Black HolesBlack HolesRanjith SRanjith S

A huge great enormous thing, like — like nothing. A huge big — well, like a — I don’t know — like an enormous big nothing ...

Piglet describes the Heffalump,

in Winnie the Pooh by A.A. Milne

Huge GravityHuge Gravity

• Black Holes are Gravity Centers of The Universe

• Size ~ 0 and Density ~ α• Two Types

– Static• Karl Schwarzschild solutions

– Rotating• Kerr solutions

Chandrasekhar LimitChandrasekhar Limit

• Death of Star• Red Giant• White Dwarfs

– Mass of star<1.4 Solar mass– Electron Degeneracy Pressure

• Neutron Stars– 1.4 solar mass<Mass of star<3.0 solar mass– Neutron Degeneracy Pressure

• Black Holes– Mass of star >3.0 Solar mass

The Transition The Transition

• Pauli Exclusion Principle: No two electrons can occupy the same position in space

• Electron Degeneracy Pressure :- Electrons are packed side by side in a white dwarf This prevents it from collapsing any further

• Neutron Degeneracy Pressure : - Neutrons are packed side by side in a Neutron Star This prevents it from collapsing any further

• More Mass More Gravity :- Nothing can stop Collision

• -> Black Holes

Event HorizonEvent Horizon

• Area around Black Hole, from where nothing can be escaped to outside

• Inside event horizon escape velocity is greater than speed of light.

John Wheeler

Schwarzschild RadiusSchwarzschild Radius

• Distance from singularity to event horizon is called Schwarzschild radius

• Schwarzschild radius is a measure of the size of black hole

Karl Schwarzschild (1876-1916)

Black Hole infinite abyss in space-time

Albert Einstein (1879-1955)

Falling into a Black hole:

Time dilation

Spaghettification!

Singularity Theorem

• Every black hole must have a singularity inside itself

• There is no existence of a naked singularly in the universe

Naked Singularity

A singularity that is not inside a black hole (not surrounded by an event horizon), and therefore can be seen by someone outside it

Roger Penrose (b1931)

Cosmic Censorship Cosmic Censorship HypothesisHypothesis

• The laws of physics prevent naked singularities from forming when a star collapses

No-Hair TheoremNo-Hair Theorem

• A black hole has almost no hair; its only ‘hair’ are its

– mass

– angular momentum

– electric charge

Types of Black HolesTypes of Black Holes

• Schwarzschild (1916)

– mass

• Reissner-Nordström (1916, 1918)

– mass, electric charge

• Kerr (1963)

– mass, angular momentum

• Kerr-Newman (1965)

– mass, angular momentum, electric charge

Roy Kerr

Space-Time DiagramSpace-Time Diagram

Schwarzschild Black HoleSchwarzschild Black Hole

Kerr Black Hole

WormholeWormhole

Penrose ProcessPenrose Process - - Energy Energy

extraction extraction from a Kerr from a Kerr

black holeblack hole

Event Horizon Ergo sphere

Top View

Black Hole Dynamics

• First Law

• Second Law

• Third Law

First Law

• If a body with a fixed mass and angular momentum is fall into a black hole then the mass and angular momentum of the black hole increases that much.

• Resembles with the First law of thermodynamics

• Energy conservation theorem

Second Law

• The surface area of a black hole is not reduced in any process

• If two black holes combined then the resultant surface area is greater than the sum of surface areas of each black holes.

• Surface area ->Entropy• We cannot reduce the entropy of a

system.

Third Law

• The surface gravity of a black hole is never become zero.

• Resumbles to third law in thermodynamics

• We cannot reduce the temp: to absolute zero.

Virtual Particles

•In quantum theory, there is an intrinsic uncertainty in energy and time: ∆E ∆t ≥ h/4p•This implies the existence of ‘virtual particles’ even in a vacuum•Virtual particles appear in pairs, consisting of a particle and its corres-ponding antiparticle

Hawking Radiation

Stephen W. Hawking (b1942)

• One partner of a virtual-particlepair could fall into a black hole, carrying negative energy with it

• Effectively, the black hole appearsto be emitting particles and losingmass!

