You can define a volume element on a null surface in terms of an affine parameter along the null generators. But it won't be unique.sadegh4137 said:Consider we have a null hypersurface. how we can calculate volume element on it?
Yes, very good! See Eq (3.2.7)George Jones said:Section 3.2 from "A Relativist`s Toolkit" by Poisson might be useful; draft version at
http://www.physics.uoguelph.ca/poisson/research/agr.pdf.
Then this should have been stated immediately. It shouldn't take us 6 posts to discover what it is you are actually looking for, and the fact that you already had an answer in hand and were dissatisfied with it.sadegh4137 said:exactly i Studied this section of Poisson's book
, but here he defined a directed volume element
I don't know how to calculate volume element exactly.
A volume element for null hypersurface is a mathematical concept used in the study of space-time in general relativity. It is a mathematical tool used to measure the volume of a region on a null hypersurface, which is a surface in space-time representing the boundary between regions of space-time with and without matter or energy.
A volume element for null hypersurface is calculated using the metric tensor, which is a mathematical object that describes the geometry of space-time. The metric tensor is used to calculate the area of a null hypersurface, which is then integrated to obtain the volume element.
A volume element for null hypersurface is important in the study of general relativity because it allows us to measure the volume of a region on a null hypersurface. This is useful in understanding the geometry and dynamics of space-time, as well as in solving Einstein's field equations.
Yes, a volume element for null hypersurface can change over time. This is because the geometry of space-time can change over time, which can affect the area of a null hypersurface. This change in the volume element is important in understanding the evolution of space-time.
A volume element for null hypersurface is related to black holes because it is used in the study of the event horizon, which is the boundary of a black hole. The volume element can help us understand the properties of black holes, such as their size and mass, and can also be used in the calculation of the Hawking radiation emitted by a black hole.