In astrophysics, Chandrasekhar potential energy tensor provides the gravitational potential of a body due to its own gravity created by the distribution...

stress-energy tensor The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical...

in the form of a tensor equation which related the local spacetime curvature (expressed by the Einstein tensor) with the local energy, momentum and stress...

natural to assume that the field equation for gravity relates this tensor and the Ricci tensor, which describes a particular class of tidal effects: the change...

Laue gave a more comprehensive proof of M0 = ⁠E0/c2⁠ from the stress–energy tensor, which was later generalized by German mathematician Felix Klein in...

system has a lower (i.e., more negative) gravitational potential energy than the sum of the energies of its parts when these are completely separated—this...

admits a remarkable Killing tensor. There is a pair of principal null congruences (one ingoing and one outgoing). The Weyl tensor is algebraically special...

u_{i}u_{j}x_{k}x_{\ell }\,d\mathbf {x} ,\quad \mathrm {etc.} } and the Chandrasekhar potential energy tensor moments are W i j = − 1 2 ∫ V ρ Φ i j d x , W i j ; k =...

various ways, most notably to a tensor form. If the force between any two particles of the system results from a potential energy V(r) = αrn that is proportional...

E ~ i j {\displaystyle {\tilde {E}}_{ij}} is a traceless tensor. Then the Bardeen potentials are defined as Ψ ≡ A + H ( B − E ′ ) , + ( B + E ′ ) ′ ,...

metric tensor of 15 components. Ten components are identified with the 4D spacetime metric, four components with the electromagnetic vector potential, and...

formalism. In the tensor calculus formulation, the electromagnetic tensor Fαβ is an antisymmetric covariant order 2 tensor; the four-potential, Aα, is a covariant...

of a scalar–tensor theory, a gravitational theory in which the gravitational interaction is mediated by a scalar field as well as the tensor field of general...

classification of the energy–momentum tensor and the Petrov classification of the Weyl tensor. There are various methods of classifying these tensors, some of which...

is also the stress–energy tensor for the electromagnetic field, namely the electromagnetic stress–energy tensor. The metric tensor allows one to define...

relationship between curvature of spacetime and the stress–energy tensor. The Ricci tensor becomes R ´ α β = 8 π G c 4 ( A 2 T ´ α β + B 2 T ´ g α β )...

Therefore, to describe the system, one defines the average energy per unit mass for a given potential V ( x ; ω ) {\displaystyle V(x;\omega )} as follows E...

Balasin, Herbert; Nachbagauer, Herbert (1994). "Distributional energy–momentum tensor of the Kerr–Newman spacetime family". Classical and Quantum Gravity...

{df}{dr_{s}}}\right)^{2},} where g is the determinant of the metric tensor. Thus, because the energy density is negative, one needs exotic matter to travel more...

regard the ether, which can be the seat of an electromagnetic field with its energy and its vibrations, as endowed with a certain degree of substantiality,...

Journal. 93: 403–410. Bibcode:1941ApJ....93..403M. doi:10.1086/144279. Chandrasekhar, S. (1950). Radiative Transfer. Oxford, UK: Oxford University Press...

independently by Felix Pirani in 1957. We can think of a fourth rank tensor such as the Weyl tensor, evaluated at some event, as acting on the space of bivectors...

of the metric tensor of spacetime, which describes its geometry. The geodesic paths of spacetime are calculated from the metric tensor. Notable solutions...

satisfied by a metric tensor that equals the Minkowski tensor everywhere. (However, since the Riemann and hence the Ricci tensor for Minkowski coordinates...

the bilinearity of the tensor product and the last step defines a 2-tensor on component form, or rather, it just renames the tensor u ⊗ v. These observations...

419–420. Bibcode:1983PhLA...99..419Q. doi:10.1016/0375-9601(83)90946-5. Chandrasekhar, Subrahmanyan (2009). The mathematical theory of black holes. Oxford...

Lorentz force. ISBN 0387952101. Lawden, Derek F. (2012). An Introduction to Tensor Calculus: Relativity and Cosmology. Courier Corporation. p. 74. ISBN 978-0486132143...

The energy of a dynamical system is partly kinetic, partly potential. Maxwell supposes that the magnetic energy of the field is kinetic energy, the electric...

Edward Witten (positive energy theorem), Louis Witten (Witten electrovacuum solutions) Basilis C. Xanthopoulos (Chandrasekhar–Xanthopoulos colliding plane...

{\displaystyle \mathbf {v} } is the coordinate velocity of the matter. Stress-energy tensor for a perfect fluid takes form T 00 = ρ ( 1 + Π + v 2 + 2 U ) {\displaystyle...