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:

- 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)
- 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, "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. https://doi.org/10.12942/lrr-2001-6 )

# 2) The
Black Hole Information Problem by Joseph Polchinski (arxiv.org/abs/1609.04036v1)

3) Black Hole Remnants and the Information Loss Paradox (**arxiv.org/abs/1412.8366** )

4) Black hole chemistry: thermodynamics with Lambda (**arxiv.org/abs/1608.06147** )

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:

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

Reading material:

1) TASI Lectures on Inflation (**arxiv.org/abs/0907.5424**)

2) Theoretical Models of Dark Energy (**arxiv.org/abs/1212.4726** )

3) Entropic cosmology for a generalized black-hole entropy
(**arxiv.org/abs/1307.5949** )

4) Cosmological constraints on dark energy (**arxiv.org/abs/1404.7266** )

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 state*, *Phys. 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 (arxiv.org/pdf/1501.04899.pdf
)

2) An introduction to quantum cosmology (**arxiv.org/abs/gr-qc/0101003** )

Ø
**Phase transitions in the
early universe**

# Reading
material:

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