# Relativistic mass and gravity

#### frujin

Hello Guys. I am amateur so please forgive me if the question is irrelevant. As I understood it, the objects moving with relativistic speed, have their mass increased exponentially as the speed increases. Does that mean they have stronger gravity pull also?

Related Special and General Relativity News on Phys.org

#### Dale

Mentor
In relativity the source of gravity is the stress energy tensor. It cannot generally be replaced either by relativistic or by invariant mass. Both are scalars, and the stress energy tensor is a rank 2 tensor.

#### PeterDonis

Mentor
Hi, frujin, and welcome to PF!

Your question looks simple, but it actually hides a considerable amount of complexity. Rather than trying to answer it directly at once, let me first explain briefly how General Relativity (GR) describes the "gravity pull" of an object.

The central equation of GR is the Einstein Field Equation (EFE), which can be quickly summarized in the popular phrase "spacetime tells matter how to move, matter tells spacetime how to curve". "Spacetime" in this equation is described by something called the "Einstein tensor", and "matter" is described by something called the "stress-energy tensor" (SET). The "mass" of the object is part of what is described by the SET.

The key thing about this equation is that it is the same regardless of what coordinates you express it in. For example, if some massive object is moving relative to you, the EFE looks the same whether you look at it in coordinates in which you are at rest, or coordinates in which the massive object is at rest. (By "looks the same", I don't mean literally that every number in the equation is the same--I just mean that the structure of the equation is the same, and there is a well-defined way to transform the specific terms in it from any set of coordinates to any other set.)

So in this sense, the "gravity pull" of the massive object doesn't change when you change coordinates. The specific components of the SET will change, so it will look like the "mass" changes if you just look at particular components, but the overall prediction for how objects will move in the gravity field of the object doesn't change.

There are also other ways your question could be interpreted, but I'll let you respond to the above first.

#### frujin

Hello, and thanks for the answers. Unfortunately, I can't understand the reasons ;) - mathematics used are quite complex to me, but I am having now the impression that the answer is: the object moving at relativistic speeds wont "gravitationaly attract" other objects any stronger. Is this correct?

But, doesn't the curvature of spacetime around an object increase significantly as its speed approaches speed of light? (sorry of this is redundant question)

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving