ASTM041 Relativistic Astrophysics Notes 4 of 6 (QMUL)

AG Polnarev, Relativistic Astrophysics, 2007. Lecture 4 , Black holes.

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Lecture 4. Black Holes

A black hole is a region of space in which the gravitational field is so powerful that nothing can escape after having fallen inside so called the event horizon, which is the boundary of the black hole. The name comes from the fact that even electromagnetic radiation (e.g. light) is unable to escape, rendering the interior invisible, i.e. black.

We know that black holes exist. We know how they are born, where they occur, and why they exist in different sizes. We even know what would happen if you fell into one. Our discoveries have revealed one of the strangest objects in the Universe.

The golden age of black hole physics was ushered in when advances in our theoretical understanding of the Schwarzschild geometry and gravitational collapse in general coincided with new astronomical observations of highly energetic objects that clearly pointed to a gravitationally collapsed object as their central engine.

[Page 2] A G Polnarev, Relativistic Astrophysics, 2007. Lecture 4 , Black holes. 1. How invisible black holes can be observed

1. How invisible black holes can be observed Black holes can be detected only by their gravitational interaction with matter and electromagnetic waves outside the event horizon.

Example 1. The gas spirals inward, heating up to very high temperatures and emitting large amounts of radiation in the process.

[Page 3] A G Polnarev, Relativistic Astrophysics, 2007. Lecture 4 , Black holes. 1. How invisible black holes can be observed

Example 2. Many black holes interacting gravitationally with the matter outside form relativistic jets. An artists concept of an active galactic nuclei with black hole inside.

Supermassive Black Holes Stars near the center of a galaxy have varied speeds and directions of their orbital motions - that is termed their “velocity dispersion.�

The cause of all this chaotic behavior appears to be a super-massive black hole that lurks at the galactic center!

[Page 4] A G Polnarev, Relativistic Astrophysics, 2007. Lecture 4 , Black holes. 1. How invisible black holes can be observed

Example 3. Simulated view of a black hole in front of the Milky Way. The hole has 10 solar masses and is viewed from a distance of 600 km. An acceleration of about 400 million g is necessary to sustain this distance constantly.

[Page 5] AG Polnarev, Relativistic Astrophysics, 2007. Lecture 4 , Black holes. 2. Anatomy of Black Holes

2. Anatomy of Black Holes According to General Relativity black holes are arranged like this:

[page 6] AG Polnarev, Relativistic Astrophysics, 2007. Lecture 4, BLACK HOLES. 3. The Limit of stationarity (Static Limit)

3. The Limit of stationarity (Static Limit)

Let us consider the interval ds for test particle in rest, putting

dr = dθ = dφ = 0.

In this case 2

ds2 = g00 dx0 , We can see that if

g00 = 0, then

ds2 = 0, which means that the world line of particle in rest is the world line of light. Hence, at the surface

g00 = 0 no particle with finite rest mass can be in rest. For this reason this surface is called the limit of stationarity.

[page 7] AG Polnarev, Relativistic Astrophysics, 2007. Lecture 4, BLACK HOLES. 4. Event Horizon

4. Event Horizon

Let us consider a spherically symmetric surface

F (r) = const.

Its normal vector is defined as usually as

ni = F,i = δi1

dF dr

Here we work not with cartesian but with spherical coordinates and x1 ≥ r.

If at this surface

g 11 = 0 then

ik

11

g ni nk = g n1 n1 = g

11

dF dr

!2

= 0,

which means that ni is a null vector and any particle with finite rest mass can not move outward the surface g 11 = 0, thus this surface is the event horizon.

AG Polnarev, Relativistic Astrophysics, 2007. Lecture 4 , Black holes.

5. Event horizon and light cones

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5. Event horizon and light cones What is presented below is a space-time view of a black hole

An event horizon at rg =r_s= 2GM/c^2 is shown in green. The light cones of an observer falling into the black hole become increasingly tilted, until they completely tip over at the event horizon.