In physics

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, a perfect fluid is a fluid

Fluid

In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

 that can be completely characterized by its rest frame energy density

Energy density

Energy density is a term used for the amount of energy stored in a given system or region of space per unit volume. Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored...

 ρ and isotropic pressure

Pressure

Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

 p.

Real fluids are "sticky" and contain (and conduct) heat. Perfect fluids are idealized models in which these possibilities are neglected. Specifically, perfect fluids have no shear stress

Shear stress

A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...

es, viscosity

Viscosity

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

, or heat conduction

Heat conduction

In heat transfer, conduction is a mode of transfer of energy within and between bodies of matter, due to a temperature gradient. Conduction means collisional and diffusive transfer of kinetic energy of particles of ponderable matter . Conduction takes place in all forms of ponderable matter, viz....

.

In tensor notation, the energy-momentum tensor

Stress-energy tensor

The stress–energy tensor is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields...

 of a perfect fluid can be written in the form
where U is the velocity

Velocity

In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

 vector field

Vector field

In vector calculus, a vector field is an assignmentof a vector to each point in a subset of Euclidean space. A vector field in the plane for instance can be visualized as an arrow, with a given magnitude and direction, attached to each point in the plane...

 of the fluid and where is the metric tensor of Minkowski spacetime.

Perfect fluids admit a Lagrangian

Lagrangian

The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...

 formulation, which allows the techniques used in field theory to be applied to fluids. In particular, this enables us to quantize

Quantization (physics)

In physics, quantization is the process of explaining a classical understanding of physical phenomena in terms of a newer understanding known as "quantum mechanics". It is a procedure for constructing a quantum field theory starting from a classical field theory. This is a generalization of the...

 perfect fluid models. This Lagrangian formulation can be generalized, but unfortunately, heat conduction and anisotropic stresses cannot be treated in these generalized formulations.

Perfect fluids are often used in general relativity

General relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

 to model idealized distributions of matter

Matter

Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...

, such as in the interior of a star.

See also

• Equation of state
  Equation of state
  In physics and thermodynamics, an equation of state is a relation between state variables. More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions...
  
  
• Ideal gas
  Ideal gas
  An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...
  
  
• Fluid solutions in general relativity
  Fluid solution
  In general relativity, a fluid solution is an exact solution of the Einstein field equation in which the gravitational field is produced entirely by the mass, momentum, and stress density of a fluid....
  
  

External links

• Mark D. Roberts, [A Fluid Generalization of Membranes http://www.arXiv.org/abs/hep-th/0406164 hep-th/0406164].