But this effect is very tinyfor normal black holes

• For a solar mass black hole– Temperature = 10 - 7 K– Lifetime = 10 6 7 years

(age of universe = 10 1 0 years)

• Since T ∝ 1/M, this effect is morepronounced for small black holes

• Mini black holes created duringthe Big Bang?

Microlens event

Black hole in globular cluster

Disk in galaxy NGC 7052

NGC 4438

Galaxy NGC 6251 nucleus

M87

Expanding Universe

• Gravitational Field Equations Expanding universe

∀ λ Steady Universe• Edwin Hubble and Milton

Heumanson (Mount Wilson Observery)

• Expanding Universe• Red Shift

Edwin Hubble

Freedman-Robertson-Walker Model

• Critical Mass• Closed Universe

– Mu <Critical Mass

– Universe started Contracting after a particular time

• Flat Universe– Mu = Critical Mass

– Expansion rate of universe become constant

• Open Universe– Mu > Critical Mass

– Expansion rate increases with time

Possible Fates of the Universe

Big Bang Theory

• Lemaither and Gamove• Universe Formed from a Big Bang• Singularity is Big Bang Singularity• The total universe formed from

that. Lemaither

George Gamow

Picture

Pic

Big Bang Theory Proofs

• Background Radiation

• Large Scale of universe

• Distribution of Galaxies

Other Theories

• Stedy State Theory

• Inflation Theory

• Big Crunch Theory

• Oscillatory state Theory

Will the Universe Recollapse?

• Gravitational pull of the galaxies on each other is slowing down the rate of expansion

• Required density for the universe to recollapse is 4.5 x 10-30 g/cm3

• Observed density of luminous material (stars, galaxies) is about 3 x 10-31 g/cm3

Dark Matter• But there may be about 10

times this amount in the form of ‘dark matter’

• So the universe is very close to the threshold for recollapse!

Measurements of the velocities of stars ina galaxy show that there must be morematter in the galaxy than is apparent.This ‘dark matter’ is known to form aninvisible halo around the galaxy

Gravitational Waves• The Variations in space-time (When

body Accelerated) causes Gravitational Waves.

• Speed of Wave = C• Large gravity related Phenomena• Supernova, Black Holes etc…

Gravitational Wave Detector

• When GW passing through a body it will expands the body in that direction and contracts in opposite direction by measuring this we can detect GW.

LIGO• The Laser Interferometer

Gravitational-Wave Observatory Caltech.

Forces of Nature

• Gravitational

• Electromagnetic

• Weak

• Strong

Standard Model - Quarks

• 6 Quarks [up,down,top,bottom,strange,charm]

• Gluons – Exchange Particles

• Super Symmetry

Graviton

• Exchange Particle for Gravity

Unification of the Four Forces• Electricity + Magnetism

= Electromagnetism

• Electromagnetism + Weak = Electroweak

• Electroweak + Strong = Grand Unified Theory (GUT)

• GUT + Gravity = Theory of Everything (TOE)??

• Due to geometry rather than exchange of particles

• Remains impossible to incorporate within the framework of quantum field theory like the other forces

Gravity

Quantum Gravity?

• Does space-time fluctuate ina quantum fashion at very small scales?

• Called space-time foam

• How to describe this mathematically?

Superstring Theory

• Best candidate for a TOE is superstring theory

• Assumes all fundamental particles are actually string-like objects rather than point-like objects

• Different particles correspond to different vibrational modes of the same string

Point particles and strings interact differently

Extra Dimensions?• Superstring theory

predicts that space-time is 10-dimensional (9 space + 1 time)

• The extra 6 dimensions are thought to be rolled up to a very small size

Unsolved Problems

• Why Gravity happens?

• No – Graviton in Standard Model

• Dark Mater

ThanksThanks