Australia: The Land Where Time Began 

Black Holes
There is a limit to the mass a white dwarf (the Chandrasekhar limit) can
have, beyond which the star cannot support the weight of the martial
composing it. There is also a limit to the mass a neutron star can
support, the current estimates putting this figure at about 23 M_{ʘ}.
The most massive outer layers may not have been dispersed into space
during the explosion in some supernovae, with matter possibly falling
back onto the core that is already dense. The core of the neutron star
may have been pushed above its limit by this extra material, and neutron
degeneracy pressure will not be able to fend off gravity.
The core will continue to collapse catastrophically and not even the
increasing temperature and pressure can stop the inevitable result. As
is seen from Einstein’s equation E = mc^{2}, energy is
equivalent to mass, therefore the energy associated with the very
extreme temperatures and pressure that is concentrated the core, that is
now tiny, acts like additional mass, thereby hastening the collapse.
Nothing is known of that is able to stop the crush of gravity. The core
collapses without end, forming a black hole, at the end of the life of
the star.
A rigorous description of a black hole requires a thorough background in
tensor calculus and general relativity, though the broad description of
such an exotic object is quite simple, and according to Inglis it is
very easy to calculate a few of its basic characteristics.
If the star core contains about 3 or more solar masses, nothing will
stop it collapsing even beyond the neutron degeneracy stage. The core
collapses to an object that has zero radius. Something with zero radius
has no physical size, it has no size at all. The core collapses and
therefore its density and surface gravity increases. If it collapses to
zero size, the gravity becomes infinite. This entity, that has no
physical size yet has infinite gravity, is the singularity.
The escape velocity is the velocity required by an object to allow it to
escape from the pull of gravity of a celestial object. E.g. a spacecraft
needs to achieve a velocity of about 11 km/second to escape from Earth’s
gravity. The mass of the celestial body and the distance of the escaping
object from the centre of the celestial body both determine the value of
the escape velocity that is required to actually escape the
gravitational field of the celestial body. Thus the escape velocity
would increase if the escaping object was very massive or very small.
There may be a point at which not even light, the fastestmoving thing
in the universe, can escape as it can’t achieve the escape velocity, so
light would never escape and the object could never be seen. There will
be an area of space, usually spherical, that surrounds the singularity
where the escape velocity will be so high that not even light can
escape. The entity called a black hole is the sphere of space within
which the escape velocity is equal to, or greater than, the escape
velocity of light, and so could never be seen. Rotating black holes are
oblate, and so not spherical. Therefore their description is far more
complicated. Where there is no central pulsar or neutron star in a
supernova remnant there may be a black hole.
Therefore, an object inside a black hole would need to travel faster
than light to escape the gravitational pull of the black hole; outside
the black hole this need for speed is much less. The event horizon is
the boundary between these 2 regions; any event occurring within the
event horizon can never been seen by an observer outside the event
horizon.
Albert Einstein was the first person to combine space and time into a
single entity, spacetime, and it was his theories that showed that
gravity could be portrayed as a curvature of spacetime. Karl
Schwarzschild solved Einstein’s equations to give the first ever
relativistic description of a black hole. Nonrotating black holes are
now called ‘Schwarzschild black holes, to distinguish them from rotating
black holes.
Schwarzschild showed that if the conditions are right, such as if matter
is packed into a small enough volume of space, then spacetime can curve
back on itself. This means that an object, or light, can follow a path,
aka a geodesic, into a black hole, though inside the black hole the
curvature of spacetime is so extreme that there is no path that leads
out.
The event horizon is the boundary that separates the universe from
region inside the event horizon which is forever isolated, a region of
extreme curved spacetime, the black hole. The radius of the black hole,
i.e. the distance from the singularity to the event horizon, is called
the Schwarzschild radius, R_{Sch}.
The size of a black hole
To determine the approximate radius of a black hole, the Schwarzschild
radius, R_{Sch}, the progenitor mass, in relation to the Sun’s
mass M_{ʘ}, is needed.
The radius is given by the formula: R_{Sch }~ 3M_{ʘ }
where R_{Sch} is in kilometres.
Example:
Χ^{2} Orionis is a Btype supergiant star in the constellation
Orion, which has an estimated mass of 42 M_{ʘ}. Determine the
radius of a black hole that may form when the star eventually dies as a
supernova, leaving a remnant core of mass ~5 M_{ʘ}.
R_{Sch }~ 5M_{ʘ }
R_{Sch }~ 3x 5
~
15 km
Therefore, a star with a mass of 42 M_{ʘ} could form a black
hole with a diameter of 30 km.
Where does Einsteinian gravity take over from Newtonian gravity?
At a large distance a black hole exerts a gravitation force according to
Newton’s Law. However, there is a point that is reached where Newton’s
laws are no longer valid, beyond which the gravitation effects are now
explained by using general relativity of Einstein. The change occurs at
a distance of about 3 R_{Sch}.
Example
Χ^{2} Orionis could form a black hole that has a radius of about
15 km. At what distance from the black hole does the gravity increase
from what Newton’s Law predicts?
Using the above formula this distance is about 3 R_{Sch}, thus:
3 R_{Sch} ~ 3 x 15
~ 45 km.
The gravitation force will increase to considerably more than is
predicted by Newton’s Law as the black hole is approached past 45 km.





Author: M.H.Monroe Email: admin@austhrutime.com Sources & Further reading 