The sound of the Universe: The search for Gravitational Waves Giovanni Santostasi, Ph. D. Baton Rouge Community College, Baton Rouge, LA.

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.