Chandrasekar Limit--white dwarfs form with remnant under 1.3 M sun

Remnant: End State: Supporting Pressure: < 1.3 MO White Dwarf Electron degeneracy 1.3 MO<M<3.0 MO Neutron Star Neutron > 3.0 MO Black Hole None

Chandrasekar Limit--white dwarfs form with remnant under 1.3 Msun.

NOTES: BLACK HOLES

Laplace (1796) is usually given credit. John Michell, 13 years earlier (1783), discovered that if matter were concentratedenough, Newton's Laws would give an escape velocity greater than light. Sun would be dark if squeezed to a ball 3 km in diameter.Schwarzschild (~1920) did a calculation which showed Einstein's GTR predicted that a highly concentrated spherical mass would shrink to a point and have an event horizon around it beyond which nothing could escape (Vescape> c).The Schwarzschild radius,

R(event horizon) = 3 km x mass (in solar masses).Oppenheimer (~1940) demonstrated that a stellar remnant above 3 solar masses could not be held up by neutron pressure and would collapse furtherPenrose (~1968) showed the GTR called for an eventual singularity (point mass) in the case of mass that large.John Wheeler gave the 'black hole' its name.

Laplace (1796) is usually given credit. John Michell, 13 years earlier (1783), discovered that if matter were concentrated enough, Newton's Laws would give an escape velocity greater than light. Sun would be dark if squeezed to a ball 3 km in radius.

Laplace--mathematician

"If the semi-diameter of a sphere of the same density as the Sun were to exceed that of the Sun in the proportion of 500 to 1, a body falling from an infinite height towards it would have acquired at its surface greater velocity than that of light, and consequently supposing light to be attracted by the same force in proportion to its vis inertiae (inertial mass), with other bodies, all light emitted from such a body would be made to return towards it by its own proper gravity." 

-John Michell on the concept of black holes

Schwarzschild (~1920) published a calculation which showed Einstein's GTR predicted that a highly concentrated spherical mass would shrink to a point and have an event horizon around it beyond which nothing could escape (Vescape> c).

German astrophysicist Karl Schwarzschild calculated the first rigorous solution to the field equations in Albert Einstein's theory of general relativity while serving on the Russian front during World War 1.

The event horizon:

The Schwarzschild radius,

R(event horizon) = 3 km x mass (in solar masses).

Robert Oppenheimer (~1940) demonstrated that a stellar remnant above 3 solar masses could not be held up by neutron pressure and would collapse further into a black hole.

Should we call it ‘The Oppenheimer Limit’?

Roger Penrose (~1968) showed the GTR called for an eventual singularity (point mass) in the case of mass that large.

Get the point?

He was Stephen Hawking’sPhD advisor

John Wheeler gave the 'black hole' its name in the late ’60s.He played a key role in the development of the atom bomb.

We distinguish between

1. Stellar mass black holes < 100 Msun

and

2. Supermassive black holes—bigger than that.

Confirming a stellar mass black hole requires:

1.A strong x-ray source

2. A inferred mass of over 3 Msun

Stellar mass black holes: only seen when material is falling in producing an accretion disk. This happens when, for example, a star (originally bigger than about 5 solar masses) has a companion and draws in material from the other star. X-rays are produced as the material heats as it fall in.

Cygnus X-1: first stellar mass black hole discovered by the Uhuru (means 'freedom' in Swahili) satellite in 1971

Stephen Hawking (~1968) said that black holes radiate!Black holes are not black!? No proof yet…

With a temperature—it radiates as a black bodyAnd loses the mass equivalent to the energy.

BHs are simple: they can have only mass, charge, & spin.

This is called The 'no hair' theorem: they can have no fields along surface, like magnetic fields. Hair on a head must have a part or swirl, and black holes are toosimple for that.

White hole: time reverse of a black hole. One way membrane 'out', BH is a one way membrane 'in'.

Novikov (1964) suggested Big Bang might have white holes (he called them retarded cores--little Bang an example?)These go off like delayed explosions in fireworks.

Penrose: energy may be extracted from ergosphere (rotating spacetime) around rotating BH.

Einstein-Rosen Bridge (1930's)--wormhole. Theory that a closed (massive) universe might have BH-->WH tunnels connected different places and times.

Wormhole connects black to white hole.

Fall into a BH might not be fatal: 1. If BH is large enough, event horizon is large and provides little tidal force. 2. If BH is rotating fast enough you could enter wormhole. 3. Wormholes only exist in a massive universe. 4. You must have antigravity material pasted on your spacecraft. (Kip Thorne) 5. You must be prepared to travel in time or to another universe without returning.

A rotating black hole’s singularity is like an opening in space-time.

Baby Universes: a closed universe with 1028 Joules of energy in a localized region can produce a baby universe. Its time is 'imaginary'.

Star Clusters:Open Clusters: less than 1,000 Population I stars–young, composed of recycled material with heavy elements. Not gravitationally bound.Ex: The Pleiades and The Hyades.

Globular Clusters: thousands to millions of stars in a spherical bound group. Population II stars–old, made of primordial H and He. From 12-14 billion years old. Stars have small mass.

Globular cluster in Hercules, M13

Cluster age: Determined by where the cluster is turning off the main sequence–the turnoff point.