Wormholes

The simplest example The r = 2m singularity is more complicated than previously mentioned… Has solution (the Schwarzschild metric):

This is what the vicinity of the space- like singularity looks like (with 2 dimensions suppressed):

The solution actually has two parts, the black hole part in one universe where matter flows in and essentially a white hole part in another universe where matter flows out.

The connection is unstable and the gravitational attraction pinches off the wormhole

A wormhole could be kept open by filling its throat, or the region around it, with an ingredient called exotic matter. This is strange stuff which doesn’t exist in the classical physics world, but may be allowed by quantum physics. Exotic matter is repelled, rather than attracted, by gravity and is said to have negative energy - meaning it has even less than empty space.

Scientists like John Wheeler and particularly Kip Thorne, realized that Einstein’s laws of gravity do not: 1.determine the topology of the spacetime – that is determined by the matter distribution. 2.give a direction to time. What does 1) mean?

Topologically, a coffee cup is the same as a donut!! Since Einstein’s equations don’t determine the topology of space time, then maybe we can fold it and do this:

A jet emerging from a wormhole!!! Not!!!! A jet emerging from a wormhole!!!

Scientists like John Wheeler and particularly Kip Thorne, realized that Einstein’s laws of gravity: 1.Do not determine the topology of the spacetime – that is determined by the matter distribution. 2.Do not give a direction to time. What does 2) mean?

We could use wormholes to travel in time! Heres one scheme – A traveler could move from event A to B using stationary Wormholes and then back in time using a moving wormhole.

Critical thinking exercise – Why won’t these schemes work? Exotic matter Could use anything – fairy godmothers, aliens, mental telepathy, inflation, dark energy… Direction of time The laws of Thermodynamics give time a direction – gravity must obey thermodynamics

What do we mean by dark matter and dark energy?

Dark matter Not dark matter Dark Stuff in the Universe

Dark Matter: An undetected form of mass that emits little or no light but whose existence we infer from its gravitational influence Dark Energy: An unknown form of energy that seems to be the source of a repulsive force causing the expansion of the universe to accelerate Unseen Influences

For groups of stars, galaxies, clusters of galaxies, we measure the velocities of the member objects, then assume there has to be enough mass there for gravity to stop them from flying apart. When we measure these velocities, it turns out that more mass is needed! So we assume there is dark stuff. The first to observe this behavior was Fritz Zwicky in He was looking at galaxies in clusters. No one believed him. He was quite a character!

What is the evidence for dark matter in clusters of galaxies?

We can measure the velocities of galaxies in a cluster from their Doppler shifts

The mass we find from galaxy motions in a cluster is about 50 times larger than the mass in stars!

Clusters contain large amounts of X- ray emitting hot gas Temperature of hot gas (particle motions) tells us cluster mass: 85% dark matter 13% hot gas 2% stars

Gravitational lensing, the bending of light rays by gravity, can also tell us a cluster’s mass

All three methods of measuring cluster mass indicate similar amounts of dark matter

Vera Rubin detected this lack of luminous stuff in individual galaxies in the early seventies. No one believed her! She is still a character!

Mass within Sun’s orbit: 1.0 x M Sun Total mass: ~10 12 M Sun

Spiral galaxies all tend to have flat rotation curves indicating large amounts of dark matter

The visible portion of a galaxy lies deep in the heart of a large halo of dark matter

What is the Dark Matter? Some Possibilities:

Ordinary Matter: Dust, Gas, Planets, Jupiters, Brown Dwarfs, Faint Stars, White Dwarfs, bowling balls, black holes, MACHOs … Current theories/observations say there just isn’t enough mass possible. Plus the Hot Big Bang idea doesn’t produce enough “baryonic matter” (protons, neutrons, electrons etc.) to do it.

Not-so-ordinary Matter: Neutrinos are an example of a particle that interacts with matter through the weak nuclear force. There are so many neutrinos in the universe, however, that even a small mass would be important for dark matter; a mass of 92 eV, one five-thousandth the mass of the electron, would close the universe!

WIMPS Most exotic matter candidates fall into the category of WIMPS, or Weakly Interacting Massive Particles. These are heavy particles that only interact weakly with other matter (or else they would have been discovered by now). There are many possible – e.g., neutralinos, axions, etc.

Change Gravity: Another possibility – Perhaps gravity on large scales, such as the size of galaxies, doesn't work the same way as gravity does on the small scales we can measure. MOND – MOdified Newtonian Dynamics Milgrom Bekenstein Sanders

Change Gravity: MOND – MOdified Newtonian Dynamics

In the past few years, astronomers have observed that the light from very far supernovae is fainter than it should be. The current explanation for this is that they are more distant than originally thought, which implies that the expansion of the universe must be accelerating.

Accelerating universe is best fit to supernova data

This astonishing result can be explained if the space between galaxies is filled with a mysterious dark energy. We have no idea what it is!

As the universe expands, it creates more dark energy. The repulsive behavior could eventually get badly out of hand. It is possible that several billion years from now, the ever- increasing dark energy could pull space apart so rapidly that galaxy clusters would scatter, followed by the disintegration of individual galaxies such as the Milky Way, then solar systems, until finally matter itself would be shredded by accelerating space. The universe would end in a "big rip."

Exploding Death Star