Rotating black holes
- The Kerr-Newman (KN) geometry
describes the geometry of empty
space around a spinning, possibly charged, black hole.
- Real black holes probably spin.
- Centrifugal force causes the KN geometry to be gravitationally repulsive in its core.
- The phenomenology of the KN geometry
is quite similar to that of the RN geometry:
the gravitational repulsion causes the KN geometry to have
both inner and outer horizons,
and blackhole-wormhole-whitehole connections to new universes.
- The KN geometry is, again, inconsistent,
because the black hole cannot be empty in its core if the core is repulsive.
- The singularity of the KN geometry forms a ring, kept open by the centrifugal force.
- The outer horizon and inner horizon are confocal ellipsoids,
with the ring singularity at the focus.
- The other side of the disk bounded by the ring singularity
is a new region, the "antiverse", at negative radius.
In the antiverse, the black hole appears to have negative mass.
- In the antiverse, circles around the axis near the disk are timelike.
These circles form "closed timelike loops" (CTLs),
where time keeps repeating itself.
- The inner horizon is, as in the charged black hole, violently unstable.
- As in a charged black hole,
the instability causes the region inside the inner horizon
to contain a dense, relativistic plasma, which would fry an infaller.
Week 14
This week was on
Hawking radiation.
- Hawking radiation is quantum mechanical radiation from black holes.
Quantum mechanically, virtual pairs of particles can pop out of the vacuum.
The black hole swallows one of the particles (which effectively carrys negative energy),
leaving the other particle (carrying positive energy) to go off to the outside world.
- Hawking radiation has a black body spectrum.
- The characteristic wavelength of Hawking radiation is roughly equal to
the diameter of the black hole.
Thus if you could see a black hole by its Hawking radiation,
it would look fuzzy, a quantum mechanical object.
- The Hawking temperature and luminosity of astronomical black holes is tiny.
The radiation observed from near astronomical black holes is emitted
by hot gas from an accretion disk, not Hawking radiation.
- The Hawking temperature and luminosity of so-called mini-black holes
is much larger.
Stephen Hawking hypothesized that mini-black holes might be created in the Big Bang,
but there is no observational evidence for their existence.
- A mini-black hole with mass less than the mass of a mountain
can evaporate in the age of the Universe.
A mini-black hole of 1000 tons will evaporate in 1 second,
in a burst of gamma rays and high energy particles.
From a human point of view this is a large explosion,
but astronomically it is a tiny explosion,
far less energetic than a nova, supernova, or gamma-ray burst.
Week 15
This week was on cosmology.
Cosmology is one of the major applications of general relativity,
the other major application being black holes.
A third major application, gravitational waves,
will become important in the next two decades
with the advent of gravitational wave astronomy.
To allow you time to prepare thorougly for the final,
none of the material presented in the last two weeks (15 and 16) of the semester
will be tested on the final.
In particular,
Cosmology will not be tested on the final.
- The Standard Model of Cosmology.
- Hubble's law v = H_{0} d,
recession velocity = Hubble's constant H_{0} times distance.
- Implies that the Universe is expanding, and that there was a Big Bang.
- H_{0} determines the age of the Universe, t » 1/H_{0}
(the equality is not exact because of the deceleration or acceleration of the Universe).
- W = (actual density of the Universe)/(critical density of the Universe).
- Through Einstein's equations of general relativity,
W determines the curvature, and also the fate, of the Universe.
- Open, flat, and closed geometries of the Universe.
- The Cosmic Microwave Background (CMB) is the radiation remnant of the primeval hot Big Bang fireball.
- Observationally, the Cosmic Microwave Background:
- Has an exquisite black body spectrum, with a temperature of 2.726 Kelvin.
- Is almost uniform on the sky.
- Shows a "dipole" distortion from the motion of the Sun through the CMB, at 365 km/s.
- After subtraction of the dipole distortion,
the residual temperature fluctuations are tiny, a few parts in 10^{5}.
- The power spectrum of fluctuations shows a pattern of acoustic peaks
in remarkable agreement with the predictions of the theory of Inflation.
- Theoretically, the Cosmic Microwave Background:
- Supports the idea that there was a hot Big Bang.
- The CMB cools as the Universe expands,
the wavelengths of CMB photons being stretched (redshifted) by the expansion of the Universe.
- Its uniformity and black body spectrum tell us that the Universe used to be much simpler when it was young.
- Comes to us from the Epoch of Recombination,
when the Universe was 370,000 years old, and the temperature was 3000 Kelvin.
- At Recombination, hydrogen and other elements combined
from an ionized plasma of nuclei and free electrons
to a neutral gas of atoms.
As a result, the Universe changed from being opaque to transparent,
allowing the CMB to propagate freely to us from that time.
- The theory of Inflation postulates that the during its earliest moments
(the first 10^{-33} seconds or so),
the mass-energy of the Universe was dominated by vacuum energy.
Vacuum energy is gravitationally repulsive,
and would cause the Universe to expand exponentially (inflate),
doubling in radius every 10^{-35} seconds.
- Inflation solves all of the following problems:
- The Horizon Problem.
How come regions of the CMB more than 2° apart have the same temperature,
even though they were causally disconnected at the time of Recombination?
- If gravity is always attractive, then why is the Universe expanding?
- How come the Universe is so flat?
- How come the Universe is so large?
- Where did the mass-energy content of the present day Universe come from?
- What produced the small fluctuations that grew by gravity into galaxies and stars today?
Answer: quantum fluctuations of the vacuum.
- Inflation predicts several key observed features of fluctuations in the temperature of the CMB:
- A scale-invariant spectrum of fluctuations at large scales (much larger than the horizon size at Recombination).
- A regular sequence of acoustic peaks.
- Flat curvature.
- A random (Gaussian) noise pattern.
- Inflation ends when the vacuum energy decays into other forms of energy,
namely matter and radiation.
This is where matter and radiation in today's Universe came from.
- The vacuum energy that powers inflation is thought to be the energy of the unification of forces.
Specifically, the energy is thought to be associated with the hypothesized
unification of the electroweak and color (or strong) forces into a GUT (Grand Unified Theory) Force.
The energy scale is not accessible to present day particle accelerators,
so the nature of the unification is not well understood.
Week 16
Spring 2005 ASTR 2030 Homepage
Updated 2005 Apr 27