• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.

### 2.1 Foundations in theory

Albert Einstein published his theory of general relativity in 1915.It, like his earlier theory of special relativity, described space and time as a unified spacetime subject to what are now known as the Einstein field equations.
There are 10 of such equations. The problem start to define these equations for actual examples.
This was first published by Richard Arnowitt, Stanley Deser, and Charles W. Misner in the late 1950s in what has become known as the ADM formalism.
The problem also here is to find the equations for actual examples.

### 2.2 Early results

The first realistic calculations of rotating collapse were carried out in the early eighties by Richard Stark and Tsvi Piran in which the gravitational wave forms resulting from formation of a rotating black hole were calculated for the first time.

### 2.3.1 Excision

In the excision technique, which was first proposed in the late 1990s, a portion of a spacetime inside of the event horizon surrounding the singularity of a black hole is simply not evolved.
The issue is what has the "event horizon" to do with the physical behaviour of a BH?. See also Event horizon - Reflection 1
Thus if one simply does not solve the equations inside the horizon one should still be able to obtain valid solutions outside.
IMO the horizon has nothing to do with the behaviour of the gravitational field which starts at the rim of the object (BH)
While the implementation of excision has been very successful, the technique has two minor problems. etc
The second problem is that as the black holes move, one must continually adjust the location of the excision region to move with the black hole.
This seems more than reasonable. That is simulations with only one BH are not very interesting, realistic.

### 3. Recent developments

One of the most surprising predictions is that the merger of two black holes can give the remnant hole a speed of up to 4000 km/s that can allow it to escape from any known galaxy
This is a very remarkable result and I doubt if that is true.
Most probably what will happen if two BH's collide is that the speed of the remnant will be smaller than the speed of the BH's before the collision.
If each BH is part of a galaxy (in that case you speak of a two galaxies that collide) the resulting BH will not escape from the new to form galaxy. In fact the new BH will be surrounded by a sphere of stars.
In principle a BH can escape from a Galaxy but in these cases IMO always more BH's are involved.

See: Numerical relativity documents

### Reflection part 1

Numerical Relativity in some sense the same as when you want to simulate for example the planets around the Sun using Newton's Law. The difference is that the differential equations that describe Newton's Law are much simpler that the Einststein equations of General Relativity. These equations are extremely complex.
In the case of a simulation of the planets around the Sun we know, based on observations, what the outcome of such a simulation should be. When it does not match we know than something is wrong.
What makes Numerical relativity so complex is that very often the mathematics involved does not give stable solutions. In that case you try to find simplifications or approximations in order to get stable solutions. However this raises a serious questions: are your solutions correct.
This is a specific problem in all cases when BH's are involved because neither the initial conditions nor the outcome can be visible checked. I specific write here BH's. When you want to simulate the stars around the BH Sagitarius A in our Milky Way, this is "relative" simple using GR, because the positions of the stars can be monitored.

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Created: 11 October 2016

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