developed. Basically, the idea of entropic cosmology is to add extra entropic force terms into the Friedmann equation and the acceleration equation. This force is supposed to be responsible for the current acceleration as well as for an early exponential expansion of the universe and it was especially compared with supernovae data. However, supernovae tests are not very strong and so the it got criticized on the basis of a galaxy formation problem. It is pertinent to mention that the entropic cosmology assumes that gravity is still a fundamental force and that it includes extra driving force terms or boundary terms in the Einstein field equations. This is unlike Verlinde, who considers gravity as an entropic force, but not as a fundamental force. Entropic cosmology is a special case of dynamical vacuum energy models. But the basic notion behind the both the models is different. In entropic cosmology, we define entropy and temperature on the boundary or screen associated with the universe. Entropy of the universe is increasing and due to this increasing entropy, there will be an entropic force acting on the boundary of the universe. As a result, the expansion of the universe is accelerating due to entropic force acting on the boundary of the universe.

Dr. Gohar’s papers related to this topic:


  1. M.P. Dabrowski and H. Gohar, "Abolishing the maximum tension principle" , Physics Letters. B 748, 428-431 (2015)
  2. M.P. Dabrowski, H. Gohar and V. Salzano,"Varying constants entropic-Lambda CDM cosmology", Entropy 18(2), 60 (2016)
  3. H. Gohar,"Cosmology with Varying Constants from a Thermodynamic Viewpoint", Universe 3(1), 26 (2017)


Reading material:

1) TASI Lectures on Inflation (

2) Theoretical Models of Dark Energy ( )

3) Entropic cosmology for a generalized black-hole entropy ( )

4) Cosmological constraints on dark energy ( )


Ø    Gravity from thermodynamic viewpoint


Due to the work of Bekenstein and Hawking, it opened different paths to investigate gravity from a thermodynamics perspective. For example, the Einstein field equations is derived from the proportionality of the entropy and the area of the causal horizon, assuming that the heat flows across the horizon. Such a gravity thermodynamics correspondence was developed by Jacobson in 1995. In the Padmanabhan’s approach, one uses the so–called holographic equipartition law to derive the Friedmann and acceleration equations which describe the expansion of the Universe. According to the holographic equipartition law, the expansion of the cosmic space is due to the difference between the degrees of freedom on the surface and in the bulk of a region of space. Verlinde derived gravity as an entropic force, which originated in a system as a result of the statistical tendency to increase its entropy. He assumed the holographic principle, which stated that the microscopic degrees of freedom could be represented holographically on the horizons, and this piece of information (or degrees of freedom) could be measured in terms of entropy. These all new approaches give a new insight into the problem of quantum gravity and which could possible explore the emergence of space-time from a thermodynamics perspective.


Reading material:

1) On the origin of gravity and the laws of Newton (Verlinde, E. J. High Energ. Phys. (2011) 2011: 29. doi:10.1007/JHEP04(2011)029)

2) T. Jacobson, Thermodynamics of space-time: The Einstein equation of statePhys. Rev. Lett. 75 (1995) 1260 [gr-qc/9504004]


Ø     Canonical quantum gravity


Direct canonical quantization of general relativity is one of the first and very powerful approach to unify gravity and quantum mechanics. By using Wheeler-Dewitt approach, I have been working on quantizing black holes and wormholes. It would be also interesting to relate quantizing wormholes with ER=EPR conjecture, which could possibly give insight into the information loss problem.

Reading material:

1) Quantum cosmology: a review ( )

2) An introduction to quantum cosmology ( )


Ø    Phase transitions in the early universe

Reading material:

1) Black holes and the multiverse (

2) The Dynamics of False Vacuum Bubbles (Phys.Rev. D35 (1987) 1747 )

Research Publications: 

  • A. Alonso-Serrano, M.P. Da¸browski, H. Gohar “Minimal  length  and  the  flow  of entropy from black holes”, International Journal of Modern Physics D27 no.14, 1847028 (2018)
  • A. Alonso-Serrano, M.P. Da¸browski, H. Gohar “Generalized uncertainty principle onto the black hole information flux and the sparsity of Hawking radiation”, Physical Review D 97, 044029 (2018)
  • M.P. Da¸browski, H. Gohar and V. Salzano,“Varying  constants  entropic–ΛCDM cosmology”, Entropy 18(2), 60 (2016)
  • M.P.  Da¸browski  and  H.  Gohar,  “Abolishing  the  maximum  tension  principle”  , Physics Letters. B 748, 428-431 (2015)
  • K. Jan and H. Gohar, “Hawking radiation of scalars from accelerating and rotating black holes with NUT parameter”, Astrophysics and Space Sciences. 350 (1), 279- 284 (2014)
  • A. Ejaz, H. Gohar, H. Lin, K. Saifullah, S-T. Yau, “Quantum tunneling from three-dimensional black holes”, Physics Letters. B 726 (4), 827-833 (2013)
  • H. Gohar and K. Saifullah, “Quantum tunneling from scalar fields in rotating black strings’’, Astroparticle Physics. 48, 82-85 (2013)
  • H. Gohar and K. Saifullah, “Emission of scalar particles from cylindrical black holes”, Astrophysics and Space Sciences. 343 (1), 181-185 (2013)
  • H. Gohar and K. Saifullah, “Scalar field radiation from dilatonic black holes”, General Relativity and Gravitation. 44 (12), 3163-3167 (2012)
Conference proceedings
  • H. Gohar,“Cosmology with Varying Constants from a Thermodynamic Viewpoint”, Universe 3(1), 26 (2017) (Conference: Varying Constants and Fundamental Cos- mology (VARCOSMOFUN’16) 11-17 Sep 2016. Szczecin, Poland)

​Featured articles
  • Our paper, Phys. Rev. D97, 044029 (2018), is featured in New Scientist as “Shrinking black holes avoid paradox by oozing hidden information’’, published on February 2, 2018​

postgraduate course

  • ​Mathematical methods in physics (Quaid-i-Azam University)

undergraduate course

  • Electricity, Magnetism and Thermal physics (Quaid-i-Azam University)
  • Mathematical methods in Physics-II
  • General Relativity