The sound of the Universe: The search for Gravitational Waves Giovanni Santostasi, Ph. D. Baton Rouge Community College, Baton Rouge, LA
Mar 27, 2015
The sound of the Universe:The search for Gravitational Waves
Giovanni Santostasi, Ph. D.
Baton Rouge Community College,
Baton Rouge, LA
Newton
and Einstein:
theories of Space and Time Special Relativity = Space-Time
constant velocityconstant velocityGeneral Relativity = Geometry-
Space-Timeaccelerationacceleration
Space and Time UnifiedTime and Space are not separated quantities but different
aspects of a same reality (Space-Time continuum)
Light unifies Space and Time
Velocity of Light c=300,000 Km/s =3x10^8 m/s=6.7 x 10^8 miles/hour
Relativity of the reference system
“Absoluteness” of the laws of Physics
Equivalence Principle:the fundamental principle that unifies inertial and
gravitational mass
M_inertial=M_gravitational
This simple experimental fact is the essential basis for Einstein’s theory of Gravity: General Relativity
Acceleration It is not possible to distinguish between gravity
and an uniformly accelerated system
Gravity can be simulated by an
accelerated system
The absence of gravity is equivalent to free fall
The presence of gravity can be
neutralized in a Reference system in free fall
The observer in free fall with the elevator doesn’t see any change
in the vertical position of the sphere
In the meanwhile the observer on the ground sees an horizontal and
vertical change in position and interprets the motion as a
“curved” path
Also light can be bent
Gravity = curvature in the
Fabric of Space-Time
As observed by the observer inside the elevator
As observed by external observer
The other way around If the acceleration is produced by gravity
if accelerationis produced by rocketthis is what it will be observed
The essential effects of gravity are of tideal nature
The difference is that gravity has
GLOBALGeometric properties
(locally just undistinguishable from accelerated
frame)
Curvature of Space Time caused by the sun
This is a quasi-static situation for what
concerns space-time
Matter tells space-time how to curve; the curvature “tells” to matter how to move
Einstein ‘s Equation
G= G/c^4 T
http://www.pbs.org/wgbh/nova/einstein/relativity/animations.html
Acceleration of Mass creates Gravitational
Waves
The waves travel at the velocity of light (3x10^8m/s) and the waves’ amplitude
goes downs with distance
Gravitational radiation has 2 polarizations and the energy is emitted mostly in the quadrupole (“football shape distribution
of matter required”)
The wave arrives in the direction
perpendicular to the circle
Polarization (plus) +
Polarization (cross) x
Sources of gravitational waves
• Supenovae
• Neutron Stars that rotate (or wobble in space)
• Coalescent Binary Systems of Black Holes and/or Neutron Stars
• Cosmic Background
caused by the Big Bang
Detectors of Gravitational Waves
• Resonant Bars (LSU)
• Sphere (Rome ?)
• Interferometers
(LIGO)
Resonant BarsCylindrical Bars, typically made of alluminum (about 1 ton. ). They work on the principle of
resonance, they are tuned at about 1000 Hz, the resonant frequency of neutron stars . The wave
interacts with the bar and the motion is transmitted to a sophisticated “microphone” that transform the mechanical motion into an
electrical impulse: this is our signal.
The noise Problem
Noise is bigger than signal in the current detectors (we don’t see anything than
noise !). Noise at h=10^-20
Signal maybe at h=10^-21 or less
Mathemathical tools to extract signal: Filtering. For continuous signals: Integration with long observation times.
Sources of noise: How to control
• Seismic (suspension system)
• Thermal (low temperature)
• Eletronic (SQUID)
Interferometers
Range of sensitivity on earth 10-1000 Hz
In space 10^-4-1 Hz
Mirror
Mirror
Semi-transparent Mirror
4 km
Laser 10 Watts
Photodetector
Vacuum Pipes• LIGO (USA, Louisiana & Washington)
• VIRGO (ITALY, Pisa)
•TAMA (JAPAN)
• GEO 600 (GERMANy, Postdam)
• LISA (NASA-ESA, In space, 2016)
Neutron stars
Continuous sources. They rotate up to frequencies of 1000 Hz. To emit GW they have to be tri-axial
(football shaped).
The strain (h=deformation/length measured )
for a star with 3 axis is:
They can also wobble: if axis of rotation doesn’t coincide with symmetry axis. In this case star doesn’t need to be a football to emit Gravitational Waves.
)2sin(2 24
tIRc
Gh
Burst sources:Supernovae and Coalescent
Systems•Explosion of Supernovae have to be asymmetric to radiate gravitationally. The neutron star that is
left over after the explosion vibrate violently (~1000 Hz)
•Coalescent Systems: compact objects as black holes and neutrons stars. Binary Systems are very “football shape” like. They emit Gravity Waves so they loose energy. The system is inspiraling until it collides (in time scales of millions of years). Indirect evidence of GW: pulsar 1913+16 (Taylor and Hulse: 1993 Nobel Prize winners).
Cosmic Background
• The most ancient evidence of the birth of the Universe. Electromagnetic Background300,000 years after the Big
Bang (a young baby, 0.7 day old).
• Gravitational Background is a “polaroid” of the birth of the Universe (as it was born !) Gravity doesn’t interact a lot with
matter.
• We don’t know what to expect but we have some vague ideas from other cosmological observations.
Conclusion: What can we learn from Gravitational Waves?• Another, fundamental confirmation of General
Relativity (Viva Einstein !)
•New window on the Universe.
•Radiation very different from EM and particles.
•Bulk Motion of mass.
• GW do not interact well with matter. We can probe very high density region of the universe as neutron
stars and the core of black holes.
• Birth Cry of the Universe.