BLACK HOLES - Stony Brook University

BLACK HOLES[Image by A. Hamilton]

Karl Schwarzschild’s WorkIn 1916 Schwarzschild read Einstein’spaper on general relativity. He wasinterested in the physics of stars,and had a lot of spare time betweenbattles on the Russian front, so he solvedEinstein’s field equation for the regionoutside a massive spherical object.His solution had many interesting features,includingq prediction of space warping in stronggravity, and invention of embeddingdiagrams to visualize it.q verification gravitational time dilation,just as Einstein had pictured it.q prediction of black holes, though thiswas not recognized at the time.[slide courtesy of D. Watson]

Schwarzschild’s solutionDescribes the spacetime curvature near a massive, sphericallysymmetric body. Solution ONLY depends on BH MASS.[Figure from Thorne’s “Black Holes and Time warps”]

In curved space, rules of geometry different thanEuclidean .

In flat space, the distancebetween any two circumferences in the figure is 1.In the curved space around a BH,the distance between any twocircumferences is greater than 1.{Images by D. Watson]

[slide courtesy of D. Watson]

Predictions of the Schwarchild’s solutionFor an object of a given mass, the spacetime curvature increases as its size decreases[Figure from Thorne’s “Black Holes and time warps”]

As the radius of the object becomes smaller than a criticalvalue, the spacetime curvature becomes infiniteBLACK HOLE

What characterizes a Black Hole?Presence of a “surface” called EVENT HORIZON, fromwhich nothing, not even light can escape.The radius of this surface is called theSCHWARZCHILD S 2 3(M / M Sun ) kilometerscspeed oflight

Black Holes To a stationary observer far away, time is dilated neara black hole, and at the critical surface (at RS), it isslowed down infinitely. Light emitted close to the critical surface is severelyred-shifted (the frequency is lower) and at the criticalsurface, the redshift is infinite.From insidethis regionno informationcan escapered-shiftedred-shifted intooblivion[slide courtesy of M.Begelman]

Time Dilation near a Black Hole (here M 6Msun)[ This and next three slides courtesy of D. Watson]

The dangers of getting too close toa small black hole .This effect is colloquially known as “spaghettification”

Light close to a Black Hole[[Image from “Gravity’s fatal attraction” byM. Begelman & M. Rees]In the vicinity of a blackhole, light is severelydeflected.The amount of deflectionbecomes larger closer tothe black hole. When thedistance is D 1.5 Rs,light goes around in acircular orbit. A light ray emittedtangentially to the horizonat a distance 1.5 Rs wouldbe captured. In order to escapeit would have to be emitted atan angle 1800. As the radiusis decreased from 1.5 Rs to Rs,the range of angles from whichlight can escape decreases, tobecome 00 at the horizon, atwhich point light can no longerescape.

An observer at D 1.5 Rs would be ableto see the back of her head![Image from “The PhysicalUniverse” by F. Shu]

[This and following slide courtesy of D. Watson - Image from Thorne’s “Black Holes and time Warps”]

Black Holes red-shifted red-shifted into oblivion From inside this region no information can escape [slide courtesy of M.Begelman] Time Dilation near a Black Hole (here M 6Msun) [ This and next three slides courtesy of D. Watson] The dangers of getting too close to a small black hole . This effect is colloquially known as “spaghettification” Light close to a Black Hole In the vicinity .