Helpful material for Research Students in Cosmology and Mathematical Physics .

2. Submitted To: Dr. Wardat-Us-Salam
Submitted by: Laiba Zahid
Roll no: Bsf1801086
Bs. Mathematics 8th Semester

3. Shadow of rotating
Hayward black hole
bounded by Perfect fluid
dark matter

4. Content list
 Black hole Formation
Rotating Black hole
 Shadow of black hole
 Charged Black hole
 Perfect fluid
 Non-linear magnetic Field
Geodesic motion
 Dark Matter
 Quintessence
 Energy Emission Rate
 Photon Orbit
 Hawking Temperature

5. Black Hole Formation
Definition
• A region in space where gravitational field is so penetrating that even light cannot escape. The
gravity is so intense as matter has been clasped into a small space. Black Holes have not fix size
they are large or small. Researchers predict that tiniest black holes are like one atom and have
enormous mass.
• When big stars collapse with other stars then Stellar black holes are made it causes supernova
with collapse of huge stars. A supernova is an explosion of a star in tiny space.

6. Rotating Black Hole
Which has angular momentum and rotates around its axis of symmetry.
and has no Electric charge
A charged non -rotating black hole is called Reisner-Nordstrom black hole
while, a charged rotating black hole is called a Kerr- Newman black hole.
In Einstein-Maxwell field equations, this metric has stationary solution because it loses its
mass and angular momentum.

7. Shadow of rotating black hole
• In presence of strong gravitational field in
blackhole produced two-dimensional dark zone in
celestial sphere which is known as a shadow of
rotating black hole.
• Its dark sector is often surrounded by bright light
sphere. The event horizon of black holes into a
larger dark shadow magnifies by Gravitational
lensing

8. Charged Black Hole
• It is analogous to Schwarzschild black hole, consisting of two horizons:
• Event horizon It’s a border around black hole
• Cauchy horizon. It’s a inner event horizon

9. Perfect Fluid
• A fluid that can entirely categorized mass density and
isotropic pressure at its rest frame.
• Precisely, perfect fluid has no sheer stress and viscosity.

10. Non linear magnetic field
 A field that describes the magnetic effect on moving electric charges and
magnetic resources are known as magnetic field. Magnetic field signified
by magnetic flux lines.
 Though magnetic fields are tied with gravitational field so universe
accelerates due to nonlinear magnetic field.

11. Geodesic Motion
In general relativity, it is a
motion of particle in four-
dimensional space time
continuum along a geodesic
path.
This motion happens in the
absence of nongravitational
force

12. Dark Matter
o Dark matter was discovered in 1933 by Fritz Zwicky. In
this Universe there is 25% dark matter which we cannot
observed.
o It is a hidden matter which behaves alike a gravitational
pull to our universe.
o We cannot see it directly.
o It releases no light.
o It is totally different from stars or planets.
o It is observed indirectly by rotation of galaxies,
gravitational lensing, cosmic microwave radiations and so
on.
o Its proof is confirmed by Dark Matter.

13. Quintessence
 It is actual form of energy but different from any normal
matter or dark matter.
 It explains accelerating rate of expansion of the universe.
 The name quintessence (fifth essence) refers (Earth,
water, air and fire).
 It has been suggested a fifth fundamental force.
 The major difference among quintessence and the
cosmological constant is that quintessence can differ with
space and time.

14. Energy Emission Rate
 It is due to change of state of higher energy to lower energy state, which results in the
production of light.
 Absorption of high energy cross section of black hole oscillates around restraining constant
𝜎𝑙𝑖𝑚 .
 The black hole shadow resembles to high energy absorption. Here we use formula
•
𝑑2𝐸(𝜔)
𝑑𝜔𝑑𝑡
=
2𝜋2𝜎𝑙𝑖𝑚
𝑒𝜔/𝑡−1
𝜔3
• 𝜔 signify the frequency of photon

15. A photon orbit is a region of space
where gravity is so intense that
photons are forced to revolve in
orbits. In this region light bends but
still not escape out.
The radius of photon is sphere,
which is also lower bound for
stable orbit for Schwarzschild black
hole.
Photon Orbit

16. • Particles around black hole boundary by Hawking
radiation.
• indicates black hole have temperature that are
inversely proportional to their mass.
• BH temperature is measured by surface gravity.
Formula of Hawking temperature for outer event
horizon is
• 𝑇 = 𝑙𝑖𝑚
𝜃=0,𝑟→𝑟+
𝜕𝑟 −𝑔𝑡𝑡
2𝜋 𝑔𝑟𝑟
Hawking Temperature

17. Main Core Work of Research Briefly

18. Question Please?