View
63
Download
0
Category
Tags:
Preview:
DESCRIPTION
Utrecht University. GRAVITATIONAL WAVES. Gerard ’t Hooft VSV `Leonardo da Vinci’ Symposium, TU Delft, March 16, 2007. J.C. Maxwell 1864. The electro-magnetic force. Gravitation. The fourth force:. Gravity is an accumulative force !. All atoms in the Earth - PowerPoint PPT Presentation
Citation preview
Gerard ’t Hooft
VSV `Leonardo da Vinci’ Symposium, TU Delft, March 16, 2007
Utrecht University
The electro-magnetic force
J.C. Maxwell 1864
Gravitation
The fourth force:
Gravity is an accumulative force !
All atoms in the Earthpull all atoms in your
body to the same direction (downwards) !
Curved coordinates
time
Coordinateshight
Near a source of gravity (such as the Earth),space and time are curved
General Relativity
There is a “curvature conservation law”
There is also a “matter conservation law”(energy, momentum and forces)
In Einstein’s attempts to find a formula, they did not match !
To make them match, you must assume thatnot only matter (or Energy ) is the source ofgravity, but also pressure !
2/ c
This you will not notice, under ordinary circumstances
negative pressure (tension)
pressure
The total pressure always cancels out !!!
Einstein had to add an extra term to his equation.
12
3
8
E p
GR R g T
grav. source
3E E p
For light, and electro-magnetic fields, 3E p
So, light couples twice as strong to gravity as matter !
Light rays bend twice as much asone might expect !
time
Why does“Dark energy”
make the Universeexpand ? -
Dark energy requiresdark pressurewhich is negative !
3 2
p E
E p E
The Black Hole
Electromagnetism: like charges repel, opposite charges attract → chargestend to neutralize
Gravity: like masses attract → masses tend to accumulate
horizon
Where is the gravitational field strongest? The formation of a Black Hole
even light cannot
escape from within this
region ...
Black Hole
The Schwarzschild Solution to Einstein’s equations
( )2
2 2 222
2 2 2d sid
d 1 d ( )d1
nMr M
r
rs t r q q j= - - + + +
-
Karl Schwarzschild1916
“Über das Gravitationsfeldeines Massenpunktes nachder Einsteinschen Theorie”
As seen by distantobserver
As
experienced by astro-
naut himself
They experience time differently. Mathematics tells usthat, consequently, they experience particles differently
as well
Time stands stillat the horizon
Continueshis waythrough
Stephen Hawking’s great discovery:the radiating black hole
Electro-magnetic radiation
gravitational radiation
The photon has spin = 1
The graviton has spin = 2
Heavy gravitating bodies emit gravitational radiation
In the process, they loose energy: the orbit shrinks
The binary pulsar PSR 1913+16
(Figure from Weisberg et al. 1981)
(Figure from Weisberg et al. 1981)
Orbit shinks 3.1 mm per orbit
Violent events in the cosmos
LISA A gravitational antenna
LIGO Hanford, WaLaser Interferometer Gravitational wave Observatory 4 + 4 km
VIRGO Gascina (near Pisa) 3 + 3 km
LISA
Main Spacecraft
Spacecraft # 3 Spacecraft # 2
Secondaries
photon graviton g
The PhotonSpin = 1 Spin = 2
PP PP
PPPP
PPPP
PP PP
Equal charges repel one another ...
Equal masses attractone another ...
The Graviton
MoonMoon
Moon
Earth
Sun 0 180 360o o o
strength of force This is the wave function of a spin 2 particle
Graviton
Force and spin
The Universal Force Law:
nst 1 22
CQ Q
ForceR
Gravitation:
1 22
M MForce G
R
Distance
ForceMaxwell & YM:
There are two kinds of curvature:
Riemann curvature (space and time near Earth)
Ricci curvature (only inside Earth, the real source of gravity)
Einstein tried a formula: 4 GR T Ricci curvature Matter density
But there was something wrong !
(for a curved piece of paper, these are the same, only in many-dimensional space-time, Ricci is more special.
There is a “curvature conservation law”
There is also a “matter conservation law”(energy, momentum and forces)
In Einstein’s original formula, they did not match !
To make them match, you must assume thatnot only matter (or Energy ) is the source ofgravity, but also pressure !
2/ c
This you will not notice, under ordinary circumstances
negative pressure (tension)
pressure
The total pressure always cancels out !!!
Einstein had to replace by4 GR T
12
12
(3 )
( )8
E p E
R T T gG
grav. source
Recommended